<figure><img src="image_20.png" /><figcaption>Figure 18 Primary transport lines in Valenciennes and exchange hubs</figcaption></figure>

(Source: https://www.transvilles.com/lignes-essentielles)

The total volume of transport users is around 17,000,000 passengers per year. Table 9 shows the number of passengers per year and the number of passengers using the “transport-on-demand” service. Table 9 shows the number of regular users decreasing year after In 2018, however, there was an increase in the number of PWD that used the Sésame service. Unfortunately, we do not have data on PWD use of other modes of transportation provided by Transvilles, such as bus and tram, etc.
<table><caption>Table 9 The volume of transport per year (Source: https://www.simouv.fr/)</caption><thead><tr><th>Year</th><th>Passenger</th><th>Transport on demand</th></tr></thead><tbody><tr><td>2014</td><td>17155033</td><td></td></tr><tr><td>2015</td><td>16667534</td><td>10548</td></tr><tr><td>2016</td><td>16870412</td><td>11120</td></tr><tr><td>2017</td><td>15519879</td><td>10237</td></tr><tr><td>2018</td><td>13 220 479</td><td>9 793</td></tr></tbody></table>

Various modes of transport operate in Valenciennes, including a tramway, bus, and transport-on-demand. The volume of users per kilometer and per mode is shown in Table 10.

<table><caption>Table 10 Evolution of kilometers by users and mode (Source: https://www.simouv.fr/)</caption><thead><tr><th>Year</th><th>Tramway</th><th>Bus</th><th>Transport on demand<br>Sésame Propres</th></tr></thead><tbody><tr><td>2014</td><td>1724573</td><td>4513462</td><td>306622</td></tr><tr><td>2015</td><td>1770854</td><td>3976076</td><td>352375</td></tr><tr><td>2016</td><td>1756200</td><td>3890325</td><td>348493</td></tr><tr><td>2017</td><td>1509902</td><td>3531151</td><td>366016</td></tr><tr><td>2018</td><td>1369649</td><td>3598443</td><td>461083</td></tr></tbody></table>

According to the SIMOUV 2018 activity report (SIMOUV, 2018), there is the following transport distribution: 16% Tramway; 44% Bus; 6% Transport-on-demand (Sésame Propres); 27% Shuttle bus (Bus affrétés); 1% Transport-on-demand (outsourced) (Sésame sous-traités); 2% Taxival and 4% Regional lines (Lignes régionales sous convention SIMOUV). So buses are the dominant mode of transport.

<table><caption>Table 11 Transport distribution in 2018</caption><thead><tr><th>2018</th><th>%</th></tr></thead><tbody><tr><td>Tramway</td><td>16</td></tr><tr><td>Bus</td><td>44</td></tr><tr><td>Transport on-demand<br>(Sésame Propres)</td><td>6</td></tr><tr><td>Shuttle bus<br>(Bus affrétés)</td><td>27</td></tr><tr><td>Transport-on-demand (outsourced)<br>(Sésame sous-traités)</td><td>1</td></tr><tr><td>Taxi Val</td><td>2</td></tr><tr><td>Regional lines</td><td>4</td></tr></tbody></table>
4.2.2 Transport organization for PWD – “Sésame”

“Sésame” - the current transport organization for PWD - holds a fleet of 14 vehicles. The vehicle depot of Transville is positioned in Saint Saulve, which is not one of the hubs. Only one of 14 vehicles is located in hub Station Denain-Espace Villars. The “Sésame” service is organized by routes, which group people whenever possible. These routes are offered for access to work, internships, higher education, and leisure travel.

This service is based on the "reservation ahead" principle: each transportation request needs to be sent at least two weeks before planned travel; Transvilles examines the request and notifies the user about the decision within 48 hours. Besides integrating PWD to public transport, we also notice a problem in the transport on-demand organization Valenciennes is more rural than urban, and there has been a move towards urbanization (périurbanisation). The associated changes have led to adverse outcomes for the organization of co-ordinated travel that favors individual modes. A further issue is that each group responsible for organizing transport (SIMOUV, Department of North, or TER) has its own particular plans, particularly on the provision of accessibility for PWD. As a result, all documents have to be aligned to enable collaboration on different levels of decisions.

Public transport for PWD needs to be improved, although Valenciennes public transport is generally efficient. The network is experiencing an increasingly marked imbalance in the services offered. There is a good frequency of use of the tramways, but dissatisfaction with the rest of the network. Valenciennes has a diversity of transport offerings (TER, Tram, Bus, Transport-on-demand Sésame), which must serve the development of public transport in the area.

The entire travel infrastructure needs improvements (buildings, roads, public spaces, transportation, and housing). A solution must be developed for rural areas and sidewalks accessibility. Evidently, re-organizing an entire transport network needs a lot of time, effort, and resources. Consequently, we will focus here on an approach that can be implemented in the short term to address the challenges of integrating PWD into the public transport system.

This chapter drew most elements from a real-life database to analyze the possible application of location models to the Valenciennes transport network. The data configuration indicates that the potential application of a clustering model could result in better dial-a-ride solutions, which could significantly impact the organizations of buses. One of the constraints of organizing transport by coaches is the number of vehicles that are accessible to PWD. In
addition to accessibility, another critical parameter is availability. Availability relates to the
provision of a service in the locality adjacent to PWD's intended journey destination.

## 4.3 Problem description

In recent years, public transport systems have been required to accommodate an increasing diversity of users, and in parallel, the number of users has generally increased, particularly persons with disabilities.

As stated previously, the World Health Organization reported one billion PDW, which represents 15% of the total population (World Health Organization, 2011). In addition, French demographic trends have been characterized by a rapid increase in the number of people who have mobility difficulties, with a forecast of 17 million people aged 60 and over, and 4 million people aged 80 and over after 2020. From 2010, the French people aged over 60 have exceeded those under 20 (Egis France Villes & Transport). A similar study of Egis France has shown that the overall population of Valenciennes is aging. The percentage of young people decreases, while the number of elderly people increases, particularly those aged over 75 years.

Public transport systems are required to comply with increasingly demanding regulations to meet the needs of PWD. Meanwhile, the design of transport systems has not fundamentally changed. The default consideration is still on the standard user, while PWD users do not yet have full recognition as a new potential source of clients. PWD has yet to be recognized by transport companies in terms of its potential as a source of additional revenue. The quantities of users and the diversity of their needs make transport planning very complex. This complexity increases when the specific needs of PWD have to be met. The range of disabilities includes physical, intellectual, motor, and visual, and each category's needs have to be defined. This huge range of criteria meant that we limited our investigation to PWD wheelchair users - the physical group. In addition to the number and diversity of PWD involved, PWD transport is limited by the factors such as the infrastructure's particular characteristics: - the network, routes, vehicles, etc.

Several combined complex optimization problems arise in the network's design,) when routes across - or flows through - the network are required. Familiar routing challenges include the *shortest path problem*, *minimum spanning tree problem*, *traveling salesman problem*, *vehicle routing problem*; amongst other interesting optimization problems that have additional practical constraints (Bast et al., 2016; Feremans, Labbé, & Laporte, 2003; Turner, 2011).
In addition to the network design, studies have recognized several optimization problems that could potentially deliver better transport services to persons with disabilities. For example, the transport-on-demand problem, otherwise known as *dial-a-ride* problem (Archetti et al., 2018; Cordeau & Laporte, 2007; Molenbruch et al., 2017). Section 3.3.3 describes in detail existing optimization models in the transport journey for PWD.

The intention here, as stated previously, is to improve the inclusion of PWD in an existing public system using different optimization models. In this section, the focus is simplified by considering specifically the transport organization for PWD in Valenciennes (Section 4.2.3). The mode of transport for PWD is exclusively transport on-demand referred to as “Sésame.” The transport-on-demand provides a service for PWD moving from origin A to destination B without using the regular public network.

Alternatively, the “shortest path” applies to Valenciennes’s regular public network once PWD reaches it. PWD can move through the public network following the shortest path from where they enter the network to the point where they left. The Transvilles application and website provide access to the itinerary that does not include a specific option for PWD.

It is generally known that all tram lines are fully accessible for PWD. All stations along their routes and their associated fleets can accommodate PWD. On the other hand, in the bus system, the problem is the accessibility of PWD to the stations since the accessibility to the vehicles is provided.

However, the interchanges between different modes of transport and various lines take place at the hubs. These locations are the key points for the independent mobility of PWD.

Here, we consider how these two models, transport on-demand and the shortest path - can be used simultaneously to design routes for PWD that partially involve the public transport network. Specifically, suppose PWD wants to travel from point A to B. In that case, PWD can initially transfer to the public network (using transport on-demand), then travel through the system using the shortest path, and finally, transfer to destination B (transport on-demand).

In order to integrate these two optimization problems, the geo-position of hubs is defined to determine the best routing methodology. The identification of hubs occurs in the first leg of the transportation trip (where PWD enters the network) and the last leg of the transportation trip (where PWD leaves the network). To solve this problem and resolve the
first and last transport legs' challenge, a clustering analysis of the Sésame's data set is carried
out. The "Sésame" data set provides information on the users' departure and arrival location.
The other data set contain information on the geo-location of the network, accessibility to
stations (stops), and the location of existing hubs. In order to make use of this data for this
scenario, the cluster analysis model is proposed (Hartigan, 1975; Kaufman & Rousseeuw,
2009; Meyer & Miller, 2001). The following section provides more details on the clustering
methodology.

## 4.4 Clustering approach

Cluster analysis is the classification of objects according to their similarities and organizing
objects into groups (L. Kaufman & P. J. Rousseeuw, 1990; Kaufman & Rousseeuw, 2009; Späth,
1980). Clustering techniques belong to the group of unsupervised methods within the class
identifiers that do not use existing knowledge. The main aim of clustering is to identify the
fundamental structure in a given set of objects (also called data). Besides the classification and
pattern recognition, the model placing and optimization present other attributes of the
grouping.

Classification is the primary component of exploratory data mining. Clustering is a
standard statistical data analysis technique used in many fields, particularly for the data sets
in complex systems. It could be said that clustering is a persuasive generator for the
computerized analysis of data (Everitt, Landau, Leese, & Stahl, 2011; Han, Kamber, & Tung,
2001). This persuasive generator has features that incorporate a range of methods to arrive
at a correct and feasible solution. These methods have been demonstrated to be useful in a
wide range of applications.

Practical models are employed to illustrate the theory's application, and figures are used
broadly to describe graphic techniques (Everitt et al., 2011). As already stated, clustering can
help identify the characteristics of any structure or patterns present in a given data set. It is a
useful approach that emerged from anthropology and psychology to understand relations
within groups. This is the field where clustering was initially discovered (Driver & Kroeber,
1932; Zubin, 1938).
Many equivalent terms are used for clustering, as revealed in the literature, such as data classification, grouping, numerical taxonomy, etc. Clustering helps in assessment, prediction, and then arriving at a decision. These diverse classifications are the result of different scenarios and different data types. Depending on the particular aim, techniques can be employed, such as partitioning, hierarchical, graph-theory methods, and methods based on mathematical programming formulations (Carrizosa et al., 2013; Hanafi & Yanev, 2011).

The focus is on partition techniques, which separate objects into particular group representations by minimizing or maximizing a given objective function (Everitt et al., 2011). Examples of these techniques include K-means and K-medoids algorithms, which try to minimize average squared distance, generating so-called centroids. K-means and K-medoids algorithms allocate each object to one of the K clusters from a given set of objects, minimizing the within-cluster sum of squared distances. In this case, we used the K-medoids method, as it is more robust in relation to outliers, and also because this method deals with both interval-scaled sizes and vague variation coefficients (Balasko, Abonyi, & Feil, 2014; Đorić, El Cadi, Hanafi, Mladenović, & Artiba, 2017; Everitt et al., 2011).

The K-medoids method relies on the minimum sum-of-squares criterion (MSSC). The minimum sum-of-squares criterion is one of the favourite among various models used for cluster analysis, as it expresses both homogeneity and separation. Using the MSSC, K-medoids partition a given set of *n* objects into K clusters, minimizing the total squared distance from the objects to their cluster's centroid. The *n* objects to be clustered are represented as points $x^i \in \mathbb{R}^s$, $i = 1, ..., n$; while K cluster centers are chosen among points $x^i$. The squared distance between two points is defined as the squared Euclidean distance between the two points $x^i$ and $x^j$, in the *s*-dimensional space under consideration: $d(x^i, x^j) = \sum_{k=1}^{s}(x_{ik} - x_{jk})^2$. In our case, the data set is the geographical position (geo-location) of PWD present by the longitude and longitude. The data set is later translated in the Euclidean space.

Mathematically, the K-medoids may be expressed as a mixed-integer programming (MIP) model, which uses the binary decision variables $w_{ic}$ which express the assignment of the object *i* to the cluster *c*, with the center at $x^c$ and binary decision variable $y_c$ which indicates if a centroid is located in point $x^c$ or not.
So a MIP formulation of K-medoids can be expressed as follows:

$$ \min_{w,y} \sum_{i=1}^{n} \sum_{c=1}^{n} w_{ic} d(x^i, x^c) $$

Subject to:

$$ \sum_{c=1}^{n} y_{c} = K, $$

$$ \sum_{c=1}^{n} w_{ic} = 1, \quad \forall i \in \{1, 2, \dots, n\} $$

$$ w_{ic} \le y_c, \forall i, c \in \{1, 2, \dots, n\} $$

$$ w_{ic}, y_c \in \{0,1\}, \forall i, c \in \{1, \dots, n\}. $$

The objective function expresses the minimum sum-of-squares criterion. The first constraint ensures that exactly *K* points are chosen to be centroids. The next constraints allow each point to be assigned to precisely one centroid (cluster), while the third set of constraints guarantees that each point is awarded only to an established centroid.

Regarding computational complexity, K-medoids in the Euclidean metric for general values of *K* and *s* have been shown to be NP-hard (Aloise, Deshpande, Hansen, & Popat, 2009).

In our case, we apply the k-medoids approach on the data set available for the public network of Valenciennes. The objects in the real data set are the geo-location of PWD. The objective is to analyze transportation flow with their geo-location of clusters in the departure and/or arrival of PWD. We are also interested in seeing how these clusters are positioned concerning the existing network and examining cluster centers' position relative to the existing hubs on the network. The Clustering – nodes - network example is shown in Figure 19, where points belonging to the same cluster are marked in the same color.
<figure><img src="image_21.png" /><figcaption>Figure 19 Clustering – hubs - network example</figcaption></figure>

## 4.5 Computational experiments

In this section, we present the outcome of experiments obtained by applying the clustering approach to the public transport network in the city of Valenciennes. The public transport network, transport flow, and position of existing hubs in Valenciennes are analyzed and compared. For the analysis, real examples are used to perform k-medoids clustering (L. Kaufman & P. Rousseeuw, 1990; MacQueen, 1967; Pelleg & Moore, 1999; Rousseeuw & Kaufman, 1987) with a different number of clusters. In addition, the optimal number of clusters was sought. All tests were run in the MATLAB R2016b, on machine Hp Zbook, Intel® Xeon® Processor E3-1505M v5 2.80 GHz.

In addition, we performed a retrospective analysis of the obtained clusters. We examined the number of “satisfied” PWD users within each cluster. A user is “satisfied” if he/she is not more than 1000, 400, or 150 meters away from the center of the cluster he/she belongs to. The distance of 1000 meters is assumed for regular users. It is routinely suggested in transport and town planning literature that all people should have access to a bus service that stops within 400 meters (¼ mile) of their home and destination (Broome et al., 2012; Murray, 2003; Murray, Davis, Stimson, & Ferreira, 1998). Some references even proposed 150 meters as a recommended walking distance without rest for wheelchair users (P. R. Oxley &
transport network with accessibility. In accordance with the MATLAB performances, the maximum number of iterations is set at 10000, 100000, and 1000000 with 1, 100, 1000, 10000 replications. Additionally, all tests are run ten times to get an average number. The detailed tables are presented in Appendix E (Table 17, Table 18, and Table 19) presents the results for the total number of PWD at departure and arrival, which is 5537. Results show that the optimal number of clusters is close to the maximum number of clusters.

The same conclusion applies to the departure and arrival cases, which are presented in Table 18 and Table 19. Table 12 only shows the results for 1 000 000 iterations and 10 000 replications which are the most precise. When the maximum number of clusters is set at 9, 7 and 5 clusters for the arrivals, the optimal number of clusters is 7, 5, and 4, respectively. For the departures, the optimal number is 8, 6, and 4, while for both arrivals and departures, we obtain 7, 5, and 4, respectively, the same as the arrivals.

<table><caption>Table 12 Optimal number of clusters</caption><thead><tr><th>Instances</th><th>MaxIteration</th><th>Replicates</th><th>No of stations= Max no of cluster</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>Avg</th></tr></thead><tbody><tr><td rowspan="10">ARRIVAL</td><td rowspan="10">1 000 000</td><td rowspan="10">10 000</td><td>420</td><td>416</td><td>419</td><td>418</td><td>420</td><td>419</td><td>419</td><td>419</td><td>415</td><td>420</td><td>417</td><td>418</td></tr><tr><td>210</td><td>207</td><td>209</td><td>208</td><td>204</td><td>209</td><td>209</td><td>197</td><td>210</td><td>210</td><td>200</td><td>206</td></tr><tr><td>105</td><td>104</td><td>96</td><td>94</td><td>104</td><td>104</td><td>102</td><td>100</td><td>99</td><td>105</td><td>104</td><td>101</td></tr><tr><td>50</td><td>49</td><td>46</td><td>50</td><td>47</td><td>46</td><td>49</td><td>48</td><td>48</td><td>48</td><td>45</td><td>48</td></tr><tr><td>25</td><td>22</td><td>20</td><td>25</td><td>22</td><td>20</td><td>18</td><td>17</td><td>23</td><td>24</td><td>22</td><td>21</td></tr><tr><td>12</td><td>9</td><td>11</td><td>8</td><td>12</td><td>12</td><td>8</td><td>7</td><td>7</td><td>8</td><td>8</td><td>9</td></tr><tr><td>9</td><td>7</td><td>8</td><td>9</td><td>7</td><td>4</td><td>4</td><td>9</td><td>4</td><td>9</td><td>7</td><td>7</td></tr><tr><td>7</td><td>6</td><td>4</td><td>4</td><td>4</td><td>6</td><td>6</td><td>4</td><td>4</td><td>4</td><td>7</td><td>5</td></tr><tr><td>5</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td>420</td><td>420</td><td>418</td><td>420</td><td>411</td><td>415</td><td>412</td><td>418</td><td>417</td><td>419</td><td>419</td><td>417</td></tr><tr><td>210</td><td>194</td><td>203</td><td>210</td><td>210</td><td>206</td><td>207</td><td>206</td><td>210</td><td>210</td><td>204</td><td>206</td></tr><tr><td>105</td><td>104</td><td>104</td><td>100</td><td>104</td><td>102</td><td>102</td><td>105</td><td>104</td><td>102</td><td>104</td><td>103</td></tr><tr><td>50</td><td>49</td><td>44</td><td>50</td><td>40</td><td>49</td><td>50</td><td>50</td><td>45</td><td>50</td><td>50</td><td>48</td></tr><tr><td rowspan="9">DEPARTURE</td><td rowspan="9">1 000 000</td><td rowspan="9">10 000</td><td>25</td><td>23</td><td>21</td><td>24</td><td>25</td><td>21</td><td>22</td><td>21</td><td>22</td><td>20</td><td>25</td><td>22</td></tr><tr><td>12</td><td>10</td><td>12</td><td>12</td><td>11</td><td>8</td><td>9</td><td>12</td><td>10</td><td>9</td><td>12</td><td>11</td></tr><tr><td>9</td><td>8</td><td>9</td><td>7</td><td>9</td><td>9</td><td>7</td><td>9</td><td>7</td><td>7</td><td>9</td><td>8</td></tr><tr><td>7</td><td>6</td><td>6</td><td>6</td><td>4</td><td>7</td><td>6</td><td>7</td><td>4</td><td>6</td><td>6</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td>420</td><td>416</td><td>419</td><td>417</td><td>416</td><td>415</td><td>420</td><td>417</td><td>420</td><td>417</td><td>419</td><td>418</td></tr><tr><td>210</td><td>210</td><td>208</td><td>208</td><td>210</td><td>210</td><td>210</td><td>210</td><td>210</td><td>207</td><td>204</td><td>209</td></tr><tr><td>105</td><td>96</td><td>99</td><td>103</td><td>103</td><td>101</td><td>100</td><td>105</td><td>101</td><td>94</td><td>101</td><td>100</td></tr><tr><td>50</td><td>45</td><td>50</td><td>50</td><td>50</td><td>50</td><td>46</td><td>50</td><td>48</td><td>48</td><td>50</td><td>49</td></tr><tr><td rowspan="6">ALL</td><td rowspan="6">1 000 000</td><td rowspan="6">10 000</td><td>25</td><td>20</td><td>20</td><td>25</td><td>22</td><td>19</td><td>25</td><td>24</td><td>23</td><td>25</td><td>22</td><td>23</td></tr><tr><td>12</td><td>12</td><td>10</td><td>12</td><td>8</td><td>9</td><td>11</td><td>12</td><td>10</td><td>12</td><td>7</td><td>10</td></tr><tr><td>9</td><td>9</td><td>4</td><td>7</td><td>6</td><td>4</td><td>9</td><td>4</td><td>8</td><td>9</td><td>7</td><td>7</td></tr><tr><td>7</td><td>4</td><td>4</td><td>4</td><td>6</td><td>6</td><td>6</td><td>4</td><td>7</td><td>4</td><td>6</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr></tbody></table>
### 4.5.3 Clustering of the geographical positions of PWD

The purpose of clustering in this research is to provide data analysis. The optimal number of clusters provided in section 4.5.2. with the experiment results in Appendix E, is used as the input for further analysis. Since the number of clusters produced by k-medoids tends to get close to the maximum number, we have chosen to analyze the situation with five, seven, and nine clusters, as it is explained below.

As well, for the k-medoids method, the number of clusters sought needed to be defined in advance. There are five hubs on the public transport network map (Station Anzin-Hôtel de Ville, Station Denain-Espace Villars, Station-Famars Université, Station Gare, Station Saint Waast). In the first series of experiments, we set the parameter K to five, i.e., the requested number of clusters is five. In this way, we could check if the situation on the ground corresponds to the demands of PWD. That is, whether the hubs are well located or not in relation to PWD requests. Also, we examined how an increase in the number of clusters impacts the relationship between PWD demands and hub locations. In this regard, additional tests were carried out with the value of parameter K set to seven and nine. The geo-position data sets in departure and arrival were processed, and all tests were run for both geo-positions, respectively. The test for the complete database with departures and arrivals is reported numerically. The results are presented both numerically and graphically for departures only and arrivals only.

#### 4.5.3.1 Clustering of the geographical positions of PWD at departure

For departures, clustering is applied to 2,763 users. The number of searched clusters, K, varies from 5 to 9, as previously explained. The results of clustering for three different values of K are shown in Table 13. For each value of K, the number of users per cluster (Columns "Size of cluster") are reported, and the number of satisfied PWD users in each cluster (Columns "Satisfied"). Also, for each cluster, the percentage of satisfied users in relation to the total number of users in that cluster is calculated. Results are given in columns "%."

The results show for the case of 5 clusters and 1000m radius an average of 18% satisfied users, with the percentage per cluster ranging from 4% to 49%. For 7 clusters, there is a 4% increase, which represents an average of 22% of satisfied users. Nevertheless, now, the percentage per cluster ranges from 3% to 53%. A significant percentage of satisfied users is noted in the 9 clusters case. An average of 35% of users is satisfied, with the percentage per
cluster ranging from 11% to 70%. For 400m, the percent of the satisfied users are 1, 6, and 8 % for 5,7, and 9 clusters percent and around 1%, respectively. In a case of 150m, the percent of satisfied users for all situations is 1%.

<table><caption>Table 13 Results of clustering at departure, K= 5, 7, 9</caption><thead><tr><th rowspan="2">DEPARTURE</th><th colspan="3">5 Clusters</th><th colspan="3">7 Clusters</th><th colspan="3">9 Clusters</th></tr><tr><th>Size of cluster</th><th>Satisfied</th><th>%</th><th>Size of cluster</th><th>Satisfied</th><th>%</th><th>Size of cluster</th><th>Satisfied</th><th>%</th></tr></thead><tbody><tr><td>1000m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>185</td><td>90</td><td>49%</td><td>177</td><td>94</td><td>53%</td><td>302</td><td>33</td><td>11%</td></tr><tr><td>Cluster 2</td><td>955</td><td>223</td><td>23%</td><td>330</td><td>84</td><td>25%</td><td>310</td><td>60</td><td>19%</td></tr><tr><td>Cluster 3</td><td>390</td><td>14</td><td>4%</td><td>173</td><td>6</td><td>3%</td><td>327</td><td>84</td><td>26%</td></tr><tr><td>Cluster 4</td><td>887</td><td>89</td><td>10%</td><td>723</td><td>182</td><td>25%</td><td>123</td><td>27</td><td>22%</td></tr><tr><td>Cluster 5</td><td>346</td><td>84</td><td>24%</td><td>863</td><td>207</td><td>24%</td><td>753</td><td>337</td><td>45%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>176</td><td>9</td><td>5%</td><td>79</td><td>55</td><td>70%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>321</td><td>33</td><td>10%</td><td>509</td><td>256</td><td>50%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>171</td><td>94</td><td>55%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>189</td><td>24</td><td>13%</td></tr><tr><td>Total</td><td>2763</td><td>500</td><td>18%</td><td>2763</td><td>615</td><td>22%</td><td>2763</td><td>970</td><td>35%</td></tr><tr><td>400m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>887</td><td>12</td><td>1%</td><td>863</td><td>22</td><td>3%</td><td>675</td><td>60</td><td>9%</td></tr><tr><td>Cluster 2</td><td>185</td><td>8</td><td>4%</td><td>177</td><td>58</td><td>33%</td><td>309</td><td>5</td><td>2%</td></tr><tr><td>Cluster 3</td><td>955</td><td>3</td><td>0%</td><td>173</td><td>3</td><td>2%</td><td>173</td><td>36</td><td>21%</td></tr><tr><td>Cluster 4</td><td>346</td><td>6</td><td>2%</td><td>330</td><td>6</td><td>2%</td><td>343</td><td>3</td><td>1%</td></tr><tr><td>Cluster 5</td><td>390</td><td>3</td><td>1%</td><td>176</td><td>5</td><td>3%</td><td>695</td><td>79</td><td>11%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>321</td><td>5</td><td>2%</td><td>123</td><td>21</td><td>17%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>723</td><td>79</td><td>11%</td><td>105</td><td>1</td><td>1%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>88</td><td>14</td><td>16%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>252</td><td>9</td><td>4%</td></tr><tr><td>Total</td><td>2763</td><td>32</td><td>1%</td><td>2763</td><td>178</td><td>6%</td><td>2763</td><td>228</td><td>8%</td></tr><tr><td>150m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>955</td><td>1</td><td>0%</td><td>863</td><td>2</td><td>0%</td><td>123</td><td>1</td><td>1%</td></tr><tr><td>Cluster 2</td><td>185</td><td>5</td><td>3%</td><td>177</td><td>4</td><td>2%</td><td>753</td><td>1</td><td>0%</td></tr><tr><td>Cluster 3</td><td>390</td><td>2</td><td>1%</td><td>173</td><td>3</td><td>2%</td><td>171</td><td>3</td><td>2%</td></tr><tr><td>Cluster 4</td><td>346</td><td>4</td><td>1%</td><td>723</td><td>2</td><td>0%</td><td>509</td><td>18</td><td>4%</td></tr><tr><td>Cluster 5</td><td>887</td><td>5</td><td>1%</td><td>176</td><td>5</td><td>3%</td><td>327</td><td>4</td><td>1%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>330</td><td>4</td><td>1%</td><td>302</td><td>4</td><td>1%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>321</td><td>4</td><td>1%</td><td>189</td><td>11</td><td>6%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>79</td><td>2</td><td>3%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>310</td><td>1</td><td>0%</td></tr><tr><td>Total</td><td>2763</td><td>17</td><td>1%</td><td>2763</td><td>24</td><td>1%</td><td>2763</td><td>45</td><td>2%</td></tr></tbody></table>

Figure 20 shows the result of clustering in the geo-situation departure for five clusters. The first ones (the five hubs already on the network) are shown in grey rectangles. New clusters are indicated by blue rectangles, and red circles centered at a centroid with a radius of 1,000 meters indicate satisfied users. PWD users, or the point where “Sésame” picks them up, are small dots in blue, red, cyan, green, and pink. Higher resolution versions of Figure 20, Figure 21, and Figure 22 can be found in Appendix F (Figure 33, Figure 34, and Figure 35). Note that users in the same cluster appear in the same color.

Having applied the clustering, Figure 20 shows that only three hubs fall into the circles of satisfied users, and there is no match between an existing hub and a cluster center. Also, it is clear that two hubs (Station Anzin Hôtel de Ville and Station Saint Waast) are inside the new cluster. Consequently, matching between existing hubs and clusters happens in only two of five cases.
<figure><img src="image_22.png" /><figcaption>Figure 20 Geographical position at departure: 5 clusters</figcaption></figure>

Interestingly, the Station Gare and Station Famars Université hubs sit outside the circles. For Station Gare this could be because there are three adjacent hubs in a small area in the city center. Alternatively, the Station Famars Université is replaced by the nearest new one at Aulnoy-lez-Valenciennes. This may be because Station Famars Université is located at the end of Valenciennes's public transport network, and clustering suggests moving this hub more centrally. Also, there are two new clusters in Quiévrechain and St-Amand SNCF's geo-location at the border of Valenciennes Metropole. It is anticipated that this is to improve the Valenciennes Metropole area.

The 7 clusters scenario is shown in Figure 21. The same indication as the previous case applies here. Again, in the city center, two hubs (Station Saint Waast and Station Anzin Hôtel de Ville) sit within the same circle. However, now we have met all existing hubs. The hub Gare is also part of one circle, unlike the previous case with five clusters. Also, this time, there is no new hub at Aulnoz-lez-Valenciennes, but instead at Conde - Le Boulon, which is also the terminus for tramline 2. Alternately, Quiévrechain and St-Amand SNCF are the same as the 5 cluster cases.

The nine clusters example is shown in Figure 22. Existing hubs are located as for the seven clusters case. Nothing has changed. Inevitably, there are new clusters. Some of these are in related positions, as previously. The two new centers are at Bouchain and Escaupont.
<figure><img src="image_23.png" /><figcaption>Figure 21 Geographical position at departure: 7 clusters</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Figure 22 Geographical position at departure: 9 clusters</figcaption></figure>
### 4.5.3.2 Clustering of the geographical positions of PWD at arrival

As already mentioned, the previous tests have been studied in the case of departure when the vehicle takes PWD users. The arrival event is when the vehicle delivers the user to the requested address. Table 14 shows the clustering results applied to 2,747 users, with the number of requested clusters set at five, seven, and nine. There are 16 fewer users at arrival because some users get out at the same place.

In the case of 5 clusters, the results are equal in the departure and the arrival leading to the same average percentage of satisfied users. The same applies to the case with 7 clusters. However, for the case of 9 clusters, there are some differences. There are 24% satisfied users, which is 9% less than for the departure situation. Also, the minimum rate of satisfied users in a cluster is now 4%, compared to the departure situation, which was 11%. The radius of 400m reported 2% of satisfied users with 5 clusters, 6% within 7 clusters, and 8% in the case of 9 clusters. Radius 150m shows an improvement of 1% in 5 and 7 clusters and 2% for 9 clusters.

<table><caption>Table 14 Results of clustering at arrival, K= 5, 7, 9</caption><thead><tr><th rowspan="2">ARRIVAL</th><th colspan="3">5 Clusters</th><th colspan="3">7 Clusters</th><th colspan="3">9 Clusters</th></tr><tr><th>Size of cluster</th><th>Satisfied</th><th>%</th><th>Size of cluster</th><th>Satisfied</th><th>%</th><th>Size of cluster</th><th>Satisfied</th><th>%</th></tr></thead><tbody><tr><td>1000m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>390</td><td>14</td><td>4%</td><td>173</td><td>6</td><td>3%</td><td>171</td><td>6</td><td>4%</td></tr><tr><td>Cluster 2</td><td>953</td><td>222</td><td>23%</td><td>330</td><td>84</td><td>25%</td><td>703</td><td>182</td><td>26%</td></tr><tr><td>Cluster 3</td><td>171</td><td>76</td><td>44%</td><td>723</td><td>182</td><td>25%</td><td>159</td><td>80</td><td>50%</td></tr><tr><td>Cluster 4</td><td>346</td><td>84</td><td>24%</td><td>319</td><td>33</td><td>10%</td><td>272</td><td>57</td><td>21%</td></tr><tr><td>Cluster 5</td><td>887</td><td>89</td><td>10%</td><td>863</td><td>207</td><td>24%</td><td>302</td><td>25</td><td>8%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>163</td><td>80</td><td>49%</td><td>174</td><td>37</td><td>21%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>176</td><td>9</td><td>5%</td><td>741</td><td>246</td><td>33%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>121</td><td>27</td><td>22%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>104</td><td>5</td><td>5%</td></tr><tr><td>Total</td><td>2747</td><td>485</td><td>18%</td><td>2747</td><td>601</td><td>22%</td><td>2747</td><td>665</td><td>24%</td></tr><tr><td>400m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>1766</td><td>21</td><td>1%</td><td>814</td><td>79</td><td>10%</td><td>159</td><td>36</td><td>23%</td></tr><tr><td>Cluster 2</td><td>212</td><td>3</td><td>1%</td><td>346</td><td>3</td><td>1%</td><td>88</td><td>14</td><td>16%</td></tr><tr><td>Cluster 3</td><td>347</td><td>6</td><td>2%</td><td>159</td><td>36</td><td>23%</td><td>695</td><td>79</td><td>11%</td></tr><tr><td>Cluster 4</td><td>246</td><td>3</td><td>1%</td><td>88</td><td>14</td><td>16%</td><td>105</td><td>1</td><td>1%</td></tr><tr><td>Cluster 5</td><td>176</td><td>26</td><td>15%</td><td>334</td><td>6</td><td>2%</td><td>674</td><td>60</td><td>9%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>883</td><td>6</td><td>1%</td><td>123</td><td>21</td><td>17%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>123</td><td>21</td><td>17%</td><td>308</td><td>5</td><td>2%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>252</td><td>9</td><td>4%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>343</td><td>3</td><td>1%</td></tr><tr><td>Total</td><td>2747</td><td>59</td><td>2%</td><td>2747</td><td>165</td><td>6%</td><td>2747</td><td>228</td><td>8%</td></tr><tr><td>150m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>347</td><td>4</td><td>1%</td><td>334</td><td>4</td><td>1%</td><td>739</td><td>8</td><td>1%</td></tr><tr><td>Cluster 2</td><td>246</td><td>2</td><td>1%</td><td>814</td><td>2</td><td>0%</td><td>323</td><td>4</td><td>1%</td></tr><tr><td>Cluster 3</td><td>1766</td><td>11</td><td>1%</td><td>346</td><td>2</td><td>1%</td><td>714</td><td>2</td><td>0%</td></tr><tr><td>Cluster 4</td><td>176</td><td>2</td><td>1%</td><td>159</td><td>3</td><td>2%</td><td>139</td><td>1</td><td>1%</td></tr><tr><td>Cluster 5</td><td>212</td><td>3</td><td>1%</td><td>88</td><td>14</td><td>16%</td><td>159</td><td>3</td><td>2%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>883</td><td>1</td><td>0%</td><td>260</td><td>1</td><td>0%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>123</td><td>1</td><td>1%</td><td>87</td><td>14</td><td>16%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>121</td><td>1</td><td>1%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>205</td><td>29</td><td>14%</td></tr><tr><td>Total</td><td>2747</td><td>22</td><td>1%</td><td>2747</td><td>27</td><td>1%</td><td>2747</td><td>63</td><td>2%</td></tr></tbody></table>
The outcome of cluster analysis for the arrivals in the case of a radius of 1000m is depicted in Figure 23, Figure 24, and Figure 25. The high resolution of the mentioned figures is presented in Appendix F (Figure 36, Figure 37, and Figure 38). Analysis of the hubs' geo-position shows an apparent difference only in the case of 9 clusters compared to the departure situation. The geo-position of cluster centers and the relationship between existing hubs and established clusters are identical in all other locations. This was not unexpected due to a similar distribution of the input data. The results of the five and seven cluster cases are shown in Figure 23 and Figure 24. In the 9 clusters example, the difference is that the hub Bouchain is not included, Figure 25. The next example is *Prouvy*, which is located more in Valenciennes' urban area, unlike *Bouchain*, which is in a rural area. The other difference is that the hub *Famars-Université* is within a 1,000 meters radius.

<figure><img src="image_25.png" /><figcaption>Figure 23 Geographical position at arrival: 5 clusters</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Figure 24 Geographical position at arrival: 7 clusters</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>Figure 25 Geographical position at arrival: 9 clusters</figcaption></figure>
### 4.5.3.3 Clustering of the geographical positions of PWD – all

The case of considering simultaneous departures and arrivals is analyzed only numerically because we were focused on the transport flow. The numerical analyses served to check the number of clusters and satisfied users.

The numerical presentation of the complete database is presented in Table 15. The graphic display is not part of this study, as it was more important to know the clusters in different transport flows. However, the numerical analysis has shown that 23% of satisfied users for 5 clusters, 25% for 7 clusters, and 29% for 9 clusters if the radius is 1000m. As expected, this ratio is smaller for a radius of 400m and 150m.

<table><caption>Table 15 Results of clustering all users, K= 5, 7, 9</caption><thead><tr><th rowspan="2">ALL</th><th colspan="3">5 Clusters</th><th colspan="3">7 Clusters</th><th colspan="3">9 Clusters</th></tr><tr><th>Size of cluster</th><th>Satisfied</th><th>%</th><th>Size of cluster</th><th>Satisfied</th><th>%</th><th>Size of cluster</th><th>Satisfied</th><th>%</th></tr></thead><tbody><tr><td>1000m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>1734</td><td>364</td><td>21%</td><td>1608</td><td>364</td><td>23%</td><td>1501</td><td>674</td><td>45%</td></tr><tr><td>Cluster 2</td><td>668</td><td>168</td><td>25%</td><td>486</td><td>10</td><td>2%</td><td>210</td><td>44</td><td>21%</td></tr><tr><td>Cluster 3</td><td>356</td><td>166</td><td>47%</td><td>1870</td><td>622</td><td>33%</td><td>605</td><td>66</td><td>11%</td></tr><tr><td>Cluster 4</td><td>820</td><td>28</td><td>3%</td><td>340</td><td>174</td><td>51%</td><td>332</td><td>174</td><td>52%</td></tr><tr><td>Cluster 5</td><td>1932</td><td>524</td><td>27%</td><td>134</td><td>30</td><td>22%</td><td>210</td><td>4</td><td>2%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>404</td><td>12</td><td>3%</td><td>168</td><td>40</td><td>24%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>668</td><td>168</td><td>25%</td><td>540</td><td>44</td><td>8%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>1440</td><td>364</td><td>25%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>504</td><td>206</td><td>41%</td></tr><tr><td>Total</td><td>5510</td><td>1250</td><td>23%</td><td>5510</td><td>1380</td><td>25%</td><td>5510</td><td>1616</td><td>29%</td></tr><tr><td>400m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>3388</td><td>42</td><td>1%</td><td>634</td><td>12</td><td>2%</td><td>1188</td><td>36</td><td>3%</td></tr><tr><td>Cluster 2</td><td>694</td><td>12</td><td>2%</td><td>306</td><td>10</td><td>3%</td><td>158</td><td>6</td><td>4%</td></tr><tr><td>Cluster 3</td><td>246</td><td>42</td><td>17%</td><td>100</td><td>6</td><td>6%</td><td>1284</td><td>158</td><td>12%</td></tr><tr><td>Cluster 4</td><td>358</td><td>52</td><td>15%</td><td>1756</td><td>158</td><td>9%</td><td>246</td><td>42</td><td>17%</td></tr><tr><td>Cluster 5</td><td>824</td><td>32</td><td>4%</td><td>288</td><td>2</td><td>1%</td><td>504</td><td>18</td><td>4%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>480</td><td>2</td><td>0%</td><td>210</td><td>2</td><td>1%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>1946</td><td>232</td><td>12%</td><td>1180</td><td>48</td><td>4%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>332</td><td>72</td><td>22%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>408</td><td>32</td><td>8%</td></tr><tr><td>Total</td><td>5510</td><td>180</td><td>3%</td><td>5510</td><td>422</td><td>8%</td><td>5510</td><td>414</td><td>8%</td></tr><tr><td>150m</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cluster 1</td><td>3534</td><td>22</td><td>1%</td><td>356</td><td>10</td><td>3%</td><td>1390</td><td>4</td><td>0%</td></tr><tr><td>Cluster 2</td><td>694</td><td>8</td><td>1%</td><td>140</td><td>4</td><td>3%</td><td>246</td><td>2</td><td>1%</td></tr><tr><td>Cluster 3</td><td>366</td><td>4</td><td>1%</td><td>1834</td><td>24</td><td>1%</td><td>210</td><td>2</td><td>1%</td></tr><tr><td>Cluster 4</td><td>492</td><td>4</td><td>1%</td><td>1672</td><td>10</td><td>1%</td><td>617</td><td>8</td><td>1%</td></tr><tr><td>Cluster 5</td><td>424</td><td>6</td><td>1%</td><td>238</td><td>2</td><td>1%</td><td>332</td><td>6</td><td>2%</td></tr><tr><td>Cluster 6</td><td>N/A</td><td>N/A</td><td>N/A</td><td>496</td><td>10</td><td>2%</td><td>1349</td><td>14</td><td>1%</td></tr><tr><td>Cluster 7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>774</td><td>4</td><td>1%</td><td>176</td><td>28</td><td>16%</td></tr><tr><td>Cluster 8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>686</td><td>4</td><td>1%</td></tr><tr><td>Cluster 9</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>504</td><td>12</td><td>2%</td></tr><tr><td>Total</td><td>5510</td><td>44</td><td>1%</td><td>5510</td><td>64</td><td>1%</td><td>5510</td><td>80</td><td>1%</td></tr></tbody></table>
## 4.6 Conclusion

This chapter proposed a clustering analysis to make the existing public transport network of Valenciennes more accessible to PWD. The primary goal was to develop a viable approach that enables PWD to use public transport freely, unlike the current arrangement where the transport of PWD is somewhat excluded. The transport of PWD in Valenciennes is achieved using a transport-on-demand service called *Sésame*, which is entirely independent of other parts of the public transport network.

The proposed clustering approach suggests possibilities for the inclusion of PWD to the public network. One option is the re-direction of PWD to nearby hubs, from where they can access the public network in the same way as other users. Applying the clustering approach shows that at least 18% of PWD at departure/arrival could use the Valenciennes public transport network. Another option is to open up new hubs, which would result in improved satisfaction for PWD users. The next possibility would be to combine transport on-demand (*Sésame*) with other public transport network sections. This could happen by bringing PWD to hubs (by either *Sésame*, or independent PWD access to the closest hub), after which the public transport network is used in the same way as regular users. Finally, they arrive at a hub from where they go to the destination - either by *Sésame*, or independently if the distance is reasonable. For this option, the key issue is the appropriate dispatch of *Sésame* vehicles to hubs to bring PWD to corresponding hubs.

Final recommendations made to Transvilles are shown using the number of clusters $K=5,7,9$ with a radius of 1000m. This radius follows the situation on the ground, where they considered network station distances in the same manner. Although considered in this thesis, the radii of 400m and 150m are not used for the final recommendation because some preliminary questionnaires revealed that the distance of 1000m would be acceptable for PWD currently. However, the analysis outcomes for 400m and 150m presented in this thesis still provide significant insights for Transvilles on how to further optimize their network for PWD in the future.

**The 5 clusters case.** We will start with the recommendations for the situation of 5 clusters, which is the present case on the network. At this stage, we reported that 18% of users could use conventional transport instead of "*Sésame*." What should be considered to change is the geo-location of current hubs. The recommendation is to introduce three new: *Aulnoy-lez-Valenciennes*, *Quiévrechain*, and *St-Amand SNCF*. The vehicles in charge of transport on demand can use some of this location as a depot, instead of having only one depot for all vehicles.
**The 7 clusters case.** The applied method indicates that up to 22% of PWD users could be brought to regular transport in the situation of 7 clusters. This percentage will be achieved if the new hubs are established in *Quiévrechain*, *St-Amand SNCF*, and *Conde - Le Boulon*. The centers *Quiévrechain* and *St-Amand SNCF* appeared in both situations, five and seven clusters. A similar recommendation at the operational level may be provided regarding vehicles: Consider the new hubs as possible depot locations.

**The 9 clusters case.** It was observed that in the case of 9 clusters, the percentages of PWD that could directly use public transport networks are 24% on arrival and 35% on departure. Enabling at least 24% of PWD users to become free users of the public transport network is a remarkable achievement. For this purpose, new hubs need to be located in *Quiévrechain*, *St-Amand SNCF*, *Conde - Le Boulon*, *Bouchain*, or *Prouvy*. Since we have a different graphic situation departure and arrival, we need to propose a unique geographic location. On arrival, we have a new hub *Prouvy*, and on departure, we have *Bouchain*. The proposition here is to develop the hub *Bouchain*, because *Prouvy* is located in the middle of two existing hubs *Denain and Famars*. Additionally, the *Prouvy* is closer to the center of Valenciennes.

These interpretations of the numerical and graphical results support our findings, but the recommendations for new hubs are in line with the map presented in Figure 26. This picture gives the establishments for disabled and/or elderly people in metropole Valenciennes. All of the specialized establishments are spread over the two Agglomeration communities.

A further recommendation is made in relation to facilities. The public transport of Valenciennes does not have the facilities to monitor the number of PWD users. Today, data on types of PWD, the mode of transportation they use is not available. In fact, this data does not exist at all. The available data set registers PWD users via an inscription for the appropriate travel subscription. After that, the current ticketing system cannot recognize different users. We strongly believe it is critical to accurately measure the use of public transport networks by diverse users. This could serve as an essential tool to help improve the service further.

This chapter proposes several potential research directions for the future. For example: optimizing further transport-on-demand by properly dispatching the existing fleet; determining the optimal number of transport-on-demand vehicles to ensure a certain level of user satisfaction; simultaneously address the dial-a-ride problem and clustering; create a user-friendly application that generates itineraries for PWD by combining dial-a-ride and the shortest path optimization problems, etc.
<figure><img src="image_28.png" /><figcaption>Figure 26 Establishments for disabled and/or elderly people in Valenciennes metropolitan region</figcaption></figure>

(Egis France Villes & Transport, 2013b)
# Chapter V
# 5 Closing statement

The same argument is applied in the closing statement as in the explanatory statement. Chapter V includes Section 5.1 Introduction, followed by Section 5.2 Main research findings, including the reframing and incomings elements. Section 5.3 is dedicated to the thesis contributions. Section 5.4 makes the recommendation for future work, and Section 5.5 concludes the chapter.

## 5.1 Introduction

As demonstrated throughout the chapters of this thesis, public transport systems are reaching out to serve more and more diverse users, particularly persons with disabilities. However, while PWD integration regulations have become increasingly demanding, the focus remains on the standard user, and transport system design has not fundamentally changed. The number of users and the diversity of their needs make transport planning incredibly complex. At the same time, we have seen this complexity increases to meet the specific needs of PWDs. On top of the number of participants, PWD transport is also limited by specific constraints, such as the types of journeys and vehicles. Optimization models such as transport-on-demand and the shortest path problem provide a starting point for one of the best-known approaches to help improve services for PWD. Still, these cannot deliver complete independence in PWD transport.

In the closing statement, we will summarize the main findings of this research and demonstrate why it was necessary to reframe the problem formulation. We found that the two basic optimization models do not fully satisfy the process. At this point, we demonstrated the decision analyst's central role in helping the client understand and formulate the problem correctly. The contributions of the thesis will be the topic of this chapter as well.
## 5.2 Summary of the main results and limitations

Notwithstanding this thesis's interdisciplinary approach, as discussed earlier, the decision-aiding process determines the development and research formalization of the thesis structure. The four stages of the decision-aiding process in this thesis are made up of the problem situation, the problem formulation, the evaluation model, and the final recommendation (Tsoukiàs, 2007) and each chapter's development. Consistent with the final recommendations, we need to consider the model's formality, the client's understanding of the model, and its legitimacy. Figure 27 shows the operational research models' steps and organizational legitimacy (Landry et al., 1996). Through the thirteen steps, the process of successful adoption of operational research inside the organization is explained. The third step, the change process through modeling, is reserved for an unforeseen element in the optimization models. This step prompted us to reframe the optimization model – clustering approach instead of transport on-demand or shortest path, which will be further explained in subsection 5.2.2 But, first, before the reframing, the main findings will be presented.

<figure><img src="image_29.png" /><figcaption>Figure 27 OR models and organizational legitimacy (Landry et al., 1996), adapted by the author</figcaption></figure>
5.2.1 Findings

In this thesis, we have addressed the efficient integration of persons with disabilities into the public transport system, using the decision support process. This approach makes it possible to better align the required adaptations of a transport system while being aware of the challenges of players in the transport system, taking careful account of the needs of persons with disabilities.

Introducing decision models based on decision theory into organizations is a sensitive process that requires detailed knowledge, both of the computational foundations underlying the models and the decision-making factors involved in organizations. This challenge is usually avoided for two main reasons: i) practical problems associated with decision theory that typically relate to already formalized fields (John C. Henderson & Nutt, 1980; Landry et al., 1996; Landry et al., 1983). A transport system already responds to an established structure that significantly restricts decisions, which provides a prerequisite suitable for modeling; ii) the concept of a decision is intimately linked to human nature (H. A. Simon, 1973; H. A. Simon, 1997; H. A. Simon, 2000). The result is an interest in instrumental decision support that focuses its intervention on a result rather than a support aiming to improve the decision-making structure.

Approached in this way, modeling can be liberated from the mere construction of a representation faithful to the transport system to consider assumptions that change its nature. Thus, by approaching PWD as stakeholders in decisions, models become a factor of inclusion that will strengthen the validity of some decision-making processes and necessitate changing others. The management of transport networks then breaks down into a generic centralized part and a decentralized part that has better consideration for the particular needs of PWD.

Centralized management remains fundamentally based on the shortest path problem incorporating accessibility constraints. Decentralized governance is based on transport-on-demand, where external resources are mobilized. It is generally considered that transport-on-demand is helpful to many rural and urban communities, particularly with the development of telematics. In the case of PWD, on-demand transport also serves urban areas that are not covered by the network.

These areas, which do not present problems for non-disabled people, may be difficult to navigate for persons with disabilities. Transport on-demand then results in consideration
of non-disabled people as a transport resource that can support PWD in rural areas adjacent
to the network journey. Standard, non-disabled users can then become leverage for the
inclusion of PWD in the transport system.

Accessibility plays one of the primary functions in bringing the transport system closer to PWD. To create such a system, it was necessary to develop the model with additional information (John C Henderson & Venkatraman, 1999). One part of this additional information relates to PWD needs. These needs have already been defined (U.S. Government Accountability Office (GAO), 2004) and presented as the 5As: Availability, Accessibility, Acceptability, Affordability and Adaptability. They represent PWDs requests, but they have not been considered in developing and evaluating optimizations models.

With this perspective of the problem, up-to-date information is needed on the service
offering. Nevertheless, this offering must also be structured in a network to establish the
vectors of inclusion. This network can be formed through strategic alliances (John C
Henderson & Venkatraman, 1999) between the transport system management and new
stakeholders that support PWD. Such stakeholders are usually part of the logic of non-
governmental organizations, which strengthens the merits of decentralized governance. From
their conception, models delimit organizational impact beyond their operational nature due
to a strategic alignment logic.

Organizational arrangements, therefore, frame models. The robust analysis of solutions generates information on the means required for the model framework. The sensitivity analysis, for its part, appears more linked to the data and their acquisition chain.

5.2.2 Reframing

According to Herbert A. Simon, 1983), the problem is not resolved within the decision-aiding process, although the process of setting and fixing the issue is the same process. In fact, in the absence of a good problem position, a good solution cannot be found. As reported in the final recommendation (Tsoukiàs, 2007), and as stated at the beginning of this chapter (Landry et al., 1996), in order to have a successful model implementation, the model must be legitimate. One way of achieving legitimacy is to change the process through modeling, referred to as reframing.

Reframing the problem results from the comprehensive analysis of PWD needs and
evaluating the corresponding models. The data set available for the actual examination
required that the problem be reframed.
At the beginning of this thesis, it was proposed that the basic optimization models transport-on-demand and shortest path only partially satisfied PWD needs, as defined through 5As. Full independence for the inclusion of PWD in public transport cannot be provided. The interaction between the public transport network and basic optimization models was reviewed and evaluated through PWD needs. The results have shown that it would be more useful to demonstrate the model's legitimacy if the clustering approach is used. The available data for the Valenciennes public transport network relates to the geo-location of transport on-demand users. This data represents an important part of model development. However, the most important function is model implementation, which brings us back to the model's legitimacy. It also provides an example of problem reframing.

### 5.2.3 Incomings

Incomings is a general reflection on the model embedded in the organization. The issue of inclusion raises the question of what optimization means to users, which is the principle that underpins the transport-on-demand and shortest path approaches, and centralized management. In the modeling approach based on the decision-aiding process, optimization is approached in three ways:

1. Identification of an issue or a sub-set of topics that legitimately resembles an optimization logic that will provide a basis of stability by centralized management models.

2. Change management according to the position of the problem in the hierarchy of issues:

* Strategic - to address mobility issues in order to restore capacities that organizational alliances and networks have reduced.

* Tactical - to create information systems that mobilize the network of non-disabled people assisting PWD.

* Operational - to implement a support network for each request received from a PWD.

3. Monitoring the organizational dynamics of disseminating data produced within the reconfigured organization to adjust the models and identify new model needs.

It should be noted that this modeling approach, taking organizational factors into account, highlights the value of reflecting on the challenges of improving the quality of service
beyond the normative approach provided by models alone. Thus, by coordinating non-
disabled people with PWD, a combination of centralized and decentralized transport
management modes reveals two different aspects of mobility. For persons with disabilities,
mobility challenges are unique to the individual. Alternately, for the non-disabled person,
movement becomes an organizational issue. More general and shared common factors are
needed to develop the transport system on a lasting basis. Subject to an individual's particular
circumstances, the issue of mobility does not have the same status. This issue, therefore,
concerns the organization responsible for the transport system. For an individual, disabled or
not, the issue is proximity, the use of the transport system being a resource to get to a
preferred destination.

The concept of non-disabled people supporting PWD is essentially a social cohesion
issue.

**5.3 Scientific contributions**

To explain scientific contributions, we will first restate the research objectives of the thesis. One of the thesis's main goals is to improve the quality of life for persons with disabilities. A key component of PWD quality of life is the extent of their inclusion in a public transport network. Another goal was to assist in the decision-making process of our client: Communauté d'agglomération Valenciennes Métropole. The third goal was to develop an optimization model to ensure the inclusion of PWD in public transport without changing the network itself.

To address the first goal, we focused on understanding the needs and obstacles for PWD
in the daily use of public transport. This was summarized by the literature review from various
disciplines, including legislation from different countries, studies, and the analysis of
international organizations, medical examinations, etc. As it was the project input to some
optimization models, a systematic review was carried out to identify the appropriate models.

For the second goal, the process of decision aiding has been comprehensively explained to clearly demonstrate the methodology's useful tools to the client and reader. Also, through the process of applying the methodology, each phase provides examples and clarification of the process related to the appropriate transportation optimization model. Ultimately, the proposed model facilitates the provision of a transport service that gives full autonomy to PWD.
The third goal was achieved through the clustering approach. Since that decision-aiding
process reveals the results that analyzed optimization models transport on-demand and the
shortest path satisfied only one part of the solution, the clustering approach is proposed as
the Analytic tool. The clustering approach is analyzed the transportation flow of PWD and
proposes the new exchange hubs with a higher number of satisfied PWD users.

The scientific contribution is presented through three themes of the thesis: theoretical, methodological, and application.

5.3.1 Theoretical

The review of the relevant literature within a single discipline is a challenging task. When a multidisciplinary review is carried out, the challenge is amplified. The organization of this research and the identification of relevant data is the most demanding job. The resulting output is our contribution.

The 5As, as defined by the U.S. Government Accountability Office (U.S. Government Accountability Office (GAO), 2004), identified the primary needs of persons with disabilities and formed a key reference for our study. The 5As are: Availability, Accessibility, Acceptability, Affordability and Adaptability, and form the foundation for the theoretical research of this thesis. As far as we are aware, this is the first time that an analysis of the optimization models has been carried out through a systematic review.

The systematic review was implemented in two parts: transport on-demand and shortest path. The six models in transport-on-demand optimization models include: Dial A Ride Problem – DARP, Demand Adaptive System – DAS; Flexible Transport System – FTS; Scheduled Paratransit Transport System – SPTS; Mobility Allowance Shuttle Transit – MAST, and Integrated Dial-a-Ride – IDAR. These were analyzed in relation to PWD needs in accordance with the 5As. The second part considered the shortest path models, which were classified into four models: Multimodal Shortest Path Problem – MSPP; Time Dependent Shortest Path Problem – TDSPP; Resource Constrained Shortest Path Problem – RCSPP; and Multi Objective Shortest Path Problem – MOSPP. For the first time, in addition to the classification contribution, all the models were defined and evaluated relative to the 5A attributes. A ranking table including detailed studies of each model component has been provided.
In addition, the framework of transport legislation relating to PWD transport rights has been provided at three levels: globally, across Europe, and nationally (France and Canada). The most significant contribution is that almost all the literature relating to the transport of persons with disabilities has been summarised in a single place.

### 5.3.2 Methodological

The methodological contribution spans several segments. The first methodological contribution comes from combining three different approaches: management, the decision-aiding process, and optimization. This interdisciplinary approach enabled the resulting high quality of research.

Management emerged as the second methodological contribution by examining numerous sources of literature. The provision of references such as numerical data, regulations, and the bibliography required a precise and systematic approach.

For the decision-aiding methodology component, we can report four contributions: - 1) Practical application of the decision-aiding process within the thesis as shown in the thesis structure; 2) The structure is maintained through each chapter; 3) In Chapter III all steps of DAP are implemented and the matrix is developed.

The matrix presents the structure of the relationships between existing optimization models, subject to public network information, particularly the actual accessibility of the public network. The decision-aiding process proposes a comprehensive analysis, enabling selecting a suitable model at any time for the inclusion of disabled persons.

As already observed, the decision-aiding process includes four approaches: normative, descriptive, prescriptive, and constructive (D. Bouyssou, 2000, 2006). Different decision-aiding approaches are dependent on different disciplinary concerns, and in this case, we were applying interdisciplinary thesis research, so all four approaches were implemented. Normative was used for the investigation on regulations, regulative investigation in Chapter II. Descriptive was used for the analysis of optimization models, also included in Chapter II. Prescriptive is provided in Chapter IV, where we proposed a clustering approach, and constructive in Chapter III.
### 5.3.3 Application

The clustering approach was used to improve actual accessibility to the public network. This contribution has demonstrated for the first time that the clustering approach can be used to bring the existing public transport network closer to PWD based on a real data set. Additionally, a case study on the network of Valenciennes has been provided.

The aim was to propose a method that helps PWDs to use the public network independently. The data used was obtained from transport-on-demand users, as this was the only transport mode provided in Valenciennes for persons with disabilities. The clustering approach helped avoid a hard requirement imposed at the beginning of research - that the network infrastructure could not be changed. Having complied with this guarantee to meet the PWD needs in this requirement, our approach improves the transport network's use just by reorganizing the hubs. Moreover, the proposed clustering approach suggests further possibilities for the inclusion of PWD into the public network.

The first contribution is based on directing PWDs to the nearest hub where they can access the public network alongside other users. The clustering approach shows that at least 18% of PWD in departure/arrival could use the public transport network of Valenciennes as freely as regular users.

Another contribution is the recommendation to open up new hubs by simply designating some of the existing stations to serve as hubs. In this way, a significant increase in the number of satisfied PWD users is achieved.

### 5.4 Recommendation for future work

Future work includes the development of organizational levers that serve the mobility of persons with disabilities. This is broken down into five components: i) organizational levers for strategic alignment; ii) social networks; iii) levers of strategic alliances and corporate networks; iv) definition of sectoral and public policy guidelines; v) data.
i. Organizational levers for strategic alignment:

a. Decision-making hierarchy of stakeholders that are strategically involved in disability; the definition of objectives and the transportation means of urban mobility; the tactics for an arrangement of the transportation means; the operation of the implementation of the transportation means, and activities of production of the effects of transportation means;

b. Decline of mobility issues from the point of view of the individual, organizations and society;

c. Analysis of the potential for the service to be offered directly by existing means of mobility, for particular citizens, or achieved by the transfer of means devoted to issues other than mobility;

d. Inventory of stakeholders in mobility services applicable to people with disabilities;

e. Information and communication vectors, social networks on the internet, and mobile applications that can make the offer and demand tangible and to guarantee to meet the PWD needs

ii. Social networks

a. Additions to mobile technologies in order to identify needs in WEB technologies and services;

b. Structuring of data flows to establish information continuity between strategy, tactics, operation and action, both within and outside the value chain;

c. Centralized and decentralized information systems that guarantee organizational continuity between stakeholders.

iii. Levers of strategic alliances and organizational network:

a. Structuring of the organizational network around shared and specific issues;

b. Contractual bases for commercial relations, partnerships and framework agreements;

c. Definition of online communities to support the productivity of agreements.

iv. Definition of sectoral and public policy guidelines:

a. Social cohesion in order to guarantee the continuity of digital technology in social connection;

b. Societal and economic value for joint development of markets, economic value, non-market value, intangible capital, and amenities;

c. Protection of vulnerable groups in order to avoid prejudicial bias, polarization, discrimination and exclusion;

d. Digital and technology education to enable stakeholders to be aware of their rights and responsibilities;

e. Safe society that protects against acts of unlawful interference, to guarantee the meeting of basic needs, and the rule of law;
f. Roles and missions of sectoral and territorial governance bodies to put in place organizational levers that guarantee respect for political boundaries.

v. Data:

a. Urban analytics to build elements of knowledge that can inform the consolidation of political boundaries and the enhancement of territories and users of urban space;

b. Protection and integrity of personal data;

c. Open data and clarification of internal public data that can be disseminated, both proprietary data and external data.

5.5 Conclusion

The closing statement is provided as a summary of the main findings and scientific contributions. As required, in this section, we have demonstrated the necessity of using an interdisciplinary approach, as well as acknowledging the steps of the decision-aiding process.
Conclusion

The earlier chapters demonstrated and clarified the multiple elements of the accumulation
process in the execution of interdisciplinary research. The main factor in the accumulation
process is the continuous gathering of information, which generates a high level of complexity.
Multidisciplinary research is not welcome everywhere. It is unusual for it to be acknowledged
even within science or in the views of administrators, technicians, and support staff. This will
remain the case until problems are encountered, then there will be a general consensus that
insists on the need to implement knowledge from different domains in a single place (Palmer,
2013).

In our case, we encountered complex problems. The first complexity was in the definition of the needs of persons with disabilities. Before addressing these requirements, it was necessary to analyze the definition of various categories of disability. The high number of categories led us to the first decision: - to consider only the needs of the persons with disabilities that were wheelchair users. The next complexity arose in the literature review in determining where and how we could find information on PWD needs. In order to make progress, we applied a management discipline through the methodology of the systematic review, with a special review of regulations relating to PWD needs. The optimization models for PWD transport obtained from the systematic review are analyzed and observed to 5As (Availability, Accessibility, Acceptability, Affordability and Adaptability) and present the scientific contribution in this part of the thesis. Again, the integration of disciplinary research generated a result.

The second complexity comes from the problem formulation, which requires a further
disciplinary domain: that of the decision-aiding process. The systematic review revealed that
basic optimization models do not meet all PWD needs. With this information, we could not
arrive at a solution providing independence for PWD in public transport, so it was necessary
to reframe the project problem formulation. Given the inadequacy of these optimization
models, this time, we wanted to highlight PWD needs, but this would have involved numerous
participants in the transportation chain.

The steps of the decision-aiding process yielded many contributions, such as: - i) the
matrix of the possible interactions between the needs and obstacles of PWD; and ii) structure
of the relationships within existing optimization models, subject to the public network
information, particularly on the current accessibility to the public network. Moreover, the
decision-aiding process suggests a comprehensive analysis, enabling the ability to choose at
any time an appropriate model for the inclusion of disabled persons.
The problem formulation confirmed that optimization models (transport-on-demand and SPP) are the primary tools to obtain an efficient solution for a part of the problem. However, the problem of accessing the network is not resolved. The lack of connectivity between the start point (International Conference on Smart et al.) and the public network (sidewalks) results in the need to define the cluster centers (hubs or exchange poles). Now we need a new discipline to solve the problem - optimization. Using the available real data set from the transport operator in Valenciennes "Transvilles," for the first time, a clustering approach is proposed to include PWD in public transport, where we succeeded in improving current accessibility to the public network.

This thesis demonstrates that an interdisciplinary approach is necessary to solve a complex problem efficiently, particularly when different information types are involved.
Bibliography

Ackoff, R. L. (1979). The Future of Operational Research is Past. *Journal of the Operational Research Society*, 30(2), 93-104. doi:10.1057/jors.1979.22

Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). *Network flows : theory, algorithms, and applications*. Englewood Cliffs, N. J: Prentice-Hall.

Aldaihani, M., & Dessouky, M. M. (2003). Hybrid scheduling methods for paratransit operations. *Computers & Industrial Engineering, 45*(1), 75-96.
doi:https://doi.org/10.1016/S0360-8352(03)00032-9

Aloise, D., Deshpande, A., Hansen, P., & Popat, P. (2009). NP-hardness of Euclidean sum-of-squares clustering. *Machine learning*, 75(2), 245-248.

Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state of the art.
*European Journal of Operational Research*, 190(1), 1-21.
doi:https://doi.org/10.1016/j.ejor.2007.06.008

Archetti, C., Speranza, M. G., & Weyland, D. (2018). On-demand public transportation. *Int. Trans. Oper. Res.*

Badger, D., Nursten, J., Williams, P., & Woodward, M. (2000). Should all literature reviews be systematic? *Evaluation & Research in Education, 14*(3-4), 220-230.

Bakas, I., Drakoulis, R., Floudas, N., Lytrivis, P., & Amditis, A. (2016). A Flexible Transportation Service for the Optimization of a Fixed-route Public Transport Network.
*Transportation Research Procedia*, 14, 1689-1698.
doi:https://doi.org/10.1016/j.trpro.2016.05.134

Balasko, B., Abonyi, J., & Feil, B. (2014). Fuzzy Clustering and Data Analysis Toolbox for Use With Matlab.

Barlas, Y. (1996). Formal aspects of model validity and validation in system dynamics. *System Dynamics Review: The Journal of the System Dynamics Society*, 12(3), 183-210.

Barton, L. (2006). *Overcoming disabling barriers: 18 years of disability and society:*
Routledge.

Bast, H., Delling, D., Goldberg, A., Müller-Hannemann, M., Pajor, T., Sanders, P., ...
Werneck, R. F. (2016). Route Planning in Transportation Networks. In L. Kliemann &
P. Sanders (Eds.), *Algorithm Engineering: Selected Results and Surveys* (pp. 19-80).
Cham: Springer International Publishing.

Beasley, J. E., & Christofides, N. (1989). An algorithm for the resource constrained shortest path problem. *Networks*, 19(4), 379-394.
Bekiaris, E., Loukea, M., Spanidis, P., Ewing, S., Denninghaus, M., Ambrose, I., ... Veitch, C. (2018). Research for TRAN Committee: Transport and Tourism for Persons with Disabilities and Persons with Reduced Mobility. In: European Parliament, Policy Department for Structural and Cohesion Policies ....

Bell, D. E., Raiffa, H., & Tversky, A. (1988). *Decision making: Descriptive, normative, and prescriptive interactions*: cambridge university Press.

Belter, T., & Gerike, R. (2008). Public Transport Systems' Accessibility for People with Disabilities in Europe.

Belton, V., & Stewart, T. J. (2002). *Multiple criteria decision analysis : an integrated approach*. Boston: Kluwer Academic Publishers.

Beverly Foundation and Community Transportation Association of America. (2004). *Innovations for Seniors: Public and Community Transit Services Respond to Special Needs*. Retrieved from Pasadena, CA, and Washington, D.C.:

Boulding, K. E. (1970). *Beyond Economics: Essays on Society, Religion, and Ethics*: University of Michigan Press.

Bouyssou, D. (2000). *Evaluation and decision models : a critical perspective*. Boston: Kluwer Academic Publishers.

Bouyssou, D. (2006). *Evaluation and decision models with multiple criteria stepping stones for the analyst*. Retrieved from Accès via SpringerLink http://dx.doi.org/10.1007/0-387-31099-1

Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Slowiński, R., Vanderpooten, D., & Vincke, P. (2012). *Aiding decisions with multiple criteria: essays in honor of Bernard Roy* (Vol. 44): Springer Science & Business Media.

Brake, J., Mulley, C., Nelson, J. D., & Wright, S. (2007). Key lessons learned from recent experience with Flexible Transport Services. *Transport Policy*, 14(6), 458-466.
doi:https://doi.org/10.1016/j.tranpol.2007.09.001

Broome, K., Worrall, L., Fleming, J., & Boldy, D. (2012). Evaluation of flexible route bus transport for older people. *Transport Policy*, 21, 85-91.
doi:https://doi.org/10.1016/j.tranpol.2012.02.005

Brown, R., & Vari, A. (1992). Towards a research agenda for prescriptive decision science: the normative tempered by the descriptive. *Acta Psychologica*, 80(1-3), 33-47.

Brown, R. V. (1989). Toward a prescriptive science and technology of decision aiding. *Annals of Operations Research*, 19(1), 465-483.

Bühler, C., Heck, H., Sischka, D., & Becker, J. (2006). *BAIM–Information for people with reduced mobility in the field of public transport*. Paper presented at the International Conference on Computers for Handicapped Persons.
Canada Gazette. (1996). *Canada Transportation Act S.C. 1996, c. 10*.

Canada Gazette. (2019). *Accessible Transportation for Persons with Disabilities Regulations (SOR/2019-244)*. Retrieved from http://www.gazette.gc.ca/rp-pr/p1/2019/2019-03-09/html/reg2-eng.html

Caprara, A., Kroon, L., Monaci, M., Peeters, M., & Toth, P. (2007). Chapter 3 Passenger Railway Optimization. In C. Barnhart & G. Laporte (Eds.), *Handbooks in Operations Research and Management Science* (Vol. 14, pp. 129-187): Elsevier.

Carrizosa, E., Mladenović, N., & Todosijević, R. (2013). Variable neighborhood search for minimum sum-of-squares clustering on networks. *European Journal of Operational Research*, 230(2), 356-363.

Cascetta, E., Carteni, A., Pagliara, F., & Montanino, M. (2015). A new look at planning and designing transportation systems: A decision-making model based on cognitive rationality, stakeholder engagement and quantitative methods. *Transport Policy*, 38, 27-39.

Chandra, S., Bari, M. E., Devarasetty, P. C., & Vadali, S. (2013). Accessibility evaluations of feeder transit services. *Transportation Research Part A: Policy and Practice*, 52, 47-63. doi:https://doi.org/10.1016/j.tra.2013.05.001

Churchman, C. W. (1957). *Introduction to operations research*. New York: Wiley.

Cimon, Y. (2004). Knowledge-related asymmetries in strategic alliances. *Journal of Knowledge Management*, 8(3), 17-30.

Cordeau, J.-F. (2006). A branch-and-cut algorithm for the dial-a-ride problem. *Operations Research*, 54(3), 573-586.

Cordeau, J.-F., & Laporte, G. (2003a). The dial-a-ride problem (DARP): Variants, modeling issues and algorithms. *Quarterly Journal of the Belgian, French and Italian Operations Research Societies*, 1(2), 89-101.

Cordeau, J.-F., & Laporte, G. (2003b). A tabu search heuristic for the static multi-vehicle dial-a-ride problem. *Transportation Research Part B: Methodological*, 37(6), 579-594.

Cordeau, J.-F., & Laporte, G. (2007). The dial-a-ride problem: models and algorithms. *Annals of Operations Research*, 153(1), 29-46.

Cordeau, J.-F., Laporte, G., Savelsbergh, M. W. P., & Vigo, D. (2007). Chapter 6 Vehicle Routing. In C. Barnhart & G. Laporte (Eds.), *Handbooks in Operations Research and Management Science* (Vol. 14, pp. 367-428): Elsevier.

Cortés, C. E., & Jayakrishnan, R. (2002). Design and Operational Concepts of High-Coverage Point-to-Point Transit System. *Transportation Research Record*, 1783(1), 178-187. doi:10.3141/1783-22
Council of Canadian Academies. (2017). *Older Canadians on the Move*. Ottawa (ON): The Expert Panel on the Transportation Needs of an Aging Population. Retrieved from
https://cca-reports.ca/wp-content/uploads/2018/08/transportaging_fullreport_en.pdf

Crainic, T. G., Errico, F., Malucelli, F., & Nonato, M. (2012). Designing the master schedule for demand-adaptive transit systems. *Annals of Operations Research*, 194(1), 151-166.
doi:10.1007/s10479-010-0710-5

Crainic, T. G., Malucelli, F., Nonato, M., & Guertin, F. (2005). Meta-heuristics for a class of demand-responsive transit systems. *INFORMS Journal on Computing*, 17(1), 10-24.

Crévits, I. (2013). *Architecture de la décision*. [HDR Disertation]. (Numéro d'Ordre : 13/07).

Crevits, I., Debernard, S., & Denecker, P. (2002). Model building for air-traffic controllers' workload regulation. *European Journal of Operational Research*, 136(2), 324-332.

Crévits, I., & Labour, M., (2012). *From preferences elicitation to values, opinions and verisimilitudes elicitation* Paper presented at the DA2PL'2012 Workshop-From Multiple Criteria Decision Aid to Preference Learning, Mons; Belgium.

Current, J. R., Re Velle, C. S., & Cohon, J. L. (1985). The maximum covering/shortest path problem: A multiobjective network design and routing formulation. *European Journal of Operational Research*, 21(2), 189-199. doi:https://doi.org/10.1016/0377-2217(85)90030-X

Current, J. R., Revelle, C. S., & Cohon, J. L. (1987). The median shortest path problem: A multiobjective approach to analyze cost vs. accessibility in the design of transportation networks. *Transportation Science*, 21(3), 188-197.

Daganzo, C. F. (1978). An approximate analytic model of many-to-many demand responsive transportation systems. *Transportation Research, 12*(5), 325-333.
doi:https://doi.org/10.1016/0041-1647(78)90007-2

Daganzo, C. F. (1984). Checkpoint dial-a-ride systems. *Transportation Research Part B: Methodological*, 18(4), 315-327. doi:https://doi.org/10.1016/0191-2615(84)90014-6

Daniels, R., & Mulley, C. (2012). Flexible transport services: Overcoming barriers to implementation in low-density urban areas. *Urban Policy and Research*, 30(1), 59-76.

Davison, L., Enoch, M., Ryley, T., Quddus, M., & Wang, C. (2014). A survey of demand responsive transport in Great Britain. *Transport Policy*, 31, 47-54.

Deo, N., & Pang, C. Y. (1984). Shortest-path algorithms: Taxonomy and annotation.
*Networks*, 14(2), 275-323.

Déry, R., Landry, M., & Banville, C. (1993). Revisiting the issue of model validation in OR: An epistemological view. *European Journal of Operational Research*, 66(2), 168-183.
Dias, L. C., & Tsoukiàs, A. (2003). *On the constructive and other approaches in decision aiding*. Paper presented at the Proceedings of the 57th meeting of the EURO MCDA working group.

Dijkers, M. P. (2009). The value of “traditional” reviews in the era of systematic reviewing. *American Journal of Physical Medicine & Rehabilitation, 88*(5), 423-430.

Dikas, G. (2014). *Paratransit services under normal and emergency conditions using public transport resources*. Doctoral thesis, Department of Financial and Management Engineering ...,

Dikas, G., & Minis, I. (2014). Scheduled paratransit transport systems. *Transportation Research Part B: Methodological, 67*, 18-34.
doi:https://doi.org/10.1016/j.trb.2014.05.001

Dikas, G., & Minis, I. (2018). Scheduled Paratransit Transport Enhanced by Accessible Taxis. *Transportation Science, 52*(5), 1122-1140.

Doerner, K. F., & Salazar-González, J.-J. (2014). Chapter 7: Pickup-and-Delivery Problems for People Transportation. In *Vehicle Routing: Problems, Methods, and Applications, Second Edition* (pp. 193-212): SIAM.

Đorić, D., El Cadi, A. A., Hanafi, S., Mladenović, N., & Artiba, A. (2017). Clustering approach in maintenance of capillary railway network. *Electronic Notes in Discrete Mathematics, 58*, 239-246.

Driver, H. E., & Kroeber, A. L. (1932). *Quantitative expression of cultural relationships* (Vol. 31): University of California Press.

Duin, C. W., & Volgenant, A. (1991). Minimum deviation and balanced optimization: A unified approach. *Operations Research Letters, 10*(1), 43-48.
doi:https://doi.org/10.1016/0167-6377(91)90085-4

Egis France Villes & Transport. (2013a). *Plan de Déplacements Urbains du Valenciennois 2013-2023*. Retrieved from https://www.simouv.fr/la-mobilite/le-pdu-les-pde/le-pdu-du-valenciennois/

Egis France Villes & Transport. (2013b). *Schéma Directeur d'Accessibilité des transports urbains du Syndicat Intercommunal des Transports Urbains de Valenciennes*. Retrieved from

Ehrgott, M. (2005). *Multicriteria optimization* (2nd ed ed.). Berlin: Springer.

Eker, S., Rovenskaya, E., Obersteiner, M., & Langan, S. (2018). Practice and perspectives in the validation of resource management models. *Nature communications, 9*(1), 5359.

Environment, M. o. T. D. o. t. (1961). Rural bus services. In: HMSO London.

Eppen, G. D., & Gould, F. J. (1984). *Introductory management science*: Prentice-Hall.
Erkul, M., Yitmen, I., & Çelik, T. (2016). Stakeholder engagement in mega transport infrastructure projects. *Procedia Engineering, 161*, 704-710.

Errico, F., Crainic, T. G., Malucelli, F., & Nonato, M. (2013). A survey on planning semi-flexible transit systems: methodological issues and a unifying framework. *Transportation Research Part C: Emerging Technologies, 36*, 324-338.

European Parliament and of the Council. (2007). *Regulation (EC) No 1371/2007 of 23 October 2007 on rail passengers' rights and obligations*.

European Parliament and of the Council. (2011). *Regulation (EU) No 181/2011 of 16 February 2011 concerning the rights of passengers in bus and coach transport and amending Regulation (EC) No 2006/2004*.

European Union. (2010). *European Disability Strategy 2010-2020: A Renewed Commitment to a Barrier-Free Europe*.

European Union. (2012). *Charter of Fundamental Rights of the European Union*.

European Union. (2014). *Commission Regulation (EU) No 1300/2014 of 18 November 2014 on the technical specifications for interoperability relating to accessibility of the Union's rail system for persons with disabilities and persons with reduced mobility*.

Everitt, B. S., Landau, S., Leese, M., & Stahl, D. (2011). *Cluster Analysis: Wiley*.

Farahani, R. Z., Hekmatfar, M., Arabani, A. B., & Nikbakhsh, E. (2013). Hub location problems: A review of models, classification, solution techniques, and applications. *Computers & Industrial Engineering, 64*(4), 1096-1109.
doi:https://doi.org/10.1016/j.cie.2013.01.012

Feremans, C., Labbé, M., & Laporte, G. (2003). Generalized network design problems. *European Journal of Operational Research, 148*(1), 1-13.
doi:https://doi.org/10.1016/S0377-2217(02)00404-6

Ferone, D., Festa, P., Guerriero, F., & Laganà, D. (2016). The constrained shortest path tour problem. *Computers & operations research, 74*, 64-77.
doi:https://doi.org/10.1016/j.cor.2016.04.002

Festa, P. (2006). Shortest path algorithms. In *Handbook of optimization in telecommunications* (pp. 185-210): Springer.

Finn, B. (2012). Towards large-scale flexible transport services: A practical perspective from the domain of paratransit. *Research in Transportation Business & Management, 3*, 39-49.

Fischer, G. W. (1989). Prescriptive decision science: problems and opportunities. *Annals of Operations Research, 19*(1), 489-497.
France, J. o. L. e. D. (2014). *Ordonnance n° 2014-1090 du 26 septembre 2014 relative à la mise en accessibilité des établissements recevant du public, des transports publics, des bâtiments d'habitation et de la voirie pour les personnes handicapées*

Franceschetti, A., Honhon, D., Laporte, G., & Van Woensel, T. (2018). A shortest-path algorithm for the departure time and speed optimization problem. *Transportation Science*, 52(4), 756-768.

Franco, L. A., & Montibeller, G. (2010). Facilitated modelling in operational research. *European Journal of Operational Research*, 205(3), 489-500.

Gallo, G., & Pallottino, S. (1986). Shortest path methods: A unifying approach. In G. Gallo & C. Sandi (Eds.), *Netflow at Pisa* (pp. 38-64). Berlin, Heidelberg: Springer Berlin Heidelberg.

Garcia, R. (2009). *Resource constrained shortest paths and extensions*. Georgia Institute of Technology,

Gelareh, S., & Nickel, S. (2011). Hub location problems in transportation networks. *Transportation Research Part E: Logistics and Transportation Review*, 47(6), 1092-1111. doi: https://doi.org/10.1016/j.tre.2011.04.009

Gough, D., Oliver, S., & Thomas, J. (2012). *An introduction to systematic reviews*. Los Angeles: SAGE.

Granat, J., & Guerriero, F. (2003). The interactive analysis of the multicriteria shortest path problem by the reference point method. *European Journal of Operational Research*, 151(1), 103-118. doi: https://doi.org/10.1016/S0377-2217(02)00594-5

Greco, S., Ehrgott, M., & Figueira, J. (2005). *Multiple criteria decision analysis : state of the art surveys*. New York: Springer.

Greco, S., Ehrgott, M., & Figueira, J. R. (2016). *Multiple Criteria Decision Analysis State of the Art Surveys*. Retrieved from Accès via SpringerLink http://dx.doi.org/10.1007/978-1-4939-3094-4

http://ariane.ulaval.ca/cgi-bin/recherche.cgi?qu=a2547635

Guerriero, F., & Musmanno, R. (2001). Label correcting methods to solve multicriteria shortest path problems. *Journal of optimization theory and applications*, 111(3), 589-613.

Gupta, D., Chen, H.-W., Miller, L. A., & Surya, F. (2010). Improving the efficiency of demand-responsive paratransit services. *Transportation Research Part A: Policy and Practice*, 44(4), 201-217. doi: https://doi.org/10.1016/j.tra.2010.01.003

Häll, C. H. (2006). *A framework for evaluation and design of an integrated public transport system*. Institutionen för teknik och naturvetenskap,
Häll, C. H., Andersson, H., Lundgren, J. T., & Värbrand, P. (2009). The Integrated Dial-a-Ride Problem. *Public Transport*, 1(1), 39-54. doi:10.1007/s12469-008-0006-1

Hämäläinen, R. P., & Lahtinen, T. J. (2016). Path dependence in operational research—how the modeling process can influence the results. *Operations research perspectives*, 3, 14-20.

Hämäläinen, R. P., Luoma, J., & Saarinen, E. (2013). On the importance of behavioral operational research: The case of understanding and communicating about dynamic systems. *European Journal of Operational Research*, 228(3), 623-634.

Han, J., Kamber, M., & Tung, A. K. (2001). Spatial clustering methods in data mining. *Geographic data mining and knowledge discovery*, 188-217.

Hanafi, S., & Yanev, N. (2011). Tabu search approaches for solving the two-group classification problem. *Annals of Operations Research*, 183(1), 25-46.
doi:10.1007/s10479-009-0581-9

Hansen, P., Mladenović, N., Todosijević, R., & Hanafi, S. (2017). Variable neighborhood search: basics and variants. *EURO Journal on Computational Optimization*, 5(3), 423-454. doi:10.1007/s13675-016-0075-x

Hartmanis, J., & Stearns, R. E. (1965). On the computational complexity of algorithms. *Transactions of the American Mathematical Society*, 117, 285-306.

He, E., Boland, N., Nemhauser, G., & Savelsbergh, M. (2020). Time-Dependent Shortest Path Problems with Penalties and Limits on Waiting.

Henderson, J. C., & Nutt, P. C. (1980). The Influence of Decision Style on Decision Making Behavior. *Management Science*, 26(4), 371-386. Retrieved from
http://www.jstor.org.acces.bibl.ulaval.ca/stable/2630421

Henderson, J. C., & Venkatraman, H. (1999). Strategic alignment: Leveraging information technology for transforming organizations. *IBM systems journal*, 38(2.3), 472-484.

Hickman, M., & Blume, K. (2001). Modeling Cost and Passenger Level of Service for Integrated Transit Service. In S. Voß & J. R. Daduna (Eds.), *Computer-Aided Scheduling of Public Transport* (pp. 233-251). Berlin, Heidelberg: Springer Berlin Heidelberg.

Hickman, M. D., & Blume, K. L. (2001). *An investigation of integrated transit service*. Retrieved from

Ho, S. C., Szeto, W. Y., Kuo, Y.-H., Leung, J. M. Y., Petering, M., & Tou, T. W. H. (2018). A survey of dial-a-ride problems: Literature review and recent developments. *Transportation Research Part B: Methodological*, 111, 395-421.
doi:https://doi.org/10.1016/j.trb.2018.02.001

Ichoua, S., Gendreau, M., & Potvin, J.-Y. (2003). Vehicle dispatching with time-dependent travel times. *European Journal of Operational Research*, 144(2), 379-396.
doi:https://doi.org/10.1016/S0377-2217(02)00147-9
Institut für barrierefreie Gestaltung und Mobilität GmbH. (2003). *Survey on information for people with reduced mobility on the field of public transport*. Retrieved from
[https://dev.emta.eu/spip.php?article269](https://dev.emta.eu/spip.php?article269)

International Conference on Smart, H., Health, T., & Abdulrazak, B. (2011). *Toward useful services for elderly and people with disabilities 9th International Conference on Smart Homes and Health Telematics, ICOST 2011, Montreal, Canada, June 20-22, 2011, proceedings*. Retrieved from Accès via SpringerLink [http://dx.doi.org/10.1007/978-3-642-21535-3](http://dx.doi.org/10.1007/978-3-642-21535-3)

[http://ariane.ulaval.ca/cgi-bin/recherche.cgi?qu=a2043654](http://ariane.ulaval.ca/cgi-bin/recherche.cgi?qu=a2043654)

Iriarte, E. G., McConkey, R., & Gilligan, R. (2015). *Disability and human rights: Global perspectives*: Macmillan International Higher Education.

Jackson, M. C., & Keys, P. (1984). Towards a System of Systems Methodologies. *Journal of the Operational Research Society*, 35(6), 473-486. doi:10.1057/jors.1984.101

Jette, A. M., & Field, M. J. (2007). *The future of disability in America*, (G, Transportation Patterns and Problems of People with Disabilities. ed.): National Academies Press.

Joksch, H. C. (1966). The shortest route problem with constraints. *Journal of Mathematical Analysis and Applications*, 14(2), 191-197. doi:https://doi.org/10.1016/0022-247X(66)90020-5

JORF, Journal Officiel de la République Française. (2015). *LOI n° 2015-988 du 5 août 2015 ratifiant l'ordonnance n° 2014-1090 du 26 septembre 2014 relative à la mise en accessibilité des établissements recevant du public, des transports publics, des bâtiments d'habitation et de la voirie pour les personnes handicapées et visant à favoriser l'accès au service civique pour les jeunes en situation de handicap*

Jozefowiez, N., Semet, F., & Talbi, E.-G. (2008). Multi-objective vehicle routing problems. *European Journal of Operational Research*, 189(2), 293-309.

Karp, R. M. (1975). On the computational complexity of combinatorial problems. *Networks*, 5(1), 45-68.

Kaufman, L., & Rousseeuw, P. (1990). *Finding groups in data; an introduction to cluster analysis* (0471878766). Retrieved from

Kaufman, L., & Rousseeuw, P. J. (1990). *Finding groups in data an introduction to cluster analysis*. Retrieved from Accès via Wiley online library
[http://onlinelibrary.wiley.com/book/10.1002/9780470316801](http://onlinelibrary.wiley.com/book/10.1002/9780470316801)

[http://ariane.ulaval.ca/cgi-bin/recherche.cgi?qu=a2619701](http://ariane.ulaval.ca/cgi-bin/recherche.cgi?qu=a2619701)

Kaufman, L., & Rousseeuw, P. J. (2009). *Finding groups in data: an introduction to cluster analysis* (Vol. 344): John Wiley & Sons.
Keller, L. R. (1989). Decision research with descriptive, normative, and prescriptive purposes—Some comments. *Annals of Operations Research, 19*(1), 485-487.

Kelly, J., Jones, P., Barta, F., Hossinger, R., Witte, A., & Wolf, A. (2004). Successful Transport Decision-making: a project management and stakeholder engagement handbook.

Kett, M., Cole, E., & Turner, J. (2020). Disability, Mobility and Transport in Low-and Middle-Income Countries: A Thematic Review. *Sustainability, 12*(2), 589.

Kim, M., Levy, J., & Schonfeld, P. (2019). Optimal zone sizes and headways for flexible-route bus services. *Transportation Research Part B: Methodological, 130*, 67-81.
doi:https://doi.org/10.1016/j.trb.2019.10.006

Kim, M., & Schonfeld, P. (2014). Integration of conventional and flexible bus services with timed transfers. *Transportation Research Part B: Methodological, 68*, 76-97.
doi:https://doi.org/10.1016/j.trb.2014.05.017

Koehler, D. J., & Harvey, N. (2008). *Blackwell handbook of judgment and decision making*: John Wiley & Sons.

Koffman, D. (2004). *Operational Experiences with Flexible Transit Services*. Retrieved from TCRP Synthesis Report, Transportation Research Board:

L'Institut national de la statistique et des études économiques France. (2016). *Populations légales 2016 Commune de Valenciennes (59606)*. Retrieved from
https://www.insee.fr/fr/statistiques/3681328?geo=COM-59606

Landry, M. (1995). A note on the concept of 'problem'. *Organization studies, 16*(2), 315-343.

Landry, M., Banville, C., & Oral, M. (1996). Model legitimisation in operational research. *European Journal of Operational Research, 92*(3), 443-457.

Landry, M., Malouin, J.-L., & Oral, M. (1983). Model validation in operations research. *European Journal of Operational Research, 14*(3), 207-220.

Lapointe, A., & Cimon, Y. (2009). Leveraging intangibles: how firms can create lasting value. *Journal of Business Strategy, 30*(5), 40-48.

Leonardi, M., Bickenbach, J., Ustun, T. B., Kostanjsek, N., & Chatterji, S. (2006). The definition of disability: what is in a name? *The Lancet, 368*(9543), 1219-1221.

Li, X., & Quadrifoglio, L. (2010). Feeder transit services: Choosing between fixed and demand responsive policy. *Transportation Research Part C: Emerging Technologies, 18*(5), 770-780. doi:https://doi.org/10.1016/j.trc.2009.05.015

Liaw, C.-F., White, C. C., & Bander, J. (1996). A decision support system for the bimodal dial-a-ride problem. *IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 26*(5), 552-565.
Liberati, A., Altman, D. G., Tetzlaff, J., Mulrow, C., Gøtzsche, P. C., Ioannidis, J. P., ... Moher, D. (2009). The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate health care interventions: explanation and elaboration. *PLoS medicine*, **6**(7), e1000100.

Litman, T. (2017). Accessibility for Transportation Planning. Measuring People's Ability to Reach Desired Goods and Activity. TDM Encyclopedia, Victoria Transport Policy Institute, (2017). In.

Liu, L., Mu, H., Luo, H., & Li, X. (2012). A simulated annealing for multi-criteria network path problems. *Computers & operations research*, **39**(12), 3119-3135.

Lozano, A., & Storchi, G. (2001). Shortest viable path algorithm in multimodal networks. *Transportation Research Part A: Policy and Practice*, **35**(3), 225-241.

Lubin, A., & Deka, D. (2012). Role of Public Transportation as Job Access Mode: Lessons from Survey of People with Disabilities in New Jersey. *Transportation Research Record*, **2277**(1), 90-97. doi:10.3141/2277-11

Luce, R. D., & Von Winterfeldt, D. (1994). What common ground exists for descriptive, prescriptive, and normative utility theories? *Management Science*, **40**(2), 263-279.

Lusby, R. M., Larsen, J., & Bull, S. (2018). A survey on robustness in railway planning. *European Journal of Operational Research*, **266**(1), 1-15.
doi:https://doi.org/10.1016/j.ejor.2017.07.044

MacLachlan, M., & Swartz, L. (2009). *Disability & international development*: Springer.

MacQueen, J. (1967). *Some methods for classification and analysis of multivariate observations*. Paper presented at the Proceedings of the fifth Berkeley symposium on mathematical statistics and probability.

Malucelli, F., Nonato, M., Crainic, T. G., & Guertin, F. (2001). Adaptive memory programming for a class of demand responsive transit systems. In *Computer-Aided Scheduling of Public Transport* (pp. 253-273): Springer.

Malucelli, F., Nonato, M., & Pallottino, S. (1999a). Demand adaptive systems: some proposals on flexible transit. In *Operational research in industry* (pp. 157-182): Springer.

Malucelli, F., Nonato, M., & Pallottino, S. (1999b). Demand Adaptive Systems: Some Proposals on Flexible Transit1. In T. A. Ciriani, S. Gliozzi, E. L. Johnson, & R. Tadei (Eds.), *Operational Research in Industry* (pp. 157-182). London: Palgrave Macmillan UK.

Maria, J., Pangilinan, A., & Janssens, G. K. (2007). *Evolutionary algorithms for the multiobjective shortest path planning problem*. Paper presented at the International journal of computer and information science and engineering.
Marttunen, M., Lienert, J., & Belton, V. (2017). Structuring problems for Multi-Criteria Decision Analysis in practice: A literature review of method combinations. *European Journal of Operational Research, 263*(1), 1-17.

Meinard, Y., & Tsoukiàs, A. (2019). On the rationality of decision aiding processes. *European Journal of Operational Research, 273*(3), 1074-1084.

Meyer, M. D., & Miller, E. J. (2001). *Urban transportation planning : a decision-oriented approach* (2nd ed ed.). Boston: McGraw-Hill.

Minoux, M. (1989). Solving combinatorial problems with combined Min-Max-Min-Sum objective and applications. *Mathematical Programming, 45*(1), 361-372.
doi:10.1007/BF01589111

Modesti, P., & Sciomachen, A. (1998). A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks. *European Journal of Operational Research, 111*(3), 495-508.

Molenbruch, Y., Braekers, K., & Caris, A. (2017). Typology and literature review for dial-a-ride problems. *Annals of Operations Research, 259*(1-2), 295-325.

Mulley, C., Nelson, J., Teal, R., Wright, S., & Daniels, R. (2012). Barriers to implementing flexible transport services: An international comparison of the experiences in Australia, Europe and USA. *Research in Transportation Business & Management, 3*, 3-11.

Murray, A. T. (2003). A coverage model for improving public transit system accessibility and expanding access. *Annals of Operations Research, 123*(1-4), 143-156.

Murray, A. T., Davis, R., Stimson, R. J., & Ferreira, L. (1998). Public transportation access. *Transportation Research Part D: Transport and Environment, 3*(5), 319-328.

Nachtigall, K. (1995). Time depending shortest-path problems with applications to railway networks. *European Journal of Operational Research, 83*(1), 154-166.

Nuanmeesri, S. (2019). Mobile application for the purpose of marketing, product distribution and location-based logistics for elderly farmers. *Applied Computing and Informatics*.
doi:https://doi.org/10.1016/j.aci.2019.11.001

Nuworsoo, C. (2009). Providing Senior Citizen Mobility at Minimum Public Cost.

Orda, A., & Rom, R. (1990). Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. *Journal of the ACM (JACM)*, 37(3), 607-625.

Orda, A., & Rom, R. (1991). Minimum weight paths in time-dependent networks. *Networks*, 21(3), 295-319.

Oxley, P. (1980). Dial/a/ride: a review. *Transportation Planning and Technology, 6*(3), 141-148.
Oxley, P. R., & Britain, G. (2002). *Inclusive Mobility: a guide to best practice on access to pedestrian and transport infrastructure*: Department for Transport.

Pallottino, S., & Scutella, M. G. (1998). Shortest path algorithms in transportation models: classical and innovative aspects. In *Equilibrium and advanced transportation modelling* (pp. 245-281): Springer.

Palmer, C. L. (2013). *Work at the Boundaries of Science: Information and the Interdisciplinary Research Process*: Springer Netherlands.

Papadimitrou, C. H., & Steiglitz, K. (1982). Combinatorial optimization: algorithms and complexity.

Papanikolaou, A., Basbas, S., Mintsis, G., & Taxiltaris, C. (2017). A methodological framework for assessing the success of Demand Responsive Transport (DRT) services. *Transportation Research Procedia*, 24, 393-400.

Paquette, J., Cordeau, J.-F., & Laporte, G. (2009). Quality of service in dial-a-ride operations. *Computers & Industrial Engineering*, 56(4), 1721-1734.

Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008a). A survey on pickup and delivery models

Part II: Transportation between pickup and delivery locations. *Journal für Betriebswirtschaft*, 58(2), 81-117.

Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008b). A survey on pickup and delivery problems

Part I: Transportation between customers and depot. *Journal für Betriebswirtschaft*, 58(1), 21-51.

Pelleg, D., & Moore, A. (1999). *Accelerating exact k-means algorithms with geometric reasoning*. Paper presented at the Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining.

Posada, M., Andersson, H., & Häll, C. H. (2017). The integrated dial-a-ride problem with timetabled fixed route service. *Public Transport*, 9(1-2), 217-241.

Potts, J. F., Marshall, M. A., Crockett, E. C., & Washington, J. (2010). A guide for planning and operating flexible public transportation services.

Psaraftis, H. N. (1980). A dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem. *Transportation Science*, 14(2), 130-154.

Qiu, F., Shen, J., Zhang, X., & An, C. (2015). Demi-flexible operating policies to promote the performance of public transit in low-demand areas. *Transportation Research Part A: Policy and Practice*, 80, 215-230. doi: https://doi.org/10.1016/j.tra.2015.08.003

Quadrifoglio, L., & Dessouky, M. M. (2008). Sensitivity analyses over the service area for mobility allowance shuttle transit (MAST) services. In *Computer-aided Systems in Public Transport* (pp. 419-432): Springer.
Quadrifoglio, L., Dessouky, M. M., & Ordóñez, F. (2008a). Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints. *European Journal of Operational Research, 185*(2), 481-494.
doi:https://doi.org/10.1016/j.ejor.2006.12.030

Quadrifoglio, L., Dessouky, M. M., & Ordóñez, F. (2008b). A simulation study of demand responsive transit system design. *Transportation Research Part A: Policy and Practice*, 42(4), 718-737. doi:https://doi.org/10.1016/j.tra.2008.01.018

Quadrifoglio, L., Dessouky, M. M., & Palmer, K. (2007). An insertion heuristic for scheduling mobility allowance shuttle transit (MAST) services. *Journal of Scheduling*, 10(1), 25-40.

Quadrifoglio, L., Hall, R. W., & Dessouky, M. M. (2006). Performance and design of mobility allowance shuttle transit services: bounds on the maximum longitudinal velocity. *Transportation Science*, 40(3), 351-363.

Rdusseeun, L., & Kaufman, P. J. (1987). Clustering by means of medoids.

Repko, A. F., & Szostak, R. (2017). *Interdisciplinary research : process and theory* (Third edition ed.). Los Angeles: SAGE.

Roberts, P., & Babinard, J. (2004). Transport strategy to improve accessibility in developing countries.

Rosenhead, J. (2006). Past, present and future of problem structuring methods. *Journal of the Operational Research Society*, 57(7), 759-765.

Rosenhead, J., & Mingers, J. (2001). *Rational analysis for a problematic world revisited:* John Wiley and Sons.

Roy, B. (1985). *Méthodologie multicritère d'aide à la décision*. Paris: Economica.

Roy, B. (1996). *Multicriteria Methodology for Decision Aiding* (Vol. 12): Springer Science & Business Media.

Roy, B., & Bouyssou, D. (1993). *Aide multicritère à la décision : méthodes et cas*. Paris: Economica.

Roy, B., Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Slowiński, R., Vanderpooten, D., & Vincke, P. (2002). *Aiding decisions with multiple criteria: essays in honor of Bernard Roy* (Vol. 44): Springer Science & Business Media.

Roy, B., & Vanderpooten, D. (1997). An overview on "The European school of MCDA: Emergence, basic features and current works". *European Journal of Operational Research*, 99(1), 26-27.

Ryley, T. J., Stanley, P. A., Enoch, M. P., Zanni, A. M., & Quddus, M. A. (2014). Investigating the contribution of Demand Responsive Transport to a sustainable local public transport system. *Research in Transportation Economics*, 48, 364-372.
Sargent, R. G., & Balci, O. (2017). *History of verification and validation of simulation models*. Paper presented at the Proceedings of the 2017 Winter Simulation Conference.

Shrestha, B. P., Millonig, A., Hounsell, N. B., & McDonald, M. (2017). Review of Public Transport Needs of Older People in European Context. *Journal of Population Ageing*, 10(4), 343-361. doi:10.1007/s12062-016-9168-9

Simon, H. (1984). *The structure of ill-structured problems*.

Simon, H. A. (1973). The structure of ill structured problems. *Artificial intelligence*, 4(3-4), 181-201.

Simon, H. A. (1983). Search and reasoning in problem solving. *Artif. Intell.*, 21(1-2), 7-29.

Simon, H. A. (1997). *Administrative behavior : a study of decision-making processes in administrative organizations* (Fourth Edition ed.). New York: The Free Press.

Simon, H. A. (2000). Bounded rationality in social science: Today and tomorrow. *Mind & Society*, 1(1), 25-39.

SIMOUV. (2018). *Rapport d'activité 2018*. Retrieved from
[https://www.simouv.fr/fileadmin/Public/Espace_documentaire/Rapport.activite/RA_2018_32p_PAP_HD.pdf](https://www.simouv.fr/fileadmin/Public/Espace_documentaire/Rapport.activite/RA_2018_32p_PAP_HD.pdf)

Snyder, H. (2019). Literature review as a research methodology: An overview and guidelines. *Journal of Business Research*, 104, 333-339.
doi:https://doi.org/10.1016/j.jbusres.2019.07.039

Spartacus, V., Blandeau, M., Molenaar, C., Gabrielli, F., Gagnon, P. D. H., & Pudlo, P. P. ON-BOARD LIVED EXPERIENCE OF MANUAL WHEELCHAIR USERS: AIRCRAFT SEAT SATISFACTION LEVEL AND POTENTIAL SOLUTIONS TO IMPROVE COMFORT AND ACCESSIBILITY.

Späth, H. (1980). Cluster analysis algorithms for data reduction and classification of objects.

Starmer, C. (2000). Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. *Journal of economic literature*, 38(2), 332-382.

Stevenson, A. (2010). *Oxford Dictionary of English*: OUP Oxford.

Suen, S. L., & Mitchell, C. (2000). Accessible transportation and mobility. *Transportation in the New Millennium*.

The Academic Network of European Disability Experts (ANED). DOTCOM: Disability Online Tool of the Commission. Retrieved from [https://www.disability-europe.net/dotcom](https://www.disability-europe.net/dotcom)

Toth, P., & Vigo, D. (2002). *The vehicle routing problem*: SIAM.

Toth, P., & Vigo, D. (2014). *Vehicle routing: problems, methods, and applications*: SIAM.
Tsoukiàs, A. (2007). On the concept of decision aiding process: an operational perspective. *Annals of Operations Research*, 154(1), 3-27.

Tsoukiàs, A. (2008). From decision theory to decision aiding methodology. *European Journal of Operational Research*, 187(1), 138-161.

Turner, L. (2011). Variants of shortest path problems. *Algorithmic Operations Research*, 6(2), 91-104.

Turner, L., Punnen, A. P., Aneja, Y. P., & Hamacher, H. W. (2011). On generalized balanced optimization problems. *Mathematical Methods of Operations Research*, 73(1), 19-27. doi:10.1007/s00186-010-0331-4

U.S. Government Accountability Office (GAO). (2004). *TRANSPORTATION-DISADVANTAGED SENIORS: Efforts to Enhance Senior Mobility Could Benefit from Additional Guidance and Information*. (GAO-04-971). Retrieved from
[https://www.gao.gov/assets/250/243864.pdf](https://www.gao.gov/assets/250/243864.pdf)

United Nations, Department of Economic and Social Affairs, Population Division. (2006). *The United Nations Convention on the Rights of Persons with Disabilities*. Retrieved from
[https://www.ohchr.org/EN/HRBodies/CRPD/Pages/ConventionRightsPersonsWithDisabilities.aspx?fbclid=IwAR37eOFZ0Jc1cJlEwAbTeuRxcz3Hynyr169hP0Xinm5e09KdVI-uV4w_MPY](https://www.ohchr.org/EN/HRBodies/CRPD/Pages/ConventionRightsPersonsWithDisabilities.aspx?fbclid=IwAR37eOFZ0Jc1cJlEwAbTeuRxcz3Hynyr169hP0Xinm5e09KdVI-uV4w_MPY)

United Nations, Department of Economic and Social Affairs, Population Division. (2014). *World Urbanization Prospects: The 2014 Revision, Highlights*. Retrieved from
[https://population.un.org/wup/Publications/Files/WUP2014-Report.pdf](https://population.un.org/wup/Publications/Files/WUP2014-Report.pdf)

United States Congress. (1990). *Americans with Disabilities Act (42 U.S.C. § 12101)*.

Urbandictionary.com, & Peckham, A. (2012). *Urban Dictionary: Freshest Street Slang Defined*: Andrews McMeel Publishing.

Velaga, N. R., Nelson, J. D., Wright, S. D., & Farrington, J. H. (2012). The potential role of flexible transport services in enhancing rural public transport provision. *Journal of Public Transportation*, 15(1), 7.

Velho, R. (2019). Transport accessibility for wheelchair users: A qualitative analysis of inclusion and health. *International Journal of Transportation Science and Technology*, 8(2), 103-115. doi: [https://doi.org/10.1016/j.ijtst.2018.04.005](https://doi.org/10.1016/j.ijtst.2018.04.005)

Véronneau, S., & Cimon, Y. (2007). Maintaining robust decision capabilities: An integrative human–systems approach. *Decision support systems*, 43(1), 127-140.

Verseckienė, A., Meškauskas, V., & Batarlienė, N. (2016). Urban Public Transport Accessibility for People with Movement Disorders: The Case Study of Vilnius. *Procedia Engineering*, 134, 48-56. doi: [https://doi.org/10.1016/j.proeng.2016.01.038](https://doi.org/10.1016/j.proeng.2016.01.038)

Walter, E. (2008). *Cambridge Advanced Learner's Dictionary*: Cambridge University Press.
Wasfi, R., Steinmetz-Wood, M., & Levinson, D. (2017). Measuring the transportation needs of people with developmental disabilities: A means to social inclusion. *Disability and health journal, 10*(2), 356-360.

Weiner, E. (1999). *Urban transportation planning in the United States : an historical overview* (Rev. and expanded ed.). Westport, Conn: Praeger.

Wilson, N. H., Sussman, J., Wong, H.-K., & Higonnet, T. (1971). *Scheduling algorithms for a dial-a-ride system: Massachusetts Institute of Technology. Urban Systems Laboratory.*

Wilson, N. H., Weissberg, R. W., & Hauser, J. (1976). *Advanced dial-a-ride algorithms research project*. Retrieved from

Wong, J. (2013). Leveraging the general transit feed specification for efficient transit analysis. *Transportation Research Record, 2338*(1), 11-19.

World Bank. (2013). *Improving accessibility to transport for People with Limited Mobility (PLM) : a practical guidance note (English)*. Retrieved from
[http://documents.worldbank.org/curated/en/575221468278939280/Improving-accessibility-to-transport-for-People-with-Limited-Mobility-PLM-a-practical-guidance-note](http://documents.worldbank.org/curated/en/575221468278939280/Improving-accessibility-to-transport-for-People-with-Limited-Mobility-PLM-a-practical-guidance-note)

World Health Organization, World Bank. (2011). *World report on disability*. Retrieved from
[https://www.who.int/disabilities/world_report/2011/report.pdf](https://www.who.int/disabilities/world_report/2011/report.pdf)

Zhao, J., & Dessouky, M. (2008). Service capacity design problems for mobility allowance shuttle transit systems. *Transportation Research Part B: Methodological, 42*(2), 135-146. doi: [https://doi.org/10.1016/j.trb.2007.07.002](https://doi.org/10.1016/j.trb.2007.07.002)

Zubin, J. (1938). A technique for measuring like-mindedness. *The Journal of Abnormal and Social Psychology, 33*(4), 508.

Zwick, U. (2001). *Exact and approximate distances in graphs—a survey*. Paper presented at the European Symposium on Algorithms.
<table><caption>APPENDIX A. European legislative framework for transport of PWD</caption><thead><tr><td>No</td><td>Reference</td><td>Title</td><td>Transport mode</td><td>Accessibility requirements</td></tr></thead><tbody><tr><td>1</td><td>European Union Charter 2012/C 326/02</td><td>Charter of Fundamental Rights of the European Union</td><td>MULTIMODAL</td><td>General</td></tr><tr><td>2</td><td>Commission communication 2010/0636</td><td>European disability strategy 2010-2020</td><td>MULTIMODAL</td><td>General</td></tr><tr><td>3</td><td>Commission proposal for a directive 2015/0278 (COD)</td><td>Approximation of the laws, regulations and administrative provisions of the Member States as regards the accessibility requirements for products and services European Accessibility Act</td><td>MULTIMODAL</td><td>General</td></tr><tr><td>4</td><td>Commission Regulation (EC) No 1107/2006</td><td>Rights of disabled persons and persons with reduced mobility when traveling by air</td><td>AIR</td><td>Specific</td></tr><tr><td>5</td><td>Commission Regulation (EC) No 1371/2007</td><td>Rail passengers' rights and obligations</td><td>RAIL</td><td>Specific</td></tr><tr><td>6</td><td>Commission Regulation (EC) No 454/2011</td><td>The technical specification for interoperability relating to the subsystem "telematics applications for passengers' services" of the trans-European rail system (TAP-TSI)</td><td>RAIL</td><td>Detailed</td></tr><tr><td>7</td><td>Commission Regulation (EC) No 1300/2014</td><td>Technical specifications for interoperability relating to the accessibility of the Union's rail system for persons with disabilities and persons with reduced mobility (TSI-PRM)</td><td>RAIL</td><td>Detailed</td></tr><tr><td>8</td><td>Commission Directive (EU) No 2016/797</td><td>Interoperability of the rail system within the European Union (recast)</td><td>RAIL</td><td>Specific</td></tr><tr><td>9</td><td>Commission Directive (EU) No 2010/40</td><td>Framework for the deployment of Intelligent Transport Systems in the field of road transport and for interfaces with other modes of transport</td><td>MULTIMODAL</td><td>Specific</td></tr><tr><td>10</td><td>Commission implementing decision (EU) 2016/209</td><td>Standardization request to the European standardization organizations as regards Intelligent Transport Systems (ITS) in urban areas in support of Directive 2010/40/EU</td><td>INTELLIGENT - ROAD</td><td>Specific</td></tr><tr><td>11</td><td>Commission Regulation (EC) No 181/2011</td><td>Concerning the rights of passengers in bus and coach transport</td><td>ROAD</td><td>Specific</td></tr><tr><td>12</td><td>Commission directive (EC) No 2001/85</td><td>Special provisions for vehicles used for the carriage of passengers comprising more than eight seats in addition to the driver's seat</td><td>ROAD</td><td>Specific</td></tr><tr><td>13</td><td>Commission Directive (EU) NO 2016/2102</td><td>Accessibility of the websites and mobile applications of public sector bodies</td><td>INTELLIGENT - COMMUNICATION</td><td>Specific</td></tr><tr><td>14</td><td>Commission Regulation (EU) 1177/2010</td><td>Rights of passengers when traveling by sea and inland waterway</td><td>MARITIME</td><td>Specific</td></tr><tr><td>15</td><td>Council Directive 98/18/EC</td><td>Safety rules and standards for passenger ships</td><td>MARITIME</td><td>Specific</td></tr><tr><td>16</td><td>European Standard EN 16584</td><td>Infrastructure and rolling stock - Railway applications - Design for PRM Users</td><td>RAIL</td><td>Detailed</td></tr><tr><td>17</td><td>European Standard EN 16585</td><td>Rolling Stock-Railway Applications - Design for PRM Use - Equipment and Components On Board Rolling Stock</td><td>RAIL</td><td>Detailed</td></tr><tr><td>18</td><td>European Standard EN 16586</td><td>Railway applications - Design for PRM Use - Accessibility of persons with reduced mobility rolling stock</td><td>RAIL</td><td>Detailed</td></tr><tr><td>19</td><td>European Standard EN 16587</td><td>Railway applications - Design for PRM Use - Requirements for obstacle-free routes for infrastructure</td><td>RAIL</td><td>Detailed</td></tr><tr><td>20</td><td>European Standard EN 12896</td><td>TRANSMODEL - Reference Data Model For Public Transport</td><td>MULTIMODAL</td><td>Detailed</td></tr></tbody></table>
# APPENDIX B. Matrix of relation

Table 16 Matrix of relation
<table><thead><tr><th rowspan="2">Levels<br>Needs</th><th colspan="2">Strategic level</th><th>Operational level</th><th colspan="2">Tactical level</th></tr><tr><th>Institutional framework -<br>Legislation - Conceptual outlook -<br>Policy</th><th>Economic issues - Finance -<br>Budget - Funding</th><th>Operational issues</th><th>Operator and community<br>attitudes - Stakeholders<br>approaches</th><th>Information and education - Human<br>and Social resources</th></tr></thead><tbody><tr><td rowspan="2">Availability</td><td>Time</td><td>Improve the legislation - Develop<br>implementation plan - Assessment<br>of the legislation changing</td><td>Financing the creation or<br>modification of the legal<br>framework - Financial plan<br>for the action<br>implementation</td><td>Fleet capacities - Scheduling -<br>Minimizing the total vehicle travel<br>time; the total tour time; the fleet<br>size; the number of vehicles; the<br>maximum flow time; vehicle<br>timeout; travel time of each user -<br>Maximize the number of requests<br>served; the number of requests<br>served on time</td><td>Assignment to the operators -<br>Assignment to the demanding<br>time - Reliable intervals<br>between the vehicles -<br>Prompt provision of<br>compensation possibilities in<br>case of failure of the vehicles<br>- Real-time ride-matching</td><td>Staff capacities - Information systems<br>(booklets, leaflets, timetables, journey<br>planner) - Advance traffic control<br>system</td></tr><tr><td>Place</td><td>Evaluation of network - Assessment<br>of the developing the new network<br>or extending existing one - Provide<br>connection place with the hospitals<br>and the places demand by PWD-<br>Implementation plan</td><td>Financing the developing the<br>new network or extending an<br>existing one - Investment<br>plan</td><td>Network capacities - Involved<br>additional service through door-<br>to-door service - Minimizing the<br>total distance travel; the total<br>routing costs - Maximize the<br>number of requests served; the<br>number of requests served on<br>time</td><td>Assignment to the operators -<br>Assignment to the demanding<br>places - Flexible route transit</td><td>Information systems (booklets,<br>leaflets, timetables, journey planner) -<br>Corridor management</td></tr><tr><td rowspan="2">Accessibility</td><td>Pre-journey<br>planning<br>information</td><td>Legislation obligation -<br>Interconnection among transport,<br>education and system information<br>legislation</td><td>Developing the information<br>system (mobile applications,<br>websites) - Findings for the<br>new information systems -<br>Providing funds among the<br>participants in this chain -<br>Developing a comprehensive<br>citywide journey planner and<br>information system</td><td>Distribution and organization of<br>system information to reach the<br>exciting group</td><td>Providing information on the<br>website of the operators,<br>municipalities, associations</td><td>Maintaining information system -<br>Real-time information - Date base</td></tr><tr><td>Information and<br>travel training</td><td>Information at<br>transport stops and<br>stations</td><td>Legislation obligations for three<br>types of information: visual, audible<br>and tactile</td><td>Budget assessment for all<br>types of information (visual,<br>audible and tactile) -<br>Providing funds among the<br>participants in this chain -<br>Finds for real-time<br>information displays,<br>Terminal and kiosks</td><td>Distribution and organization of<br>system information to reach the<br>exciting group</td><td>Provide a responsible<br>participant (operators,<br>municipality, etc) for<br>managing and updating<br>information</td><td>Provide static visual information, real-<br>time information displays, real-time<br>and pre-recorded audible information<br>in stations, Terminals and kiosks (for<br>information and the purchasing of<br>tickets)</td></tr></tbody></table>
<table><tr><td rowspan="3">Accessibility</td><td>On-board information</td><td>Legislation obligation - Display information on vehicles concerning the vehicle route, timetable, current location, and exit routes</td><td>Budget planning for implementation of the system information in every vehicle</td><td>Adapt vehicles for the necessary information system</td><td>Provide a responsible participant (operators, municipality, etc) for managing and updating information</td><td>Operating staff and PWD training for the new information system - usage; readings and understanding information</td></tr><tr><td>Travel training</td><td>Legislation obligation - defining the responsibilities among local government, local transport operator, a charity, and define where will be provided (classroom, school, etc.)</td><td>Budget planning for providing travel training to the staff</td><td>Scheduling of staff travel training</td><td>Provide the training in all organization who are involved in this type of transport, design the programs that will meet a needs and takes into account culture issues</td><td>Community educations through the events, consultations, information and guidance, travel support and assistance, and vocational or academic training programs</td></tr><tr><td>Disability awareness training</td><td>Legislation obligation - defining who is responsible for this type of training</td><td>Budget planning - provide financial support through the subventions, private partners or voluntary work</td><td>Providing disability awareness training events, disability awareness video, disability awareness posters and leaflets</td><td>Building cooperation between operators and associations, as well as with the hospitals, etc</td><td>Community educations through the events, consultations, information and guidance, travel support and assistance, and vocational or academic training programs</td></tr><tr><td rowspan="2">Pedestrian footways and street crossing</td><td>Footways and sidewalks</td><td>Legislation obligations for the new construction, and reconstructions of footways and sidewalks</td><td>Budget planning - analyzing the costs of local labor and materials - defining the priorities for the future works</td><td>Survey on footways and sidewalks accessibility, especially to a transportation network; Works on the - Monitoring and providing data related to the mobility</td><td>Selection of materials appropriate to the climate, as maintenance of new surfaces; Consultation and planning</td><td>Training and education of local citizens and PWD of using tactile pavement and signage</td></tr><tr><td>Dropped curbs and street crossings</td><td>Legislation obligations for the new construction, and reconstructions of dropped curbs and street crossings</td><td>Budget assessment depends on the costs of local labor and materials</td><td>Implementing street accessibility in public transport through: Dropped curb, footway buildouts, zebra crossing, island refuge, raised table, footbridge/subway</td><td>Assure the environment about a street crossing is accessible to provide the PWD journey without interruption</td><td>Traffic enforcement and driver education programs for drivers to become more aware of pedestrians crossing the road</td></tr></table>
<table><tr><td rowspan="3">Accessibility</td><td>Public transport stops and station infrastructure</td><td>Bus Stops</td><td>Legislation obligations for providing the accessibility to the bus stops such as: Step-free accessibility; Step-free maneuvering space; Footways, storage places, toilets and service areas are required to have sufficient maneuvering and clear space; All operating controls and communication systems should be within reach of sitting persons; Step-free accessibility of the shelter; Sufficient parking space</td><td>For the reconstruction of the existing bus stop make a budget assessment through the costs of surfacing material, labor costs, location of the shelter, gradient, drainage, etc. - Building a new bus stations</td><td>Bus stop surfacing, bus shelters, folding or fixed seats, raised boarding structures</td><td>The space limitation, available access during construction: passengers should be prevented from standing in the roadway</td><td>Providing a survey of existing accessibility on the bus stops</td></tr><tr><td></td><td>BRT (Bus Rapid transit) and light rail stops</td><td>Legislation obligations for providing the accessibility to the BRT and light rail stops</td><td>Budget is enormous for this type of works - planning, construction, etc. - should be planed in significant transport project</td><td>Accessible BRT Station, bus mounted boarding bridges, elevator or stairlift, folding seats within stop/station</td><td>Cooperation between national and regional government - a joint project</td><td>Provide the appropriate information system, which data will be in a real-time update and use in optimization transport model.</td></tr><tr><td></td><td>Major bus/train/metro interchanges and terminals</td><td>Global strategic plans - providing the legislation obligations for intermodal passenger transport: connection points (platforms) - client assistance, accessible entrances and exit, ticketing facilities, waiting space, toilet facilities, service information</td><td>Budget is enormous for this type of works - planning, construction, etc. - should be planed in significant transport project</td><td>Ramps to provide a level, step-free environments, passenger elevator to the platform, accessible toilets, available automatic ticket barriers, accessible information and ticket desks, access terminals and kiosks</td><td>Cooperation between national and regional government - Regional transportation management system</td><td>Provide the appropriate information system, which data will be in a real-time update and use in optimization transport model.</td></tr></table>
<table><tr><td rowspan="2">Accessibility</td><td rowspan="2">Public vehicles</td><td>Buses and Mass Transit Vehicles</td><td>Legislation obligations for providing the accessibility to this type of vehicles: Step-free entrance and exit; Step-free corridors and maneuvering space; Corridors, storage places, seats, toilets and service areas are required to have sufficient maneuvering and clear space; All operating controls and communication systems should be within reach of sitting persons; Doors should be operated fully automatically - Travel patterns</td><td>Costs vary significantly between manufacturers - depend on what strategy will be used. Some potential: buy new vehicles, repair an existing one</td><td>Fleet efficiency - Flexible route - Vehicle routing problem - Demand adaptive system - Mobile allowance shuttle transit - Demand Responsive Bus Routing Problem</td><td>Cooperation between national and regional government to have the same strategy concerning the purchase of new vehicles or repairing existing - Regional transportation management system - Vehicle condition monitoring</td><td>Driver training for a safe trip with avoiding sudden braking and acceleration, assisting in boarding and alighting safely</td></tr><tr><td>Trains</td><td>Implementing Technical Specification for Interoperability (Papanikolaou, Basbas, Mintsis, &amp; Taxiltaris) - Wholly accessible rolling stock, portable manual train lifts, wheelchair ramps, automatic doors on trains, Handrails on stairs</td><td>The investment program for the new rolling stock with full accessibility - Financial budget for reconstruction of existing rolling stock to meet the needs of PWD</td><td>Line planning (max the service towards the passengers, min the operational costs of the railway system) - Timetabling - Platforming - Rolling stock circulation - Shunting - Real-time traffic control - Number of direct connections, frequencies, and reliability</td><td>European Rail Traffic Management System (ERTMS), GSM-R (communication), European Train Control System (ETCS, signaling), European Train Management Layer (ETML)</td><td>Railway staff training with the object how to use equipment (ramps and platforms) safely with an awareness of the PWD issues</td></tr><tr><td colspan="2">Private modes of transportation</td><td>Adapted vehicles</td><td>Improve legislation framework for public-private partnership - technical documentation regarding the conditions about the vehicles</td><td>Restructure public transport - Subsidies of transportation modes - Independent projects investments</td><td>Integrate transit and feeder services - Real-time response to changing demand - New personalized public transit - Define the hub center to bring PWD to the public network</td><td>Providing the infrastructure, friendly-user parking spaces to enable PWD to use adapted vehicles - Cooperation among several institutions - Regional transportation management system - Vehicle condition monitoring</td><td>Information about the aid getting in and out of the vehicle, transfer board, wheelchair ramps, button-operated clutch on the gearshift, handbrake adaptations, simple car control adaptations (steering spinners/knobs and brake/accelerator hand controls), horizontal steering wheel, wheelchair-accessible motorcycle, wheelchair accessible vehicle</td></tr></table>
<table><tr><td rowspan="2">Accessibility</td><td>Parking facilities and associated concessions</td><td>Improve legislation framework for public-private partnership - Urban planning - Parking design incorporates footways, ramps, and doorways establishing the whole journey accessible</td><td>Restructure public transport - Ticketing policy</td><td>Disabled parking permits - Enlarging parking spaces - Accommodating parking spaces closer to the public transport network</td><td>Cooperation between national and regional government - Regional transportation management system</td><td>Disability awareness training for staff members on the parking</td></tr><tr><td>Taxis and minivans</td><td>Improve legislation framework for public-private partnership - technical documentation regarding the conditions about the vehicles</td><td>Restructure public transport - Subsides of transportation modes - Independent projects investments</td><td>Integrate transit and feeder services - Real-time response to changing demand - New personalized public transit - Define hub center to bring PWD to a public network - Dial-a-ride problem - Transport on demand</td><td>Cooperation between national and regional government - Regional transportation management system - Vehicle condition monitoring</td><td>Drivers education/training to be able to provide adequate assistance to PWD - Service as board and alight the vehicle; being patient while PWD board; driving carefully</td></tr><tr><td>Acceptability</td><td></td><td>The conditions described in the scope of the service of public transport. Particular focus on safe transport</td><td>Establish the budget for the friendly users</td><td>Clean, safe, and user-friendly transport. How often should be cleaning, do they need special treatment (after some patients)</td><td>Provide user-friendly access to quality transportation services</td><td>Medical treatment education - Driver condition monitoring</td></tr><tr><td>Affordability</td><td></td><td>Financial assistance - legal base; contract, PSO (Public Service Obligation)</td><td>Restructure public transport - Subsides of transportation modes</td><td>Enhanced fare card</td><td>Cooperation between national and regional government - a joint project</td><td>Education of PWD how they can use it financial assistance - Transportation pricing</td></tr><tr><td>Adaptability</td><td></td><td>Develop the legislation to have one act for all transportation modes</td><td>Restructure public transport - Subsides of transportation modes</td><td>Quality service - Always provide a seat - Service assistance by a person, with special support if required - PWD can book by phone, by SMS, or on-line - Transport chain without interruption</td><td>Flexible route transit - Regional transportation management system - Regional transportation information clearinghouse</td><td>Driver training - Multimodal pre-trip and en-route travel information</td></tr></table>
APPENDIX C. Transport network map in metropole Valenciennes
(High resolution)
<figure><img src="image_30.png" /><figcaption># PLAN DU RÉSEAU</figcaption></figure>

Septembre 2017

<figure><img src="image_31.png" /></figure>

Transvilles

GROUPE RATP
# APPENDIX D. Exchanges poles in Valenciennes

Source of all figures in this appendix: https://www.transvilles.com/poles-echanges
<figure><img src="image_32.png" /><figcaption>Figure 28 Exchange pole: Station Saint-Waast</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>Figure 29 Exchange pole: Station Gare</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>Figure 30 Exchange pole: Station Famars Université</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>Figure 31 Exchange pole: Station Denain Espace Villars</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Figure 32 Exchange pole: Station Anzin Hôtel de Ville</figcaption></figure>
# APPENDIX E. Optimal number of clusters
<table><caption>Table 17 Optimal number of clusters: PWDs in arrival and departure</caption><thead><tr><th>ALL</th><th>MaxIteration</th><th>Replicates</th><th>No of stations-<br>Max no of cluster</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>Avg</th></tr></thead><tbody><tr><td rowspan="10">1</td><td rowspan="10">10 000</td><td rowspan="10">1</td><td>420</td><td>415</td><td>420</td><td>416</td><td>417</td><td>418</td><td>409</td><td>417</td><td>416</td><td>420</td><td>420</td><td>417</td></tr><tr><td>210</td><td>209</td><td>207</td><td>205</td><td>209</td><td>206</td><td>204</td><td>199</td><td>210</td><td>205</td><td>210</td><td>206</td></tr><tr><td>105</td><td>99</td><td>102</td><td>104</td><td>92</td><td>100</td><td>99</td><td>100</td><td>101</td><td>103</td><td>97</td><td>100</td></tr><tr><td>50</td><td>39</td><td>47</td><td>50</td><td>50</td><td>48</td><td>44</td><td>49</td><td>48</td><td>42</td><td>48</td><td>47</td></tr><tr><td>25</td><td>23</td><td>24</td><td>24</td><td>22</td><td>23</td><td>16</td><td>25</td><td>25</td><td>23</td><td>22</td><td>23</td></tr><tr><td>12</td><td>9</td><td>12</td><td>8</td><td>9</td><td>8</td><td>8</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td></tr><tr><td>9</td><td>9</td><td>4</td><td>6</td><td>8</td><td>8</td><td>4</td><td>9</td><td>8</td><td>8</td><td>6</td><td>7</td></tr><tr><td>7</td><td>4</td><td>4</td><td>6</td><td>4</td><td>4</td><td>6</td><td>4</td><td>6</td><td>4</td><td>7</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">2</td><td rowspan="10">100 000</td><td rowspan="10">1</td><td>420</td><td>419</td><td>420</td><td>420</td><td>419</td><td>418</td><td>413</td><td>420</td><td>417</td><td>416</td><td>420</td><td>418</td></tr><tr><td>210</td><td>209</td><td>209</td><td>210</td><td>210</td><td>205</td><td>210</td><td>205</td><td>209</td><td>209</td><td>209</td><td>209</td></tr><tr><td>105</td><td>99</td><td>104</td><td>101</td><td>105</td><td>105</td><td>102</td><td>98</td><td>97</td><td>105</td><td>96</td><td>101</td></tr><tr><td>50</td><td>50</td><td>48</td><td>47</td><td>50</td><td>50</td><td>50</td><td>49</td><td>48</td><td>50</td><td>50</td><td>49</td></tr><tr><td>25</td><td>24</td><td>25</td><td>24</td><td>25</td><td>25</td><td>23</td><td>25</td><td>21</td><td>18</td><td>25</td><td>24</td></tr><tr><td>12</td><td>9</td><td>11</td><td>12</td><td>11</td><td>12</td><td>11</td><td>7</td><td>9</td><td>9</td><td>12</td><td>10</td></tr><tr><td>9</td><td>7</td><td>8</td><td>8</td><td>8</td><td>4</td><td>9</td><td>9</td><td>4</td><td>9</td><td>7</td><td>7</td></tr><tr><td>7</td><td>4</td><td>7</td><td>6</td><td>7</td><td>4</td><td>4</td><td>7</td><td>6</td><td>4</td><td>4</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>5</td><td>4</td></tr><tr><td rowspan="10">3</td><td rowspan="10">100 000</td><td rowspan="10">10</td><td>420</td><td>419</td><td>418</td><td>415</td><td>420</td><td>419</td><td>413</td><td>412</td><td>420</td><td>416</td><td>417</td><td>417</td></tr><tr><td>210</td><td>205</td><td>210</td><td>207</td><td>210</td><td>207</td><td>210</td><td>204</td><td>202</td><td>205</td><td>210</td><td>207</td></tr><tr><td>105</td><td>105</td><td>105</td><td>104</td><td>105</td><td>102</td><td>101</td><td>105</td><td>100</td><td>105</td><td>91</td><td>102</td></tr><tr><td>50</td><td>45</td><td>44</td><td>50</td><td>50</td><td>50</td><td>50</td><td>50</td><td>44</td><td>49</td><td>50</td><td>48</td></tr><tr><td>25</td><td>25</td><td>25</td><td>25</td><td>25</td><td>23</td><td>25</td><td>22</td><td>24</td><td>24</td><td>21</td><td>24</td></tr><tr><td>12</td><td>8</td><td>9</td><td>7</td><td>12</td><td>8</td><td>9</td><td>8</td><td>4</td><td>7</td><td>8</td><td>8</td></tr><tr><td>9</td><td>4</td><td>6</td><td>8</td><td>8</td><td>8</td><td>7</td><td>7</td><td>9</td><td>8</td><td>8</td><td>7</td></tr><tr><td>7</td><td>4</td><td>7</td><td>4</td><td>7</td><td>4</td><td>4</td><td>6</td><td>7</td><td>4</td><td>7</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">4</td><td rowspan="10">100 000</td><td rowspan="10">100</td><td>420</td><td>415</td><td>419</td><td>414</td><td>420</td><td>419</td><td>418</td><td>419</td><td>416</td><td>417</td><td>418</td><td>418</td></tr><tr><td>210</td><td>208</td><td>204</td><td>210</td><td>208</td><td>203</td><td>210</td><td>210</td><td>206</td><td>209</td><td>203</td><td>207</td></tr><tr><td>105</td><td>104</td><td>101</td><td>104</td><td>103</td><td>103</td><td>103</td><td>105</td><td>105</td><td>103</td><td>100</td><td>103</td></tr><tr><td>50</td><td>49</td><td>49</td><td>50</td><td>50</td><td>44</td><td>45</td><td>47</td><td>47</td><td>49</td><td>49</td><td>48</td></tr><tr><td>25</td><td>20</td><td>19</td><td>25</td><td>25</td><td>22</td><td>22</td><td>24</td><td>22</td><td>21</td><td>23</td><td>22</td></tr><tr><td>12</td><td>9</td><td>9</td><td>9</td><td>11</td><td>11</td><td>8</td><td>12</td><td>10</td><td>12</td><td>10</td><td>10</td></tr><tr><td>9</td><td>9</td><td>8</td><td>4</td><td>8</td><td>8</td><td>8</td><td>9</td><td>4</td><td>9</td><td>7</td><td>7</td></tr><tr><td>7</td><td>7</td><td>7</td><td>7</td><td>4</td><td>4</td><td>6</td><td>4</td><td>4</td><td>7</td><td>7</td><td>6</td></tr><tr><td>5</td><td>4</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">5</td><td rowspan="10">1 000 000</td><td rowspan="10">100</td><td>420</td><td>419</td><td>414</td><td>419</td><td>419</td><td>416</td><td>420</td><td>414</td><td>416</td><td>419</td><td>411</td><td>417</td></tr><tr><td>210</td><td>207</td><td>208</td><td>209</td><td>209</td><td>210</td><td>207</td><td>207</td><td>208</td><td>210</td><td>206</td><td>208</td></tr><tr><td>105</td><td>93</td><td>103</td><td>104</td><td>104</td><td>100</td><td>104</td><td>105</td><td>104</td><td>105</td><td>104</td><td>103</td></tr><tr><td>50</td><td>50</td><td>50</td><td>47</td><td>50</td><td>47</td><td>50</td><td>50</td><td>48</td><td>49</td><td>47</td><td>49</td></tr><tr><td>25</td><td>25</td><td>18</td><td>25</td><td>18</td><td>18</td><td>22</td><td>24</td><td>24</td><td>25</td><td>25</td><td>22</td></tr><tr><td>12</td><td>9</td><td>10</td><td>11</td><td>7</td><td>10</td><td>7</td><td>11</td><td>10</td><td>10</td><td>11</td><td>10</td></tr><tr><td>9</td><td>6</td><td>7</td><td>9</td><td>4</td><td>8</td><td>8</td><td>7</td><td>8</td><td>4</td><td>4</td><td>7</td></tr><tr><td>7</td><td>7</td><td>7</td><td>4</td><td>6</td><td>7</td><td>7</td><td>6</td><td>4</td><td>4</td><td>7</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">6</td><td rowspan="10">1 000 000</td><td rowspan="10">1 000</td><td>420</td><td>416</td><td>417</td><td>420</td><td>416</td><td>416</td><td>419</td><td>418</td><td>410</td><td>419</td><td>419</td><td>417</td></tr><tr><td>210</td><td>207</td><td>208</td><td>201</td><td>210</td><td>207</td><td>208</td><td>209</td><td>210</td><td>207</td><td>205</td><td>207</td></tr><tr><td>105</td><td>103</td><td>104</td><td>105</td><td>99</td><td>103</td><td>102</td><td>105</td><td>105</td><td>103</td><td>101</td><td>103</td></tr><tr><td>50</td><td>50</td><td>50</td><td>45</td><td>45</td><td>37</td><td>50</td><td>48</td><td>50</td><td>50</td><td>50</td><td>48</td></tr><tr><td>25</td><td>25</td><td>21</td><td>23</td><td>24</td><td>25</td><td>25</td><td>24</td><td>23</td><td>23</td><td>25</td><td>24</td></tr><tr><td>12</td><td>12</td><td>4</td><td>12</td><td>10</td><td>9</td><td>7</td><td>9</td><td>11</td><td>10</td><td>9</td><td>9</td></tr><tr><td>9</td><td>9</td><td>7</td><td>9</td><td>7</td><td>9</td><td>8</td><td>9</td><td>8</td><td>8</td><td>7</td><td>8</td></tr><tr><td>7</td><td>6</td><td>7</td><td>4</td><td>4</td><td>7</td><td>7</td><td>6</td><td>4</td><td>7</td><td>7</td><td>6</td></tr><tr><td>5</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">7</td><td rowspan="10">1 000 000</td><td rowspan="10">10 000</td><td>420</td><td>416</td><td>419</td><td>417</td><td>416</td><td>415</td><td>420</td><td>417</td><td>420</td><td>417</td><td>419</td><td>418</td></tr><tr><td>210</td><td>210</td><td>208</td><td>208</td><td>210</td><td>210</td><td>210</td><td>210</td><td>210</td><td>207</td><td>204</td><td>209</td></tr><tr><td>105</td><td>96</td><td>99</td><td>103</td><td>103</td><td>101</td><td>100</td><td>105</td><td>101</td><td>94</td><td>101</td><td>100</td></tr><tr><td>50</td><td>45</td><td>50</td><td>50</td><td>50</td><td>50</td><td>46</td><td>50</td><td>48</td><td>48</td><td>50</td><td>49</td></tr><tr><td>25</td><td>20</td><td>20</td><td>25</td><td>22</td><td>19</td><td>25</td><td>24</td><td>23</td><td>25</td><td>22</td><td>23</td></tr><tr><td>12</td><td>12</td><td>10</td><td>12</td><td>8</td><td>9</td><td>11</td><td>12</td><td>10</td><td>12</td><td>7</td><td>10</td></tr><tr><td>9</td><td>9</td><td>4</td><td>7</td><td>6</td><td>4</td><td>9</td><td>4</td><td>8</td><td>9</td><td>7</td><td>7</td></tr><tr><td>7</td><td>4</td><td>4</td><td>4</td><td>6</td><td>6</td><td>6</td><td>4</td><td>7</td><td>4</td><td>6</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr></tbody></table>
<table><caption>Table 18 Optimal number of clusters, users in a departure</caption><thead><tr><th>DEPARTURE</th><th>MaxIteration</th><th>Replicates</th><th>No of stations= Max no of cluster</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>Avg</th></tr></thead><tbody><tr><td rowspan="10">1</td><td rowspan="10">10 000</td><td rowspan="10">1</td><td>420</td><td>418</td><td>419</td><td>417</td><td>415</td><td>419</td><td>420</td><td>418</td><td>417</td><td>415</td><td>418</td><td>418</td></tr><tr><td>210</td><td>210</td><td>209</td><td>207</td><td>209</td><td>207</td><td>209</td><td>210</td><td>208</td><td>197</td><td>207</td><td>207</td></tr><tr><td>105</td><td>105</td><td>101</td><td>100</td><td>103</td><td>105</td><td>96</td><td>102</td><td>102</td><td>104</td><td>96</td><td>101</td></tr><tr><td>50</td><td>50</td><td>48</td><td>49</td><td>42</td><td>50</td><td>50</td><td>50</td><td>49</td><td>50</td><td>50</td><td>49</td></tr><tr><td>25</td><td>24</td><td>22</td><td>23</td><td>18</td><td>24</td><td>24</td><td>25</td><td>25</td><td>24</td><td>24</td><td>23</td></tr><tr><td>12</td><td>12</td><td>7</td><td>10</td><td>12</td><td>6</td><td>8</td><td>12</td><td>12</td><td>7</td><td>10</td><td>10</td></tr><tr><td>9</td><td>8</td><td>7</td><td>6</td><td>6</td><td>8</td><td>6</td><td>7</td><td>8</td><td>8</td><td>9</td><td>7</td></tr><tr><td>7</td><td>4</td><td>7</td><td>6</td><td>5</td><td>7</td><td>4</td><td>4</td><td>4</td><td>6</td><td>4</td><td>5</td></tr><tr><td>5</td><td>5</td><td>4</td><td>5</td><td>5</td><td>4</td><td>4</td><td>4</td><td>5</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">2</td><td rowspan="10">100 000</td><td rowspan="10">1</td><td>420</td><td>417</td><td>419</td><td>412</td><td>407</td><td>420</td><td>419</td><td>420</td><td>418</td><td>417</td><td>414</td><td>416</td></tr><tr><td>210</td><td>209</td><td>206</td><td>202</td><td>200</td><td>209</td><td>207</td><td>207</td><td>201</td><td>209</td><td>210</td><td>206</td></tr><tr><td>105</td><td>104</td><td>104</td><td>104</td><td>104</td><td>100</td><td>105</td><td>102</td><td>103</td><td>105</td><td>102</td><td>103</td></tr><tr><td>50</td><td>50</td><td>46</td><td>50</td><td>48</td><td>49</td><td>48</td><td>48</td><td>50</td><td>49</td><td>50</td><td>49</td></tr><tr><td>25</td><td>22</td><td>21</td><td>22</td><td>23</td><td>25</td><td>21</td><td>16</td><td>22</td><td>21</td><td>24</td><td>22</td></tr><tr><td>12</td><td>8</td><td>11</td><td>7</td><td>12</td><td>11</td><td>8</td><td>12</td><td>9</td><td>8</td><td>9</td><td>10</td></tr><tr><td>9</td><td>6</td><td>7</td><td>7</td><td>4</td><td>4</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>7</td></tr><tr><td>7</td><td>7</td><td>7</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>7</td><td>6</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>5</td><td>4</td><td>4</td></tr><tr><td rowspan="10">3</td><td rowspan="10">100 000</td><td rowspan="10">10</td><td>420</td><td>419</td><td>420</td><td>419</td><td>420</td><td>414</td><td>419</td><td>416</td><td>418</td><td>419</td><td>419</td><td>418</td></tr><tr><td>210</td><td>210</td><td>204</td><td>209</td><td>206</td><td>209</td><td>208</td><td>203</td><td>208</td><td>208</td><td>205</td><td>207</td></tr><tr><td>105</td><td>102</td><td>99</td><td>104</td><td>100</td><td>96</td><td>105</td><td>99</td><td>105</td><td>102</td><td>104</td><td>102</td></tr><tr><td>50</td><td>50</td><td>47</td><td>47</td><td>45</td><td>50</td><td>50</td><td>48</td><td>49</td><td>50</td><td>50</td><td>49</td></tr><tr><td>25</td><td>23</td><td>22</td><td>19</td><td>25</td><td>25</td><td>25</td><td>24</td><td>18</td><td>23</td><td>21</td><td>23</td></tr><tr><td>12</td><td>8</td><td>7</td><td>10</td><td>11</td><td>9</td><td>7</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td></tr><tr><td>9</td><td>8</td><td>4</td><td>8</td><td>8</td><td>9</td><td>8</td><td>9</td><td>4</td><td>8</td><td>7</td><td>7</td></tr><tr><td>7</td><td>7</td><td>4</td><td>4</td><td>5</td><td>4</td><td>6</td><td>7</td><td>7</td><td>7</td><td>7</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">4</td><td rowspan="10">100 000</td><td rowspan="10">100</td><td>420</td><td>418</td><td>414</td><td>414</td><td>420</td><td>419</td><td>409</td><td>417</td><td>420</td><td>420</td><td>416</td><td>417</td></tr><tr><td>210</td><td>208</td><td>209</td><td>208</td><td>201</td><td>206</td><td>205</td><td>208</td><td>204</td><td>210</td><td>210</td><td>207</td></tr><tr><td>105</td><td>101</td><td>103</td><td>98</td><td>104</td><td>102</td><td>97</td><td>104</td><td>101</td><td>98</td><td>99</td><td>101</td></tr><tr><td>50</td><td>49</td><td>46</td><td>50</td><td>43</td><td>47</td><td>49</td><td>49</td><td>50</td><td>49</td><td>44</td><td>48</td></tr><tr><td>25</td><td>25</td><td>20</td><td>25</td><td>25</td><td>23</td><td>24</td><td>23</td><td>17</td><td>25</td><td>24</td><td>23</td></tr><tr><td>12</td><td>9</td><td>11</td><td>11</td><td>9</td><td>6</td><td>6</td><td>10</td><td>12</td><td>7</td><td>10</td><td>9</td></tr><tr><td>9</td><td>9</td><td>4</td><td>6</td><td>8</td><td>4</td><td>9</td><td>8</td><td>7</td><td>9</td><td>9</td><td>7</td></tr><tr><td>7</td><td>4</td><td>4</td><td>7</td><td>7</td><td>7</td><td>7</td><td>4</td><td>6</td><td>7</td><td>4</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>5</td><td>4</td></tr><tr><td rowspan="10">5</td><td rowspan="10">1 000 000</td><td rowspan="10">100</td><td>420</td><td>419</td><td>414</td><td>417</td><td>420</td><td>417</td><td>418</td><td>416</td><td>419</td><td>418</td><td>415</td><td>417</td></tr><tr><td>210</td><td>206</td><td>208</td><td>195</td><td>198</td><td>207</td><td>206</td><td>205</td><td>204</td><td>207</td><td>202</td><td>204</td></tr><tr><td>105</td><td>101</td><td>101</td><td>101</td><td>103</td><td>102</td><td>98</td><td>101</td><td>102</td><td>100</td><td>103</td><td>101</td></tr><tr><td>50</td><td>50</td><td>49</td><td>49</td><td>45</td><td>49</td><td>50</td><td>46</td><td>48</td><td>44</td><td>42</td><td>47</td></tr><tr><td>25</td><td>21</td><td>21</td><td>25</td><td>24</td><td>18</td><td>25</td><td>24</td><td>24</td><td>23</td><td>23</td><td>23</td></tr><tr><td>12</td><td>4</td><td>9</td><td>9</td><td>11</td><td>10</td><td>8</td><td>10</td><td>11</td><td>10</td><td>12</td><td>9</td></tr><tr><td>9</td><td>7</td><td>7</td><td>8</td><td>9</td><td>8</td><td>8</td><td>7</td><td>8</td><td>7</td><td>9</td><td>8</td></tr><tr><td>7</td><td>7</td><td>7</td><td>4</td><td>6</td><td>7</td><td>7</td><td>4</td><td>4</td><td>4</td><td>4</td><td>5</td></tr><tr><td>5</td><td>5</td><td>4</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">6</td><td rowspan="10">1 000 000</td><td rowspan="10">1 000</td><td>420</td><td>419</td><td>419</td><td>419</td><td>420</td><td>420</td><td>419</td><td>419</td><td>420</td><td>416</td><td>419</td><td>419</td></tr><tr><td>210</td><td>208</td><td>209</td><td>210</td><td>204</td><td>209</td><td>210</td><td>208</td><td>209</td><td>205</td><td>204</td><td>208</td></tr><tr><td>105</td><td>97</td><td>102</td><td>105</td><td>99</td><td>97</td><td>102</td><td>97</td><td>105</td><td>102</td><td>105</td><td>101</td></tr><tr><td>50</td><td>50</td><td>47</td><td>50</td><td>45</td><td>50</td><td>46</td><td>44</td><td>49</td><td>46</td><td>47</td><td>47</td></tr><tr><td>25</td><td>18</td><td>25</td><td>25</td><td>20</td><td>24</td><td>18</td><td>21</td><td>25</td><td>21</td><td>22</td><td>22</td></tr><tr><td>12</td><td>10</td><td>9</td><td>12</td><td>12</td><td>9</td><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td></tr><tr><td>9</td><td>7</td><td>9</td><td>8</td><td>4</td><td>8</td><td>7</td><td>6</td><td>7</td><td>8</td><td>7</td><td>7</td></tr><tr><td>7</td><td>6</td><td>4</td><td>4</td><td>7</td><td>7</td><td>4</td><td>7</td><td>7</td><td>7</td><td>4</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">7</td><td rowspan="10">1 000 000</td><td rowspan="10">10 000</td><td>420</td><td>420</td><td>418</td><td>420</td><td>411</td><td>415</td><td>412</td><td>418</td><td>417</td><td>419</td><td>419</td><td>417</td></tr><tr><td>210</td><td>194</td><td>203</td><td>210</td><td>210</td><td>206</td><td>207</td><td>206</td><td>210</td><td>210</td><td>204</td><td>206</td></tr><tr><td>105</td><td>104</td><td>104</td><td>100</td><td>104</td><td>102</td><td>102</td><td>105</td><td>104</td><td>102</td><td>104</td><td>103</td></tr><tr><td>50</td><td>49</td><td>44</td><td>50</td><td>40</td><td>49</td><td>50</td><td>50</td><td>45</td><td>50</td><td>50</td><td>48</td></tr><tr><td>25</td><td>23</td><td>21</td><td>24</td><td>25</td><td>21</td><td>22</td><td>21</td><td>22</td><td>20</td><td>25</td><td>22</td></tr><tr><td>12</td><td>10</td><td>12</td><td>12</td><td>11</td><td>8</td><td>9</td><td>12</td><td>10</td><td>9</td><td>12</td><td>11</td></tr><tr><td>9</td><td>8</td><td>9</td><td>7</td><td>9</td><td>9</td><td>7</td><td>9</td><td>7</td><td>7</td><td>9</td><td>8</td></tr><tr><td>7</td><td>6</td><td>6</td><td>6</td><td>4</td><td>7</td><td>6</td><td>7</td><td>4</td><td>4</td><td>6</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr></tbody></table>
<table><caption>Table 19 Optimal number of clusters, users in an arrival</caption><thead><tr><th>ARRIVAL</th><th>Maxiteration</th><th>Replicates</th><th>No of stations =<br>Max no of cluster</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>Avg</th></tr></thead><tbody><tr><td rowspan="10">1</td><td rowspan="10">10 000</td><td rowspan="10">1</td><td>420</td><td>416</td><td>419</td><td>418</td><td>417</td><td>404</td><td>404</td><td>412</td><td>417</td><td>418</td><td>419</td><td>414</td></tr><tr><td>210</td><td>205</td><td>210</td><td>209</td><td>209</td><td>207</td><td>208</td><td>202</td><td>207</td><td>202</td><td>210</td><td>207</td></tr><tr><td>105</td><td>98</td><td>103</td><td>105</td><td>103</td><td>101</td><td>96</td><td>103</td><td>100</td><td>103</td><td>103</td><td>102</td></tr><tr><td>50</td><td>50</td><td>48</td><td>49</td><td>45</td><td>48</td><td>46</td><td>50</td><td>50</td><td>49</td><td>50</td><td>49</td></tr><tr><td>25</td><td>20</td><td>23</td><td>20</td><td>24</td><td>25</td><td>24</td><td>25</td><td>15</td><td>23</td><td>23</td><td>22</td></tr><tr><td>12</td><td>10</td><td>10</td><td>12</td><td>7</td><td>10</td><td>8</td><td>11</td><td>9</td><td>8</td><td>8</td><td>9</td></tr><tr><td>9</td><td>6</td><td>9</td><td>7</td><td>7</td><td>8</td><td>7</td><td>9</td><td>9</td><td>7</td><td>4</td><td>7</td></tr><tr><td>7</td><td>6</td><td>7</td><td>6</td><td>4</td><td>4</td><td>7</td><td>4</td><td>4</td><td>7</td><td>7</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">2</td><td rowspan="10">100 000</td><td rowspan="10">1</td><td>420</td><td>420</td><td>420</td><td>411</td><td>417</td><td>417</td><td>417</td><td>420</td><td>420</td><td>416</td><td>420</td><td>418</td></tr><tr><td>210</td><td>196</td><td>204</td><td>205</td><td>206</td><td>208</td><td>207</td><td>205</td><td>201</td><td>207</td><td>208</td><td>205</td></tr><tr><td>105</td><td>105</td><td>103</td><td>100</td><td>97</td><td>103</td><td>102</td><td>104</td><td>96</td><td>105</td><td>102</td><td>102</td></tr><tr><td>50</td><td>49</td><td>49</td><td>45</td><td>49</td><td>50</td><td>49</td><td>50</td><td>48</td><td>44</td><td>50</td><td>48</td></tr><tr><td>25</td><td>25</td><td>24</td><td>18</td><td>23</td><td>23</td><td>25</td><td>24</td><td>21</td><td>22</td><td>25</td><td>23</td></tr><tr><td>12</td><td>8</td><td>9</td><td>12</td><td>9</td><td>10</td><td>12</td><td>11</td><td>9</td><td>12</td><td>12</td><td>10</td></tr><tr><td>9</td><td>7</td><td>9</td><td>8</td><td>4</td><td>7</td><td>9</td><td>7</td><td>7</td><td>4</td><td>6</td><td>7</td></tr><tr><td>7</td><td>4</td><td>7</td><td>4</td><td>4</td><td>6</td><td>4</td><td>4</td><td>7</td><td>7</td><td>7</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">3</td><td rowspan="10">100 000</td><td rowspan="10">10</td><td>420</td><td>420</td><td>419</td><td>418</td><td>419</td><td>416</td><td>420</td><td>418</td><td>420</td><td>418</td><td>419</td><td>419</td></tr><tr><td>210</td><td>207</td><td>209</td><td>209</td><td>202</td><td>209</td><td>209</td><td>210</td><td>210</td><td>210</td><td>203</td><td>208</td></tr><tr><td>105</td><td>105</td><td>98</td><td>98</td><td>102</td><td>98</td><td>101</td><td>101</td><td>104</td><td>103</td><td>104</td><td>101</td></tr><tr><td>50</td><td>49</td><td>49</td><td>46</td><td>47</td><td>47</td><td>49</td><td>49</td><td>50</td><td>49</td><td>49</td><td>48</td></tr><tr><td>25</td><td>25</td><td>23</td><td>25</td><td>22</td><td>25</td><td>19</td><td>17</td><td>25</td><td>25</td><td>21</td><td>23</td></tr><tr><td>12</td><td>11</td><td>12</td><td>10</td><td>8</td><td>9</td><td>12</td><td>8</td><td>11</td><td>9</td><td>9</td><td>10</td></tr><tr><td>9</td><td>9</td><td>7</td><td>7</td><td>8</td><td>7</td><td>8</td><td>7</td><td>4</td><td>8</td><td>8</td><td>7</td></tr><tr><td>7</td><td>4</td><td>7</td><td>4</td><td>7</td><td>6</td><td>4</td><td>4</td><td>7</td><td>7</td><td>4</td><td>5</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">4</td><td rowspan="10">100 000</td><td rowspan="10">100</td><td>420</td><td>420</td><td>415</td><td>414</td><td>416</td><td>415</td><td>420</td><td>420</td><td>417</td><td>419</td><td>419</td><td>418</td></tr><tr><td>210</td><td>210</td><td>210</td><td>209</td><td>208</td><td>210</td><td>204</td><td>209</td><td>204</td><td>209</td><td>208</td><td>208</td></tr><tr><td>105</td><td>105</td><td>104</td><td>102</td><td>101</td><td>103</td><td>105</td><td>105</td><td>105</td><td>105</td><td>105</td><td>104</td></tr><tr><td>50</td><td>48</td><td>50</td><td>50</td><td>44</td><td>49</td><td>48</td><td>44</td><td>49</td><td>50</td><td>50</td><td>48</td></tr><tr><td>25</td><td>20</td><td>22</td><td>20</td><td>23</td><td>21</td><td>24</td><td>25</td><td>24</td><td>22</td><td>23</td><td>22</td></tr><tr><td>12</td><td>9</td><td>12</td><td>9</td><td>9</td><td>11</td><td>11</td><td>9</td><td>10</td><td>12</td><td>11</td><td>10</td></tr><tr><td>9</td><td>9</td><td>6</td><td>9</td><td>9</td><td>8</td><td>6</td><td>9</td><td>4</td><td>9</td><td>7</td><td>8</td></tr><tr><td>7</td><td>4</td><td>6</td><td>7</td><td>4</td><td>4</td><td>7</td><td>6</td><td>6</td><td>6</td><td>7</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">5</td><td rowspan="10">1 000 000</td><td rowspan="10">100</td><td>420</td><td>418</td><td>415</td><td>420</td><td>420</td><td>420</td><td>417</td><td>419</td><td>420</td><td>420</td><td>420</td><td>419</td></tr><tr><td>210</td><td>204</td><td>208</td><td>206</td><td>206</td><td>208</td><td>207</td><td>207</td><td>204</td><td>207</td><td>210</td><td>207</td></tr><tr><td>105</td><td>103</td><td>102</td><td>105</td><td>102</td><td>102</td><td>105</td><td>105</td><td>99</td><td>104</td><td>99</td><td>103</td></tr><tr><td>50</td><td>49</td><td>49</td><td>49</td><td>49</td><td>47</td><td>50</td><td>45</td><td>50</td><td>50</td><td>50</td><td>49</td></tr><tr><td>25</td><td>22</td><td>24</td><td>22</td><td>23</td><td>21</td><td>25</td><td>25</td><td>25</td><td>25</td><td>21</td><td>23</td></tr><tr><td>12</td><td>11</td><td>10</td><td>12</td><td>9</td><td>12</td><td>11</td><td>11</td><td>8</td><td>8</td><td>12</td><td>11</td></tr><tr><td>9</td><td>4</td><td>8</td><td>6</td><td>7</td><td>7</td><td>9</td><td>4</td><td>8</td><td>8</td><td>7</td><td>7</td></tr><tr><td>7</td><td>4</td><td>4</td><td>7</td><td>7</td><td>7</td><td>7</td><td>6</td><td>7</td><td>4</td><td>7</td><td>6</td></tr><tr><td>5</td><td>5</td><td>4</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">6</td><td rowspan="10">1 000 000</td><td rowspan="10">1 000</td><td>420</td><td>412</td><td>419</td><td>420</td><td>419</td><td>420</td><td>415</td><td>420</td><td>420</td><td>417</td><td>418</td><td>418</td></tr><tr><td>210</td><td>210</td><td>209</td><td>210</td><td>209</td><td>210</td><td>191</td><td>208</td><td>204</td><td>203</td><td>210</td><td>206</td></tr><tr><td>105</td><td>104</td><td>102</td><td>97</td><td>91</td><td>97</td><td>101</td><td>105</td><td>101</td><td>101</td><td>105</td><td>100</td></tr><tr><td>50</td><td>46</td><td>49</td><td>44</td><td>50</td><td>50</td><td>50</td><td>47</td><td>48</td><td>48</td><td>50</td><td>48</td></tr><tr><td>25</td><td>24</td><td>25</td><td>20</td><td>20</td><td>24</td><td>23</td><td>21</td><td>23</td><td>25</td><td>21</td><td>23</td></tr><tr><td>12</td><td>11</td><td>7</td><td>7</td><td>9</td><td>11</td><td>9</td><td>12</td><td>8</td><td>10</td><td>10</td><td>9</td></tr><tr><td>9</td><td>9</td><td>0</td><td>7</td><td>9</td><td>8</td><td>4</td><td>8</td><td>9</td><td>9</td><td>7</td><td>8</td></tr><tr><td>7</td><td>7</td><td>7</td><td>4</td><td>7</td><td>4</td><td>7</td><td>7</td><td>4</td><td>7</td><td>7</td><td>6</td></tr><tr><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr><tr><td rowspan="10">7</td><td rowspan="10">1 000 000</td><td rowspan="10">10 000</td><td>420</td><td>416</td><td>419</td><td>418</td><td>420</td><td>419</td><td>419</td><td>419</td><td>415</td><td>420</td><td>417</td><td>418</td></tr><tr><td>210</td><td>207</td><td>209</td><td>208</td><td>204</td><td>209</td><td>209</td><td>197</td><td>210</td><td>210</td><td>200</td><td>206</td></tr><tr><td>105</td><td>104</td><td>96</td><td>94</td><td>104</td><td>104</td><td>102</td><td>100</td><td>99</td><td>105</td><td>104</td><td>101</td></tr><tr><td>50</td><td>49</td><td>46</td><td>50</td><td>47</td><td>46</td><td>49</td><td>48</td><td>48</td><td>48</td><td>45</td><td>48</td></tr><tr><td>25</td><td>22</td><td>20</td><td>25</td><td>22</td><td>20</td><td>18</td><td>17</td><td>23</td><td>24</td><td>22</td><td>21</td></tr><tr><td>12</td><td>9</td><td>11</td><td>8</td><td>12</td><td>12</td><td>8</td><td>7</td><td>7</td><td>8</td><td>8</td><td>9</td></tr><tr><td>9</td><td>7</td><td>8</td><td>9</td><td>7</td><td>4</td><td>4</td><td>9</td><td>4</td><td>9</td><td>7</td><td>7</td></tr><tr><td>7</td><td>6</td><td>4</td><td>4</td><td>4</td><td>6</td><td>6</td><td>4</td><td>4</td><td>4</td><td>7</td><td>5</td></tr><tr><td>5</td><td>5</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td></tr></tbody></table>
APPENDIX F. Figures of clustering analysis - High resolution
<figure><img src="image_37.png" /><figcaption>Figure 33 Geographical position in departure: 5 clusters (High resolution)</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>Figure 34 Geographical position in departure: 7 clusters (High resolution)</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>Figure 35 Geographical position in departure: 9 clusters (High resolution)</figcaption></figure>
<figure><img src="image_40.png" /><figcaption>Figure 36 Geographical position in arrival: 5 clusters (High resolution)</figcaption></figure>
<figure><img src="image_41.png" /><figcaption>Figure 37 Geographical position in arrival: 7 clusters (High resolution)</figcaption></figure>
<figure><img src="image_42.png" /><figcaption>Figure 38 Geographical position in arrival: 9 clusters (High resolution)</figcaption></figure>