# Commercial speed impact factors identification for a public urban bus transport network

Erwan Vincent, Zoltan Miklos, Simon Malinowski

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Erwan Vincent, Zoltan Miklos, Simon Malinowski. Commercial speed impact factors identification for a public urban bus transport network. ITSC 2025 - IEEE International Conference on Intelligent Transportation Systems, Sep 2025, Gold Coast, Australia. hal-05461919

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# Commercial speed impact factors identification for a public urban bus transport network

1st Erwan VINCENT
University of Rennes
Rennes, France
erwan.vincent@irisa.fr

2nd Zoltan Miklos
University of Rennes, CNRS, IRISA
Rennes, France
zoltan.miklos@irisa.fr

3rd Simon MALINOWSKI
University of Rennes, CNRS, IRISA
Rennes, France
simon.malinowski@irisa.fr

***Abstract***—Public transport operators of large cities seek continually to improve the quality of their services. Specifically they are interested to understand the different factors that can impact the commercial speed of the public bus services. In this work we propose a methodology that can identify such factors from collected service operational data using machine learning and data analysis techniques. These analytical methods are employed to identify and quantify the variables influencing commercial speed. Our methodology can help the operators and planners of public bus transit networks to make more informed decisions. With enough historical data on the network's operation, our methodology can also be applied to networks of different size. We demonstrate our methodology in the case of the city Rennes, France, and based on the data from the local operator Keolis.

***Index Terms***—Public networks, Transportation, Database processing, Feature evaluation and selection, Statistical methods

## I. INTRODUCTION

Public transport and especially bus networks are part of the urban landscape of European cities. Public transport networks are designed to meet the needs of the population (local or transiting passengers). The mobility authorities often insist on offering a public service that is as attractive as possible for the users, while they also see it as a way to reduce the pollution related to transportation. Network operators therefore work on indicators that could allow them to improve the quality of service of the public transportation.

This quality of service can be measured using several criteria [1], for example, punctuality (which allows us to know if buses running on time), commercial speed (which allows us to understand how fast the buses move through the network), customer satisfaction (customer feedback), and many other metrics [1]–[3]. In this work we focus on the analysis of the commercial speed which is a widely-used indicator, as it captures a number of aspects of the service quality.

Network operators need to understand what are the different factors that influence the commercial speed of the buses to improve the network efficiency. In this work, we present a methodology that allows to identify and quantitatively describe these factors that influence the commercial speed of the buses. Our work is based on data analysis and machine learning methods. Our goal is firstly to identify relationship between the commercial speed and the factors and lastly to describe and characterize the impact of these factors on this speed.

Our methodology works as follows. We propose to collect data about the bus network. We are using network operators data: such operational datasets are a rich source for understanding the factors impacting the commercial speed of buses. This data is then enhanced with public data from multiple sources. A such datasets enable us to model the bus network and train machine learning models that can predict the commercial speed (or another performance criteria) of the network. We have used different kinds of models to capture the relationship between the commercial speed and input features. Our approach is based on the selection of coherent model that can qualitatively explain the evolution of every feature examined in this work. Each of these models receives a score, from which we select and retain only the top-performing models. The best explanatory variables in the model are chosen thanks to a variable selection algorithms. Once the model and variables have been selected, we establish an impact criterion for each feature by using the permutation feature importance [4] which gives us a score that implies the importance that the model gives to this variable in determining commercial speed. In this study, we present a general method. Any public transport network can use it, provided there are enough features—ideally as many as possible—available. We demonstrate our methodology using a real-world data from Rennes, a major French city with an extensive bus network.

The rest of the paper is organized as follows. Section II present previous research on related topics. We give a more precise definition of the problem we investigated in Section III. Our proposed methodology is explained in Section IV. In Section V, we demonstrate the use of our methodology using a real-world example, based on our dataset from Rennes, France. We conclude up the work and discuss possible future directions in Section VI. The Appendix provides more details on the analysis of individual factors.

## II. RELATED WORK

We consider all aspects, whether physical or non-physical, that could directly affect the commercial speed of buses. These factors can impact the commercial speed in various ways, given the complex environment [5] in which the buses circulate on their commercial routes. These factors may or may not have significant effects, they might be more or less frequent or episodic, problematic or advantageous, etc. Since buses
are vehicles that operate on roads, we discuss here research on automobiles, trucks, or coaches as these work may apply to buses as well, albeit to varying degrees. In the literature, numerous types of factors are studied for their proximity to the bus network or for what seems a priori to have an impact. Among these factors, we can find several types such as:

*   **Bus traffic**, one of the most studied in the literature [5]–[7]. These analyses focus on the direct impact of other users on buses in terms of their number, speed and the mix of traffic [6], [7] (cars, bicycles, etc.). Some add other factors to these analyses, such as the distance between vehicles, relative speeds and precise driving parameters, in order to gain a better understanding of traffic dynamics [5].

*   The **weather** is another of these recurrent factors. The aim of these studies is to determine whether the ambient climatic conditions affect the operation or the performance of the bus network [8]–[11]. Some study the direct impact of weather conditions [10], [11] while others study the indirect impact through the impact that these conditions have on other users such as passengers [8], [9].

*   Additionally, a group of factors identified as **road features** or **roadway elements** have a decisive role in urban buses performance [7], [12]–[16]. Some of these articles highlight the more or less important benefits of dedicated bus lanes depending on their surrounding characteristics [7], [12], [13]. Others focus directly on specific roadway components (e.g. distances, traffic lights and the presence of road intersections), their operation, or directly on the shape of the road (e.g. the streets morphology) [7], [14]–[17].

*   **Ridership** is another factor regularly considered in the literature [18]–[21]. In other words, this is the number of people boarding or getting off the transport service. These studies highlight the impact of passengers on bus behaviour, essentially the waiting time at a station as a function of the characteristics of the passengers, the bus or the station. These characteristics can be the density of the surrounding population [18], the characteristics of the buses and stations [19], [20], the characteristics specific to the users (e.g. group age) [20] or their impact on bus consumption and emissions [21].

Most of these articles focus on a single factor or a small group of factors. They demonstrate the impact of a small number of factors, without considering other surrounding elements that may also have an impact on the bus traffic. However, [7] study a larger group of factors but the paper does not highlight the overall impact of the accumulation of impacts on buses. This research analyses the impacts individually without looking at their interdependence with other factors. Our work addresses the problem in a more systematic way, by ranking the variables according to how important they are in influencing commercial speed. We also present an evaluation of each factor's weight.

### III. PROBLEM STATEMENT

In this work we try to understand the impact of different factors on the commercial speed of urban buses. The commercial speed of an urban bus is the average speed at which a vehicle travels between two specific locations. It can be defined on different scales: on the entire network or between two specific stations. Also it can be defined on different time scales: on a given day, on specific days of the week, during specific hours (e.g. rush hours) or on a longer period (such as an entire month). The commercial speed thus reflects all delays that the vehicle can experience (such as waiting, stopping, boarding times, etc.) as well as any potential disruptions that might happen (deviations, traffic jams, etc.) [22], [23]. This indicator is intriguing since it shows the network operator how many buses to run on a specific line, how frequently the buses will pass at each station, and how much it will cost to implement such a system [7], [22]. Note that the commercial speed is different from the driving speed. It can be formally defined as $C_s = \frac{D}{T_t}$ with $T_t$ the average travel time of the bus/metro/tram/etc. on a specific distance $D$.

Network operators are interested in estimating this commercial speed as precisely as possible, as this can help to design timetables or to design or adapt the transport network operation procedures. They are not only interested in the numerical estimates, but also in understanding what are the factors that influence the commercial speed, as these factors can play a central role in regulating the public transport network. These assessments by integrating an analysis methodology, an effect assessment to facilitate prioritisation, and quantification to offer substantiated support for the decisions that operators may decide on.

Motivated by the real needs of a bus network operator, we would like to bring answers to the following questions:

*   What are the factors (e.g. weather, congestion, road characteristics, etc.) that influence the commercial speed of urban buses?

*   How to describe numerically the impact of specific factors?

*   How to estimate this impact figure for a given public transport network, based on data?

### IV. COMMERCIAL SPEED IMPACT FACTORS IDENTIFICATION

In this section we present our method to identify and characterize the factors that impact the commercial speed of buses. Our methods are data-oriented: we first discuss the data representation questions (Subsection IV-A) and then we present how to analyse the impact factors (Subsection IV-B) based on the analysis of the collected data.

As our method is based on data analysis, it is important that the collected dataset is sufficiently large (with preferably at least more than 2 features), such that we can discover the relevant connections from data.
## A. Data representation

To produce a fairly accurate model of the network, the first task is to gather all the data that can directly or indirectly represent a public transport network. This may include information on network architecture, operations, network policy, etc. We are particularly interested in data that provides a temporal context for the network (information about the day, local or global events, daily traffic status, etc.), as well as the elements structuring its environment (road features, route distance, spatial location, road policies such as roads speed limits, etc.), but also information specific to bus operations (bus frequency, bus ridership, bus type, line type, etc.). The richer the information are, the more complex the dataset will be, and possibly the more expressive it will be to describe how the network operates. Thanks in particular to the Commission Delegated Regulation of the European Union<fnref n="1" />, access to this type of transport data has become a little simpler for European transport networks data, even if these data availability remains rather limited. Access to operational data such as Automatic Vehicle Localisation (AVL) is preferable, but not always accessible to the public while these types of data are available to the majority of European public transport operators. Most importantly, we need to be able to obtain commercial or network speeds, or at least the necessary information to calculate such speeds.

Having collected all this data, the aim is to be able to accurately reconstruct the entire history of what happened on the bus network. The most appropriate format seems to be to reconstruct each bus passage at an inter-station. In other words, for a bus that has travelled between two stations in the network, combining all the information relating to that specific journey. This is certainly the most challenging step, since it depends greatly on the quantity of data previously retrieved, its quality and the ability to link them (presence or lack of commons keys or commons information between the different databases). For example, for a bus journey at an inter-station, we need to know its commercial speed, as well as all the other available data describing the situation.

The data was structured as follows: public data from the local authority and the operator were used to structure the bus network geographically (its spatial layout in GPS coordinates) as well as the order of the inter-stations. The operator's private data (AVL data) was used to retrieve operating information for each bus run (commercial speed, number of passengers, diversions, temporal information, etc.). They were associated with our network structure on the basis of common keys from the departure station to the arrival station. Next, the Open-StreetMap data was collected and merged with our dataset using GPS locations. Finally, some information was calculated from the collected data (e.g. inter-station distances were calculated using all the GPS coordinates forming the route). The data obtained are the temporal and spatial characteristics for each bus passage at an inter-station. For a specific bus journey,

we have the time, what it has encountered as a temporal event and as a constant event, characteristic of the inter-station.

## B. Component impact analysis

In this section, we describe a method to assess the impact that different features have on the commercial speed of buses. Following the methodology proposed in the previous section, we end up with a data set $D$ composed of $N$ rows and $p+1$ columns. The columns are denoted $x_1, x_2, \dots, x_p$ and $C_s$. $C_s$ represent the commercial speed on an inter-arrival and the variables $x_1$ to $x_p$ represent the features for which we want to assess the impact (for instance the number of roundabouts, or stops and this inter-arrival, ...). More details about the application case will be given in Section V. We will keep general notations here. The rows of this data set represent recordings of a bus path between two stops (for different bus lines, time of the day and of the week, ...). We hence are interested in assessing the impact that the variables $x_1$ to $x_p$ have on $C_s$, and not only individually but also mutually.

For that purpose, the data set $D$ is split into a training set $T$ and a validation set $V$. Regression models are then fitted to model $C_s$ as a function of $x_1, x_2, \dots, x_p$:

$$C_s \approx f(x_1, x_2, \dots, x_p) \quad (1)$$

The function $f$ is the regression function. We will consider here three different regression functions: a linear one, an exponential one and a polynomial one. The linear function (denoted $f_1$) is defined by $f_1(x_1, x_2, \dots, x_p) = \beta_0 + \sum_{i=1}^p \beta_i x_i$. The exponential regression function is defined by $f_e(x_1, x_2, \dots, x_p) = c + \sum_{i=1}^p a_i e^{(b_i x_i)}$. The polynomial regression function is defined by $f_p(x_1, x_2, \dots, x_p) = q_{0i} + \sum_{i=1}^p \sum_{j=1}^6 q_{ij} x_i^j$.

Before selecting the degree 6 polynomial model, we tested polynomials of degrees 2 to 5. These were less efficient and polynomials of degree 6 were time consuming to calculate, so we didn't try the higher degrees.

For any subset of variables in $\{x_1, \dots, x_p\}$, a regression model (either linear, exponential or polynomial) can be fitted using the training set. To assess the performance of a regression model, we use here two different criteria: the Mean Average Error (MAE) and the Root Mean Square Error (RMSE). They are defined as follows:

$$RMSE(y_i, \hat{y}_i) = \sqrt{\frac{\sum_{i=1}^{n} (\hat{y}_i - y_i)^2}{n}} \quad (2)$$

$$MAE(y_i, \hat{y}_i) = \frac{\sum_{i=1}^{n} | \hat{y}_i - y_i |}{n} \quad (3)$$

where $y_i$ are the real values of the target variable ($C_s$ in our application case), $\hat{y}_i$ are the prediction made by the considered regression model, $\bar{y}$ is the average value of $y$ and $n$ represents the number of samples on which the model is evaluated. In our case, RMSE and MAE will be computed on the training set (after the train model fitting).

We explain here the three steps that we have used to analyse and evaluate the impact of the features on $C_s$:

* we study the impact of the features individually

<footnote n="1">¹https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32017R1926</footnote>
* we identify a set of factors through a "forward feature selection" technique

* we compute an impact factor score for each feature

1) **Study of the features individually:** For each feature $x_i$, we build three regression models on the training set to predict $C_s$ using $x_i$: a linear one ($m_l^i$), an exponential one ($m_e^i$) and a polynomial one ($m_p^i$). Hence, 3p models are created here. For each of these models, the performance criteria presented above (RMSE, MAE) are computed. Using these criteria, we can select for each feature $x_i$ the model ($m_l^i$, $m_e^i$ or $m_p^i$) that is more adapted to predict $C_s$ using $x_i$.

The features that most impact the commercial speed can be found by comparing the values of RMSE, and MAE the best model selected for each feature. However, according to this study, we only assess the impact of individual features on the commercial speed. We will see in the next steps how to assess the impact of the different features in a coordinated way.

2) **Forward feature selection:** Amongst the entire set $\mathcal{F} = \{x^1, \dots, x^p\}$ of features, the aim of this step is to select a subset of features that have the strongest impact on $C_s$. The number of subsets of a set with $p$ elements is $2^p - 1$. Hence, exhaustive search is often prohibited when $p$ is larger than 15 or 20. Approximate searches have been designed in the multivariate regression analysis domain to faster the search of the best subset. One of the most famous method is the forward feature selection algorithm [24]. It takes as input a training set composed of instances described by $p$ features. Using a regression function $f$ and a comparison criteria $Cr$, it estimates the subset of features $\sigma$ that leads to the best value of $C_r$. It works as follows:

1) initialization: $\sigma = \{\}$

2) $\forall x \in \mathcal{F}$ and $x \notin \sigma$, fit the regression model $C_s = f(\sigma \cup x)$ and compute $Cr_x$ its performance according to $Cr$

3) Let $x^b$ be the feature such that $Cr_{x^b}$ is the best

4) if the stopping criterion is met then stop, otherwise $\sigma = \sigma \cup x^b$ and repeat the steps (2) and (3)

At the end of these steps, $\sigma$ contains the set of selected features. In Section V, we detail the application of this algorithm to our case study (i.e., which regression function, which comparison criteria, which stopping criterion, etc).

3) **Impact factor score:** For the features that have been selected by the previous step, we will now determine an impact factor score that reflects the impact that a feature has on the commercial speed of a bus. When a regression model is built using the training set, we apply a feature permutation importance algorithm for each feature selected in order to create an importance by scoring each feature [4]. The concept behind "permutation feature importance" is to randomly permute the feature values between all the available rows. Each model are run again with an unique shuffled feature and each performance criteria (RMSE, MAE) are computed again. The principle of the shuffled feature is to select a specific feature and randomly shuffle each of its values together. For a Feature $x^b$, this transforms the set of its values $\{y_1, y_2, \dots, y_n\}$ into $\{y_3, y_n, y_{n-5}, \dots, y_{n-2}\}$ for

example. The performance criteria of each model are used as baseline and the delta between each shuffled model and the baseline are computed, $\Delta_{x^b} = Crs_{x^b} - Cr_{x^b}$, with $Cr_{x^b}$ the performance of the shuffled feature and $Cr_{x^b}$ the performance of the baseline. The value of the calculated delta of each feature is used as the impact score of the features. Indeed, a high value of $\Delta$ indicates that the RMSE or MAE has increased a lot when a feature was shuffled, meaning that this feature is important to keep a low RMSE or MAE.

## V. EXPERIMENTATION

For experimental purposes, any system or network that can be represented by a dataset containing several different components can be analysed using the methodology set out in section IV. Here, we will focus on complex real-world systems such as public transport networks, and more specifically, bus networks, where many elements of the environment could have a direct impact on the network.

### A. Case study

For this article, the case of the Rennes metropolitan area was chosen. Since October 24th, 2022, STAR network has a second metro line and about 70 bus routes serving the Rennes metropolitan area. The new metro line's opening in 2022 required an in-depth rebuilding of the network, which reduced surface travel, that often used to be problematic in the morning and evening peak hours. Since the late 1980s, Keolis Rennes, a private company, has been operating the STAR network, which is owned by the Rennes Métropole, a public administrative entity of the Rennes metropolitan area.

In this paper, we used data that was collected from October 24th, 2022 to February 10th, 2023 to study this network. During this period, the network consisted of 70 major lines.

### B. Data sources

The data was collected from the operator's internal sources as well as from public available data sources to maximize the search for things that could have an effect on the bus network.

* **Network referential data:** Data source regularly updated and made accessible by the operator. Along with historical and current data, it includes a variety of network topological data. — *Open source*<fnref n="2" />

* **Automatic Vehicle Location (AVL):** Operator's first operational data production is the Automatic Vehicle Location data. It contain a lot of information about the bus operation, including its current location. — *Internal source*

* **Ticketing data:** The ticketing data relates to the passengers' ticket validation when boarding the bus. These data allow to estimate the number of passengers boarding the bus. — *Internal source*

* **OpenStreetMap (OSM):** The description of the environment itself is a crucial component in showing how a bus evolved in its surroundings. As long as the community

<footnote n="2">²https://data.explore.star.fr/explore/</footnote>
<table><caption>TABLE I
SAMPLE OF ALL THE COMPONENTS/FEATURES USED IN THIS PAPER
(TOTAL: 35)</caption><thead><tr><td>Component name</td><td>Description</td></tr></thead><tbody><tr><td>overrunning</td><td>Nb. of bus encounter at the same station at the same time (frequency)</td></tr><tr><td>time_stopped</td><td>Time stopped at the destination station</td></tr><tr><td>lanes_max</td><td>Maximal nb. of lanes</td></tr><tr><td>lanes_1</td><td>Nb. of road with 1 lane</td></tr><tr><td>lanes_2</td><td>Nb. of road with 2 lane</td></tr><tr><td>lanes_3</td><td>Nb. of road with 3 lanes</td></tr><tr><td>dist</td><td>Distance between 2 stations</td></tr><tr><td>roundaboutProp</td><td>Nb. of roundabout per 100 m (proportion)</td></tr><tr><td>mini_roundaboutProp</td><td>Nb. of mini-roundabout per 100 m (proportion)</td></tr><tr><td>turning_circleProp</td><td>Nb. of turning circle per 100 m (proportion)</td></tr><tr><td>traffic_calmingProp</td><td>Nb. of traffic calming device per 100 m (proportion)</td></tr><tr><td>give_WayProp</td><td>Nb. of give way per 100 m (proportion)</td></tr><tr><td>railwayProp</td><td>Nb. of railway per 100 m (proportion)</td></tr><tr><td>stopProp</td><td>Nb. of stop per 100 m (proportion)</td></tr><tr><td>trafficSignalsProp</td><td>Nb. of traffic signals per 100 m (proportion)</td></tr><tr><td>maxspeed_maxProp</td><td>% of road with the highest speed possible</td></tr><tr><td>maxspeed_20Prop</td><td>% of road with 20 km/h limitation</td></tr><tr><td>maxspeed_30Prop</td><td>% of road with 30 km/h limitation</td></tr><tr><td>maxspeed_50Prop</td><td>% of road with 50 km/h limitation</td></tr><tr><td>maxspeed_70Prop</td><td>% of road with 70 km/h limitation</td></tr><tr><td>maxspeed_80Prop</td><td>% of road with 80 km/h limitation</td></tr><tr><td>maxspeed_90Prop</td><td>% of road with 90 km/h limitation</td></tr><tr><td>maxspeed_110Prop</td><td>% of road with 110 km/h limitation</td></tr><tr><td>length</td><td>Length of the bus</td></tr><tr><td>doors</td><td>Nb. of doors</td></tr><tr><td>validation</td><td>Nb. of validation at the destination station in the bus</td></tr><tr><td>freeflowProp</td><td>% of road with freeflow traffic</td></tr><tr><td>slowedProp</td><td>% of road with slowed traffic</td></tr><tr><td>congestedProp</td><td>% of road with congested traffic</td></tr><tr><td>heavyProp</td><td>% of road with heavy traffic</td></tr><tr><td>impossibleProp</td><td>% of road with impossible traffic</td></tr><tr><td>unknownProp</td><td>% of road with unknown traffic</td></tr><tr><td>hour</td><td>Hour of the day</td></tr><tr><td>weekday</td><td>Day of the week (1 = Monday, ..., 7 = Sunday)</td></tr><tr><td>month</td><td>Month of the year</td></tr></tbody></table>

enters accurate data, this data source is reliable. The quantity of potential contributors is sufficient for major towns like Rennes to make it a reasonably full data source. — Open source<fnref n="3" />

* **Floating Cars Data (FCD):** Real-time car speed and position data is known as FCD. Whether it is an in-car GPS or a smartphone, this information is instantly obtained from the GPS in the car. The amount of driven cars, the precision of the on-board GPS, the quality of the data transfer, etc. are all important factors for the reliability of this data [25]. Every minute, the company Autoroute Trafic retrieves these data and makes them accessible in open access. — Open source<fnref n="4" />

Finally, for each bus travel at an inter-stations, we have: concerned inter-stations, times (arrival, departure, stop), commercial speed, road elements encounter (stops, giveaway, crossing, chicane, etc.), congestion (if available), bicycles count (if available), location, bus type, line type, number of other bus encounter, the number of ticket validations in the bus. The Table I shows samples of the variables used in this paper.

<table><caption>TABLE II
RESULT OF THE STEP-BY-STEP ANALYSIS WITH ALL THE AVAILABLE DATA</caption><thead><tr><td></td><td>Linear</td><td>Polynomial</td><td>Exponential</td></tr></thead><tbody><tr><td>Nb. of features</td><td>7</td><td>23</td><td>5</td></tr></tbody></table>

<table><caption>TABLE III
SAMPLE OF THE INDIVIDUAL CLASSIFICATION AND SCORING</caption><thead><tr><td>Feature</td><td>RMSE</td><td>MAE</td><td>Type</td></tr></thead><tbody><tr><td>time_stopped</td><td>0.087761</td><td>0.060593</td><td>polynomial</td></tr><tr><td>lanes_max</td><td>0.096419</td><td>0.069366</td><td>polynomial</td></tr><tr><td>dist</td><td>0.089557</td><td>0.065597</td><td>polynomial</td></tr><tr><td>roundaboutProp</td><td>0.096643</td><td>0.069578</td><td>linear</td></tr><tr><td>mini_roundaboutProp</td><td>0.096524</td><td>0.069332</td><td>polynomial</td></tr><tr><td>traffic_calmingProp</td><td>0.095961</td><td>0.069444</td><td>polynomial</td></tr><tr><td>give_WayProp</td><td>0.093736</td><td>0.067378</td><td>polynomial</td></tr><tr><td>maxspeed_30Prop</td><td>0.095600</td><td>0.069023</td><td>polynomial</td></tr><tr><td>maxspeed_50Prop</td><td>0.095767</td><td>0.068577</td><td>polynomial</td></tr><tr><td>length</td><td>0.095987</td><td>0.069195</td><td>polynomial</td></tr><tr><td>validation</td><td>0.096326</td><td>0.069229</td><td>linear</td></tr><tr><td>hour</td><td>0.096274</td><td>0.069187</td><td>polynomial</td></tr><tr><td>weekday</td><td>0.096620</td><td>0.069424</td><td>polynomial</td></tr></tbody></table>

### C. Impact factors determination

With such an enriched data set, it is then feasible to determine the numerous relationships between the various components and their relative evolution in regard to one another. It does not matter if the data are independent in this case; the modelling will take that into account.

As stated in Section IV, each component goes through a preliminary individual analysis to identify the primary models that most accurately represent the different data. We will be able to test various global models after determining the majority models, and the best model will yield the impact coefficients that we will use in this case.

The data available is 64 million bus trips. To limit our computing time, we have 10 times randomly selected 9,000 bus journeys for training the model and 1,000 for testing/validation. The results of RMSE and MAE are the mean of these 10 times.

1) **Individual fetaure analysis:** As mentioned in the section IV, the first step is to analyse individually all the feature to select the most appropriate model between $m_i$, $m_e$ and $m_p$.

The table III contains the results of the individual analysis. These results are obtained after a trial-and-error analyse of several possibilities. For some of these variables, such as the type of location or the type of line, are not relevant to a representation using these models. In fact, these are categorical variables and therefore do not offer a correct representation for the models tried here. For a better understanding of the distribution of selections in each category, a more simplified version of the results is presented as well in the table II. According on the Table II results, exponential, linear, and polynomial models are all together appropriate to represent the features.

2) **Forward selection and network scoring:** We have chosen the exponential, linear, and polynomial models for a thorough study based on the results shown in Table II.

In an effort to build a more efficient model, we also tried to create an hybrid model that could perform better than the

<footnote n="3">³https://www.openstreetmap.org/</footnote>

<footnote n="4">⁴https://dkan.autoroutes-trafic.fr/?q=dataset/donn%C3%A9s-trafic-rennes-m%C3%A9tropole</footnote>
<table><caption>TABLE IV
SAMPLE OF RESULT OF THE STEP-BY-STEP ANALYSIS WITH ALL AVAILABLE DATA</caption><thead><tr><th>Step</th><th>Exponential</th><th>Polynomial (6th degree)</th><th>Hybrid (exp.+lin.+poly.)</th></tr></thead><tbody><tr><td></td><td>RMSE</td><td>RMSE</td><td>RMSE</td></tr><tr><td>1</td><td>0.0855</td><td>0.0850</td><td>0.0850</td></tr><tr><td>2</td><td>0.0752</td><td>0.0748</td><td>0.0748</td></tr><tr><td>3</td><td>0.0724</td><td>0.0721</td><td>0.0720</td></tr><tr><td>4</td><td>0.0705</td><td>0.0702</td><td>0.0700</td></tr><tr><td>5</td><td>0.0692</td><td>0.0693</td><td>0.0688</td></tr><tr><td><b>19</b></td><td><b>0.0667</b></td><td>0.0651</td><td>0.0646</td></tr><tr><td><b>20</b></td><td>0.0667</td><td><b>0.0650</b></td><td>0.0645</td></tr><tr><td>21</td><td>0.0668</td><td>0.0650</td><td>0.0645</td></tr><tr><td>22</td><td>0.0667</td><td>0.0651</td><td>0.0645</td></tr><tr><td><b>23</b></td><td>0.0665</td><td>0.0651</td><td><b>0.0645</b></td></tr><tr><td>24</td><td>0.0665</td><td>0.0651</td><td>0.0645</td></tr><tr><td>30</td><td>0.0667</td><td>0.0654</td><td>0.0645</td></tr><tr><td>31</td><td>0.0668</td><td>0.0655</td><td>0.0645</td></tr><tr><td>32</td><td>0.0706</td><td>0.0656</td><td>0.0646</td></tr><tr><td>33</td><td>0.0731</td><td>0.0657</td><td>0.0646</td></tr><tr><td>34</td><td>0.5512</td><td>0.0660</td><td>0.0648</td></tr><tr><td>35</td><td>0.6912</td><td>0.0663</td><td>0.0649</td></tr></tbody></table>

3 other models. Let $E$ the group of features best represented by an exponential model, $L$ by a linear model and $P$ by a 6th-degree polynomial model. The commercial speed can be calculated as follows:

$$C_s(x_1, \dots, x_p) = c + \sum_{i=1}^{p} \begin{cases} a_i e^{-b_i x_i}, & \text{if } x_i \in E \\ a_i x_i, & \text{if } x_i \in L \\ \sum_{i=1}^{6} q_{ij} x_i^j, & \text{if } x_i \in P \end{cases} \quad (4)$$

Let us perform a forward feature selection for each model, according to the procedure in Section IV, and select the model that, in results, achieves the best score based on the scoring criteria specified in that section. The stopping criterion has been defined as follows: if the model chooses to select a feature that is always zero, $x_0$, over one of the other features $x_i$ that remain in $\mathcal{F}$, it indicates that the other features are no longer relevant to the model. In other words, if a variable that does not explain anything at all starts to become more important than remaining original variables, we consider that these other features will not help in understanding the commercial speed.

The results of the forward selection for the four different kinds of models are given in Table IV. The bolded lines correspond to the last original variable that has been selected before the null variable ($x_0$). The results of MAE score and the linear model are not showed for reasons of clarity and space constraints. The results obtained are not significant for our analysis.

Table IV indicates that among the four approaches evaluated here, the hybrid model performs the best, followed by the exponential model, polynomial model and the linear model. It is interesting to note that, if the polynomial model is the best to model individual variables, it is less true when considering multiple variables together. The computation time to achieve the feature selection for each models was 34 minutes for the exponential model, 5 minutes for the linear model, 6 minutes for the polynomial model and 18 hours for the hybrid model. The hybrid model slightly perform better than the others one

<table><caption>TABLE V
SELECTED FEATURES DURING THE STE-BY-STEP SELECTION</caption><thead><tr><th>Step</th><th>Exponential</th><th>Polynomial (6th degree)</th><th>Hybrid (exp.+lin.+poly.)</th></tr></thead><tbody><tr><td>1</td><td>maxspeed_70_prop</td><td>maxspeed_70_prop</td><td>maxspeed_70_prop</td></tr><tr><td>2</td><td>time_stopped</td><td>time_stopped</td><td>time_stopped</td></tr><tr><td>3</td><td>maxspeed_20_prop</td><td>maxspeed_20_prop</td><td>maxspeed_20 Property</td></tr><tr><td>4</td><td>trafficSignals_prop</td><td>trafficSignals Property</td><td>trafficSignals Property</td></tr><tr><td>5</td><td>dist</td><td>dist</td><td>dist</td></tr><tr><td><b>19</b></td><td><b>maxspeed_max_prop</b></td><td>congested Property</td><td>validation</td></tr><tr><td><b>20</b></td><td>lanes_3</td><td>weekday</td><td>lanes_1</td></tr><tr><td>21</td><td>maxspeed_50 Property</td><td>validation</td><td>maxspeed_max Property</td></tr><tr><td>22</td><td>trafficCalming Property</td><td>railway Property</td><td>stop Property</td></tr><tr><td><b>23</b></td><td>maxspeed_90 Property</td><td>dist</td><td>impossible Property</td></tr><tr><td>24</td><td>overrunning</td><td>length</td><td>roundabout Property</td></tr><tr><td>30</td><td>length</td><td>unkown Property</td><td>slowed Property</td></tr><tr><td>31</td><td>slowed Property</td><td>overrunning</td><td>overrunning</td></tr><tr><td>32</td><td>heavy Property</td><td>slowed Property</td><td>mini_roundabout Property</td></tr><tr><td>33</td><td>unkown Property</td><td>hour</td><td>turning_circle Property</td></tr><tr><td>34</td><td>hour</td><td>turning_circle Property</td><td>maxspeed_80 Property</td></tr><tr><td>35</td><td>weekday</td><td>maxspeed_80 Property</td><td>weekday</td></tr></tbody></table>

but takes much longer to compute all the steps. Hence, the exponential model seems to be a good trade-off between complexity and accuracy of the predictions.

From the results of Table IV and Table V, we can observe different interesting things. The last point at which the RMSE value decreases continuously corresponds to the selection of the null feature for all the models. Beyond that, the RMSE values increases continuously. Hence, for every model, the step right before choosing the null feature corresponds to the optimal values. The polynomial model comes in second place with the best outcomes, behind the hybrid model. For a relatively little performance improvement, the hybrid model is significantly slower than the polynomial model, as was previously mentioned. This is probably due to the least squares approach, used by *curve_fit()* from SciPy, that is used to fit the models. Convergence of the fitting of the hybrid model seems to be difficult to reach, which explains the high computing time.

We can observe that 13 characteristics have been commonly selected by every model. This indicates that these variables should have a strong influence on the commercial speed, but they may not be the only ones.

Then, we have applied the permutation feature importance algorithm, as described in Section IV in order to compute an impact factor associated to each variable selected by a model. For each selected feature of each model, one by one, we randomly shuffle its values and compare the accuracy of the predictions with the baseline of the corresponding model. The results of this method are available in Table VI. The results of MAE score, the linear and hybrid models are not showed for reasons of clarity and space constraints. The results obtained are not significant for our analysis.

We can see in this table that the most discriminating model is the polynomial model. This model is extremely sensitive to road elements and speed limits, and the accuracy of the predictions rapidly decays if these variables are shuffled. On the other hand, the $\Delta_{x^b}$ values for our exponential model, for instance, are quite near which restricts us from describing components that are very discriminating.
<table><caption>TABLE VI
SAMPLE OF MODELS SCORING USING THE PERMUTATION FEATURE
IMPORTANCE</caption><thead><tr><th rowspan="2">Feature</th><th colspan="2">Exponential</th><th colspan="2">Polynomial</th></tr><tr><th>RMSE</th><th>Delta</th><th>RMSE</th><th>Delta</th></tr></thead><tbody><tr><td>time_stopped</td><td>0.1524</td><td><strong>0.0856</strong></td><td>3.8414</td><td><strong>3.7763</strong></td></tr><tr><td>lanes_max</td><td>0.1433</td><td><strong>0.0766</strong></td><td>12.3301</td><td><strong>12.2650</strong></td></tr><tr><td>dist</td><td>0.1466</td><td><strong>0.0798</strong></td><td>-</td><td>-</td></tr><tr><td>traffic_calming Property</td><td>-</td><td>-</td><td>64.6610</td><td><strong>64.5959</strong></td></tr><tr><td>give way Property</td><td>-</td><td>-</td><td>0.7327</td><td><strong>0.6677</strong></td></tr><tr><td>maxspeed_30 Property</td><td>0.1441</td><td><strong>0.0774</strong></td><td>24.3931</td><td><strong>24.3280</strong></td></tr><tr><td>maxspeed_50 Property</td><td>-</td><td>-</td><td>89.9828</td><td><strong>89.9178</strong></td></tr><tr><td>validation</td><td>0.1433</td><td><strong>0.0766</strong></td><td>-</td><td>-</td></tr><tr><td>weekday</td><td>-</td><td>-</td><td>0.5233</td><td><strong>0.4582</strong></td></tr><tr><td>BASELINE</td><td><strong>0.0667</strong></td><td>-</td><td><strong>0.0650</strong></td><td>-</td></tr></tbody></table>

<table><caption>TABLE VII
TOP 5 OF THE MOST IMPACTING COMPONENTS FOR THE POLYNOMIAL
MODEL</caption><thead><tr><th>Rank</th><th>Feature</th><th>Score</th></tr></thead><tbody><tr><td>1</td><td>maxspeed 50 prop</td><td>89,9178</td></tr><tr><td>2</td><td>traffic calming prop</td><td>64,5959</td></tr><tr><td>3</td><td>lanes_1</td><td>62,4360</td></tr><tr><td>4</td><td>maxspeed 30 prop</td><td>24,3280</td></tr><tr><td>5</td><td>congested prop</td><td>15,1429</td></tr></tbody></table>

Our findings lead us to the following conclusions:

* Based on the Table II, the polynomial model best fits individually the data we have.

* Based on the Table IV, the polynomial model has a significant computational time advantage over the hybrid, making it the best-performing model in terms of time - precision.

* We may better discern between most impacting components on a bigger scale thanks to the Table VI's (appendix) $\Delta_{ab}$ of the polynomial model.

Table VII, which includes the five most significant components for the polynomial model, reveals that the first five elements have characteristics in common in that they represent urban streets that are either adjacent to or outside of the downtown area. In the Rennes area, these are high-tension areas where traffic tends to grow rather quickly. Thus, our findings using the polynomial model agree with the feedback that we had from the experts at the bus network operator.

## VI. CONCLUSION AND FUTURE WORK

We presented a methodology how to identify the factors that influence the commercial speed of urban buses. Our method is based on data analysis and requires to collect large amounts of data about the transport network end its operation. We identify the factors through data analysis and machine learning methods. Specifically, our work is based on linear, exponential and polynomial regression models and feature selection methods. To present our method, we conducted extensive experiments on a very rich dataset that we constructed from private and public data sources.

For our case study in Rennes, we showed that using this methodology, we could identify the factors that could impact bus commercial speeds. Additionally, it has made it possible for us to determine an impact coefficient, which enables us to

rank the environment components in order of importance. The public transport network operator, Keolis Rennes, will have support from these results when deciding how to arrange the roads that the buses ride on.

Previous work in the literature are mostly examined how a small limited number of components affect performance of the transport network. We collected and analysed a rich dataset with a large amount of components. We demonstrated that it is feasible to describe a complicated bus environment in terms of data.

Our model produced a coefficient for each variable, which serves as an indicator of its individual impact. The impact of each aspect under consideration can be categorised using these several criteria, either in absolute or relative terms (positive or negative). This allows for the definition of what factors operators should consider when making changes to the network in order to identify the circumstances in which the network performs at its best.

Furthermore, these insights have made it possible to select the most significant factors to include into a machine learning model, giving accurate predictions for the commercial speed on pre-existing bus network parts. This impact has the ability to be measured and may also be used to prioritise the significance of such or such component. Alternatively, failing to consider those who are irrelevant to the modelling and so potentially compromising the modelling's quality.

Individual examinations have brought attention to the implications once again, as well as the addition of components in an exponential model that are more difficult to analyse. Because of their apparent effects, these factors should be considered and not neglected when studying or modelling an urban bus network.

The study carried out in this paper was conducted on the specific case of Rennes with specific data available. However, the methodology remains general. It can be applied to other public transport networks or even other domains where there is a need to select the factors impacting a specific known target. In order to generalise about the impact factors, similar studies should be carried out in the future on cities similar to or completely different from Rennes, using the same data if possible. The results may be very similar, or with significant variations in impact.

The results obtained are the importance of the elements composing the bus environment. These results can be used for a variety of purposes. For example, when experts want to improve existing lines, they now have the support to know which components to modify, remove or add to improve the commercial speed. It can also be useful for making future predictions: in a prediction model, the elements with the highest impact will have a higher score in the regression step. This can also be an asset in discussions between network operators and the local public authority, as they can negotiate with support which structural elements are interesting or uninteresting for the design of new routes.

Subsequent to this work, we plan to use this variable selection to machine learning models that can predict the
commercial speed of buses. In order to construct and plan buses, transport network operators need to be able predict how the network will operate in advance. The most significant and explanatory variables in the network can be directly used to train models thanks to this variable selection, which allows for the retention of those that have the biggest effects. Operator interest would be attracted by a model that could predict commercial speed of buses.

An other potential path to consider would be to carry out this research in a different city network. The outcomes could vary depending on the city where the research was conducted. Further research in similar cities to see if the findings are similar, as well as in completely different cities to see if the findings are completely different, would be highly intriguing.

Despite the size of our dataset, it can be deficient in information. It would be intriguing to add more data sources that might improve the variables used and increase the accuracy of the models. Road construction, accidents, and other regular events with variable duration are among the data that can be relevant.

And last, this work caught the interest of Keolis Rennes, the company that operates the network examined in this paper, and it is currently investigating the possibility of applying these results to provide results on journey times (which can be derived from commercial speed).

## REFERENCES

[1] A. Ngoc, K. Hung, and V. Tuan, "Towards the development of quality standards for public transport service in developing countries: Analysis of public transport users' behavior," *Transportation Research Procedia*, vol. 25, pp. 4560–4579, 2017, world Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2352146517306610

[2] V. Maraglino, L. dell'Olio, D. Borri, and A. Ideas Portilla, "Methodology for a study of the perceived quality of public transport in santander," *Procedia - Social and Behavioral Sciences*, vol. 160, pp. 499–508, 2014, xI Congreso de Ingenieria del Transporte (CIT 2014). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1877042814062648

[3] H. M. Noor, N. Nasrudin, and J. Foo, "Determinants of customer satisfaction of service quality: City bus service in kota kinabalu, Malaysia," *Procedia - Social and Behavioral Sciences*, vol. 153, pp. 595–605, 2014, aMER International Conference on Quality of Life, AicQoL2014KotaKinabalu, The Pacific Sutera Hotel, Sutera Harbour, Kota Kinabalu, Sabah, Malaysia, 4-5 January 2014. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1877042814055347

[4] L. Breiman, "Random forests," *Machine Learning*, vol. 45, pp. 5–32, 10 2001.

[5] W. Liu, Y. Chen, H. Li, and H. Zhang, "Quantitative study on road traffic environment complexity under car-following condition," *Sustainability*, vol. 14, no. 10, 2022. [Online]. Available: https://www.mdpi.com/2071-1050/14/10/6251

[6] Z. Hu, L. Shidong, H. YIN, M. Minghui, and L. Ronmeng, "A prediction model for bus arrival time at bus stop considering signal control and surrounding traffic flow," *IEEE Access*, vol. 8, pp. 127672–127681, 2020.

[7] X. Courtois and F. Dobruszkes, "The (in)efficiency of trams and buses in brussels: a fine geographical analysis," *General collection*, Jun 2008. [Online]. Available: https://doi.org/10.4000/brussels.603

[8] V. Stover and E. McCormack, "The impact of weather on bus ridership in pierce county, washington," *Journal of Public Transportation*, vol. 15, pp. 95–110, 2012. [Online]. Available: http://doi.org/10.5038/2375-0901.15.1.6

[9] Q. Miao, E. W. Welch, and P. Sriraj, "Extreme weather, public transport ridership and moderating effect of bus stop shelters," *Journal of Transport Geography*, vol. 74, pp. 125–133, 2019. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0966692318300681

[10] N. S. Ngo, "Urban bus ridership, income, and extreme weather events," *Transportation Research Part D: Transport and Environment*, vol. 77, pp. 464–475, 2019. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1361920918309945

[11] X. Li, L. Shi, H. Li, Q. Liu, and J. Chen, "What affects bus passengers' travel time? a view from the built environment and weather condition," *Journal of Advanced Transportation*, vol. 2023, no. 1, p. 6629507, 2023. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1155/2023/6629507

[12] M. A. Turnquist, "Strategies for improving reliability of bus transit service," *Transportation Research Record*, no. 818, pp. 7–13, 1981. [Online]. Available: http://onlinepubs.trb.org/Onlinepubs/trr/1981/818/818-002.pdf

[13] H. J. Kim, "Performance of bus lanes in seoul: Some impacts and suggestions," *IATSS Research*, vol. 27, no. 2, pp. 36–45, 2003. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S038611214601424

[14] M. D. Abkowitz and I. Engelstein, "Factors affecting running time on transit routes," *Transportation Research Part A: General*, vol. 17, no. 2, pp. 107–113, 1983. [Online]. Available: https://www.sciencedirect.com/science/article/pii/019126078390064X

[15] A. Severino, G. Pappalardo, I. O. Olayode, A. Canale, and T. Campisi, "Evaluation of the environmental impacts of bus rapid transit system on turbo roundabout," *Transportation Engineering*, vol. 9, p. 100130, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2666691X22000288

[16] M. Li and Y. Li, "Bus predictive-control method considering the impact of traffic lights," *Journal of Advanced Transportation*, vol. 2022, no. 1, p. 5280109, 2022. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1155/2022/5280109

[17] J. Wahlstedt, "Impacts of bus priority in coordinated traffic signals," *Procedia - Social and Behavioral Sciences*, vol. 16, pp. 578–587, 2011, 6th International Symposium on Highway Capacity and Quality of Service. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S187704281101024X

[18] Y. Guillemette, C. Morency, H. Verreault, and M. Trépanier, "Performance indicators of a bus intercity service," 2019. [Online]. Available: https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2019-39.pdf

[19] R. Fernandez, P. Zegers, G. Weber, and N. Tyler, "Influence of platform height, door width, and fare collection on bus dwell time. laboratory evidence for santiago de chile," *Transportation Research Record Journal of the Transportation Research Board*, vol. 2143, pp. 59–66, 03 2010.

[20] A. Tirachini, "Bus dwell time: the effect of different fare collection systems, bus floor level and age of passengers," *Transportmetrica A: Transport Science*, vol. 9, no. 1, pp. 28–49, 2013. [Online]. Available: https://doi.org/10.1080/18128602.2010.520277

[21] N. Zacharof, O. Özener, S. Broekaert, M. Özkan, Z. Samaras, and G. Fontaras, "The impact of bus passenger occupancy, heating ventilation and air conditioning systems on energy consumption and co2 emissions," *Energy*, vol. 272, p. 127155, 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0360544223005492

[22] C. Cortes, J. Gibson, A. Gschwender, M. Munizaga, and M. Zuniga, "Commercial bus speed diagnosis based on gps-monitored data," *Transportation Research Part C: Emerging Technologies*, vol. 19, no. 4, pp. 695–707, 2011. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0968090X10001713

[23] A. Valencia and R. Fernandez, "A method to calculate commercial speed on bus corridors," *Traffic Engineering and Control*, vol. 56, pp. 215–221, 06 2012.

[24] H. Liu and R. Setiono, "Incremental feature selection," *Applied Intelligence*, vol. 9, 06 1998.

[25] S. Banach, "Betrouwbaarheid en toepassingen van floating car data," *Proceedings of Statistics Canada Symposium*, Jun 2013. [Online]. Available: https://research.tue.nl/en/studentThesis/betrouwbaarheid-entoepassingen-van-floating-car-data