# Forecasting Passenger Flow Distribution on Holidays for Urban Rail Transit Based on Destination Choice Behavior Analysis

Authors: Enjian Yao; Junyi Hong; Long Pan; Binbin Li; Yang Yang; Dongbo Guo
Journal: Journal of Advanced Transportation
 (2021)

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## Abstract

Passenger travel flows of urban rail transit during holidays usually show distinct characteristics different from normal days. To ensure efficient operation management, it is essential to accurately predict the distribution of holiday passenger flow. Based on Automatic Fare Collection (AFC) data, this paper explores the passengers’ destination choice differences between normal days and holidays, as well as one-way tickets and public transportation cards, which provides support for variable selection in modeling. Then, a forecasting model of holiday travel distribution is proposed, in which the destination choice model is established for representing local and nonlocal passengers. Meanwhile, explanatory variables such as land matching degree, scenic spot dummy, and level of service variables are introduced to deal with the particularity of holiday passengers’ travel behavior. The parameters calibrated by the improved weighted exogenous sampling maximum likelihood (WESML) method are applied to predict passenger flow distribution in different holiday cases with annual changes in the metro network, using the data collected from Guangzhou Metro, China. The results show that the proposed model is valid and performs better than the other comparable models in terms of forecasting accuracy. The proposed model has the capability to provide a more universal and accurate passenger flow distribution prediction method for urban rail transit in different holiday scenarios with network changes.


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## Body

## 1. Introduction

With the development of the economic level, the travel activities and frequencies of urban residents continue to increase, which leads to the rapid growth of urban residents’ demand for urban public transport. Urban rail transit has developed rapidly in recent years, and its superiority of traffic volume, speed, and punctuality are popular among people, which helps spur a boom in urban rail construction [1]. In recent years, a large number of new lines have opened and connected to the metro network, making the network operation effect of many cities particularly evident, significantly affecting regional accessibility and passenger flow distribution in the metro network. Furthermore, in regard to holidays, because of the exceptional flexibility of departure time and the diversity of destinations, the passenger travel characteristics are quite distinct from normal days, and the spatiotemporal distribution of holiday travel demand presents complex characteristics [2, 3].With the rapid change of the metro network, the operations have undergone quantitative and qualitative changes [4]. The particularity of holidays also aggravates travel demand’s complexity, which poses a significant challenge to the metro system. Besides, the same holiday only occurs once a year, which is not conducive to study the characteristics in terms of lacking data sources. Therefore, to effectively organize the large passenger flow and alleviate traffic congestion during holidays, it is essential to accurately predict the distribution of holiday passenger flow, which is the basis of a reasonable train operation plan-making and the development of passenger flow induction strategy.The traditional four-step methods and their modification models have been widely used in passenger flow distribution forecasting. It mainly includes the aggregate model method based on statistical rules of historical data and the disaggregate model method based on behavior analysis.In the study of the aggregate model methods, many researchers have investigated the gravity model by improving it in different contexts. Grosche et al. [5] proposed two gravity models to estimate the air passenger flow between city-pairs. They introduced geoeconomic variables describing the general economic activity and geographical characteristics as independent factors. Wang et al. [6] combined the gravity model considering the distance and free-flow travel time with the Fratar method to predict the seed O-D matrix of the expressway. More recently, Ren et al. [7] proposed three types of land-use function complementarity indices introduced into spatial interaction to improve the gravity model. In these studies, the appropriate variables are introduced to modify the model. Besides, the constrained gravity model is also used as a researching point. Tsekeris and Stathopoulos [8] used a doubly constrained gravity model that additionally incorporates the intraperiod evolution for forecasting the dynamic trip distribution. Jin et al. [9] proposed an O-D estimation model based on the doubly constrained gravity model, where the comparison of singly and doubly constrained models was made. However, the aggregate gravity model tends to overestimate when the distance-deterrence function is small, and the variables are usually less and simple, which cannot reflect the forming mechanism of passenger flow and travel behavior objectively.The disaggregate model can reveal the internal mechanism of the passengers’ destination choice from the perspective of behavior interpretation by establishing definable variables. Specifically, previous studies on the disaggregate model have focused on travel behavior analysis and demand forecasting. For example, in the research of influencing factors of travel behavior, Tsirimpa et al. [10] proposed a multinomial logit model and a mixed multinomial logit model to examine the impact of information acquisition on switching travel behavior. Yang et al. [11] proposed multinomial and nested logit models to analyze battery electric vehicle drivers’ charging and route choice behaviors. Nguyen-Phuoc et al. [12] adopted a multinomial logit model to explore factors affecting changes in the event of major public transport disruptions. In addition, the discrete choice modeling technology based on random utility-based is mainly used for destination choice modeling. Faghih-Imani [13] used a multinomial logit model to study the decision process of identifying destination locations at a bicycle station. Kelly [14] built multinomial logit models to analyze the destination choice behaviors of pedestrians within an entire region. Orvin [15] developed a random parameter latent segmentation-based logit model to investigate trip destination choice behavior of the dockless bike-sharing users. These studies show that individual attributes and alternative factors influence passenger behavior and the decision process, assisting transit agencies in getting management guidance.Focusing on the demand forecasting, Timmermans [16] proposed a model combining transportation mode selection and destination selection and predicted shopping-oriented travel. To strengthen the forecasting power, Jovicic and Hansen [17] constructed a nested logit model, where logsums integrate generation, distribution, and mode choice models as submodels. Ashiabor et al. [18] developed the nested and mixed logit model to estimate county-to-county travel demand. Travel time, cost, and traveler’s household income were used in the explanatory variables. Furthermore, recent studies [19] proposed a multistage demand forecasting model that considers the discrete choice approach, such as the binomial and multinomial logit model, for each decisional level. Moreover, Li [20] presented a new itinerary-based nonlinear demand estimator that estimates the distribution of demand based on a nested logit model. These studies contribute to the accurate prediction of travel demand with the improved disaggregate model. However, it is usually necessary to use questionnaires, such as the stated and revealed preference surveys, to obtain the data that include individual and alternative attributes for studying the behavioral characteristics. When applied to prediction, it is easy to be restricted by data conditions and difficult to use effectively.In addition, many emerging data mining technologies and methods are used to study traffic or passenger flow demand. Ye and Wen [21] proposed a destination choice model based on link flows by constructing algorithms observing the detected data from part of the links. By using data mining, Wang et al. [22] developed cell phone location tracking algorithms to track cross-region traffic activities and derived the O-D traffic flow and travel demand. In the machine learning approaches, Wang et al. [23] designed a grid embedding network via graph convolution and established a multitask learning network for forecasting the demands of O-D pairs in ride-hailing. Although the prediction accuracy of the data-driven approach depending on long-term collection may be higher, it is hard to apply the network structure changes because of lacking the newly added stations’ data in the metro. Moreover, it is often a black-box process that does not illustrate the internal behavior mechanism.Generally, due to the holidays that occurred only once a year, it is not easy to continuously collect stable and long-term data. And with the rapid development of the metro system, the network structure of holidays usually changes every year, which makes it hard to use the statistical models for prediction. Previous relevant studies focused on researching the passenger flow on normal days. However, little work has explored passengers’ choice behavior to construct special variables to effectively forecast the scenarios of holidays in the metro system. Besides, since the source of disaggregate data limits the forecasting application, new data sources are considered to replace the conventional questionnaires in this paper.At present, the Automatic Fare Collection (AFC) system is widely adopted in the urban rail transit system, which is the main support data in this paper. Under the premise of ensuring validity, this paper applies the aggregate data obtained by the AFC to the disaggregate model by modifying the maximum likelihood estimation method, which overcomes the difficulty of getting the disaggregate model data. Based on fully exploiting the holiday passenger travel rules and considering the differences in the choice behavior of different ticket type passengers, this paper constructs a holiday passenger flow distribution prediction model, in which some novel explanatory variables (such as land matching degree) are introduced. The proposed model structure can not only be suitable for the changes of urban rail transit network structure but also take into account the unique characteristics of holidays so as to have good interpretability.The remainder of this paper is organized as follows. In the next section, the holidays’ data collection effort and passenger flow characteristics are analyzed herein. Then, the modeling methodology and the explanatory variables of the utility function are described. After that, the proposed model is estimated and applied to the holiday distribution forecasting with comparisons of other traditional methods. Finally, concluding remarks are presented in the last section.


## 2. Data and Passenger Flow’s Characteristic

### 2.1. Data

Urban rail transit adopts the AFC system to implement management methods such as ticketing, ticket checking, and billing. The data are gathered and transmitted into the center and automatically store passenger travel information. The data types are shown in Table1. Under such limited data conditions and types, how to use them to construct a forecasting model suitable for the holiday scenario is the primary goal. In data processing, the data cleaning has been done by identifying outliers, such as judging whether the enter and exit stations are inconsistent, whether the enter and exit time, and the in-train time are reasonable. Besides, the stations are regarded as transportation analysis zones (TAZs) in the urban rail transit system. The boarding (origin) and alighting (destination) stations of passengers’ trips can be obtained from the AFC system directly.Table 1
The Automatic Fare Collection data types.
NameField typeFormCard typeVarcharOne-way ticket, public transportation card, etc.Card numberInt1000139∗∗∗Enter lineVarcharLine 1, Line 2, etc.Enter station nameVarcharGuangzhou East, Donghu station, etc.Enter timeDatetime“2016-01-01 08 : 00 : 00”Exit line nameVarcharLine 1, Line 2, etc.Exit station nameVarcharGuangzhou East, Donghu station, etc.Exit timeDatetime“2016-01-01 08 : 00 : 00”There are eight lines and 140 stations in Guangzhou Metro by the beginning of 2016. The daily average of raw data amounts to more than 4 million that need further processing. And more than one million passengers use one-way tickets per day during New Year’s Day, which is almost 1.84 times the weekdays. Compared with January 1, 2016, there are seventeen new stations and three new lines connected to the network on January 1, 2017. The road network structure has tremendous changes.


### 2.2. Passenger Flow’s Characteristics

Based on Guangzhou Metro’s AFC data, the passenger flow of each station during the New Year’s Day holiday from 2016 to 2017 is collected, and some travel characteristics have been found. The passenger flow, for instance, is closely related to the nature of land-use and the intensity of development around stations.As shown in Figure1, the entrance passenger flows of four typical stations from December 30, 2015, to January 4, 2016, are given. The passenger flow of Zhujiangxincheng station, which is dominated by office areas, declined significantly during the New Year’s Day. Similarly, the passenger flow of Dashadong station also decreased, as residential areas surround there. However, Guangzhouta and Beijinglu stations’ passenger flow increased significantly during the holidays, with the main areas, respectively, surrounded by scenic spots and commercial districts.Figure 1
Entrance passenger flow of typical stations during New Year’s Day.Similarly, the passenger flow, from the origin station to the destination station (O-D station) during the holidays, shows different distinct characteristics, compared with weekdays. As shown in Figure2, there are different passenger flow trends between O-D stations with different land-use types, and some of which increased significantly in holidays, while others, such as residential stations to office stations, dropped significantly.Figure 2
Comparison of O-D passenger flow during weekdays and New Year’s Day in 2016.From another perspective, there are also great differences in the distribution of people who use one-way tickets and public transportation cards during holidays. Generally, many one-way passengers are nonlocal passengers, who tend to go to scenic spots, business districts, and hub stations. In contrast, transportation card passengers are mostly local residents, whose travel purposes are diversified. This characteristic of choice behavior is especially evident during holidays. As shown in Figure3, the passenger flow of one-way tickets and public transportation cards at Guangzhouta and Beijinglu stations has increased, while the growth rate of one-way ticket is significantly higher, indicating that the stronger attraction of one-way ticket passengers.Figure 3
Comparison of passenger flow between one-way ticket and public transportation card in 2016. (a) Guangzhouta station. (b) Beijinglu station.
(a)(b)Furthermore, other characteristics can also be obtained by analyzing the passenger flow. For example, the O-D passenger flow on the same line is usually larger than that on different lines. And in the case of satisfying the purpose of passengers, they would give priority to the destination with a short ride time and transfer time. However, these features are influenced by many factors. They should be reflected in some explanatory variables to analyze how various factors jointly affect the behavior and improve the subsequent forecasting performance when modeling. Next, the approach considering passenger flow’s characteristics of holidays is introduced in detail.


## 2.1. Data

Urban rail transit adopts the AFC system to implement management methods such as ticketing, ticket checking, and billing. The data are gathered and transmitted into the center and automatically store passenger travel information. The data types are shown in Table1. Under such limited data conditions and types, how to use them to construct a forecasting model suitable for the holiday scenario is the primary goal. In data processing, the data cleaning has been done by identifying outliers, such as judging whether the enter and exit stations are inconsistent, whether the enter and exit time, and the in-train time are reasonable. Besides, the stations are regarded as transportation analysis zones (TAZs) in the urban rail transit system. The boarding (origin) and alighting (destination) stations of passengers’ trips can be obtained from the AFC system directly.Table 1
The Automatic Fare Collection data types.
NameField typeFormCard typeVarcharOne-way ticket, public transportation card, etc.Card numberInt1000139∗∗∗Enter lineVarcharLine 1, Line 2, etc.Enter station nameVarcharGuangzhou East, Donghu station, etc.Enter timeDatetime“2016-01-01 08 : 00 : 00”Exit line nameVarcharLine 1, Line 2, etc.Exit station nameVarcharGuangzhou East, Donghu station, etc.Exit timeDatetime“2016-01-01 08 : 00 : 00”There are eight lines and 140 stations in Guangzhou Metro by the beginning of 2016. The daily average of raw data amounts to more than 4 million that need further processing. And more than one million passengers use one-way tickets per day during New Year’s Day, which is almost 1.84 times the weekdays. Compared with January 1, 2016, there are seventeen new stations and three new lines connected to the network on January 1, 2017. The road network structure has tremendous changes.


## 2.2. Passenger Flow’s Characteristics

Based on Guangzhou Metro’s AFC data, the passenger flow of each station during the New Year’s Day holiday from 2016 to 2017 is collected, and some travel characteristics have been found. The passenger flow, for instance, is closely related to the nature of land-use and the intensity of development around stations.As shown in Figure1, the entrance passenger flows of four typical stations from December 30, 2015, to January 4, 2016, are given. The passenger flow of Zhujiangxincheng station, which is dominated by office areas, declined significantly during the New Year’s Day. Similarly, the passenger flow of Dashadong station also decreased, as residential areas surround there. However, Guangzhouta and Beijinglu stations’ passenger flow increased significantly during the holidays, with the main areas, respectively, surrounded by scenic spots and commercial districts.Figure 1
Entrance passenger flow of typical stations during New Year’s Day.Similarly, the passenger flow, from the origin station to the destination station (O-D station) during the holidays, shows different distinct characteristics, compared with weekdays. As shown in Figure2, there are different passenger flow trends between O-D stations with different land-use types, and some of which increased significantly in holidays, while others, such as residential stations to office stations, dropped significantly.Figure 2
Comparison of O-D passenger flow during weekdays and New Year’s Day in 2016.From another perspective, there are also great differences in the distribution of people who use one-way tickets and public transportation cards during holidays. Generally, many one-way passengers are nonlocal passengers, who tend to go to scenic spots, business districts, and hub stations. In contrast, transportation card passengers are mostly local residents, whose travel purposes are diversified. This characteristic of choice behavior is especially evident during holidays. As shown in Figure3, the passenger flow of one-way tickets and public transportation cards at Guangzhouta and Beijinglu stations has increased, while the growth rate of one-way ticket is significantly higher, indicating that the stronger attraction of one-way ticket passengers.Figure 3
Comparison of passenger flow between one-way ticket and public transportation card in 2016. (a) Guangzhouta station. (b) Beijinglu station.
(a)(b)Furthermore, other characteristics can also be obtained by analyzing the passenger flow. For example, the O-D passenger flow on the same line is usually larger than that on different lines. And in the case of satisfying the purpose of passengers, they would give priority to the destination with a short ride time and transfer time. However, these features are influenced by many factors. They should be reflected in some explanatory variables to analyze how various factors jointly affect the behavior and improve the subsequent forecasting performance when modeling. Next, the approach considering passenger flow’s characteristics of holidays is introduced in detail.


## 3. Methodology

Considering that the metro network scale is rapidly developing, the spatial passenger flow distribution of O-D stations also changes fast. New stations divert the passenger flow of old stations, and it is not easy to obtain the development data of all O-D pairs in time series, especially for newly added stations. Therefore, based on the above analysis of passenger flow’s features, this paper constructs a destination choice model to describe the characteristics of passengers. Then, a forecasting model of holiday passenger flow distribution is developed, which is suitable for the structural change of the network and does not depend on long-term data collection. Meanwhile, considering different passengers’ characteristics, the utility functions for passengers who use one-way tickets and public transportation cards are constructed separately.


### 3.1. Model Structure

The theory of random utility maximization refers to the alternatives in which traffic behavior decision-makers choose the most effective ones in their choice sets under certain conditions. If the destination choice sets of passengers from stationi are Ai and the utility of the alternative n is Uin, the requirement that the passengers select the destination j from Ai is Uij>Uin. Among them, the utility function U has divided into two parts: a deterministic term Vij and an error term εij. Therefore, the utility function Uij can be formulated as follows:(1)Uij=Vij+εij=∑βkXijk+εij,where βk is an estimable parameter of attribute k; Xijk is an observable attribute as the explanatory variable; εij is the error term that is used to address the unobserved factors that influence the choices taken by the passengers.The researcher observes some attributes of the alternatives as faced by the decision maker, labeledXij, and can specify a function that relates these observed factors to the decision maker’s utility [24]. The term εij is treated as random, and it captures the factors that affect utility but are not included in Vij. When the error term εij obeys the independent Gumbel distribution, multinomial logit (MNL) models can be derived. For the origin station i, the probability for choosing j is calculated as follows:(2)Pij=expVij∑nεAiexpVin,jεAi.Equation (2) is the destination choice model. The probability that a passenger chooses another station as the destination can be calculated. The production trips from each station are then distributed to all other stations based on the choice of probability destination. That is, the passenger flow distribution qij from the origin station i to the destination station j is computed. The formula is shown as follows:(3)qij=Qi⋅Pij,where Qi is the entrance passenger flow in station i.Considering the different levels of sensitivity of travel characteristics of different types of passengers in the particularity of holidays, two utility functions in the proposed model are constructed with passengers who use one-way tickets and public transportation cards for representing local and nonlocal passengers. The trip distribution is applied separately for each ticket type of passengers who have characteristic travel behavior, with different model parameters. Then, the distribution results of the two ticket types are added together. The formula is shown as follows:(4)qij=qijone+qijptc,where qijone is the one-way ticket passengers’ distribution prediction; qijptc is the public transportation card passengers’ distribution prediction.Equation (4) is the forecasting model of passenger flow distribution. However, it is a singly constrained model so far. There is no guarantee that the sum of the passenger flow from each station to the destination station j is equal to the attracted trips of station j. Therefore, it is necessary to modify the travel flow to enforce constraints between total origins and destinations. The Fratar method is widely used in distribution adjustment due to its fast convergence speed and high calculation accuracy. The idea of the Fratar method is a distribution of horizon year trips from a zone that is proportional to the base year trip distribution pattern modified by the growth factors of the zones under consideration [25, 26]. Therefore, this paper uses the Fratar method for equalization processing. The approach is shown as follows:(5)qijm+1=qijm·FOim·FDjm·Li+Lj2,Li=Oim∑jqijm·FDjm,Lj=Djm∑iqijm·FOim,where qij is the passenger flow of station i to station j; FOi is the growth rate of the entrance passenger flow in station i; FDj is the growth rate of the exit passenger flow in station j; Li is the adjustment coefficient of station i; Lj is the adjustment coefficient of station j; Oi is the entrance passenger flow in station i; Dj is the exit passenger flow in station j; m is the m-th iteration.


### 3.2. Model Specifications

Although personal characteristics affect destination choice, it is unable to obtain personal attributes data from the AFC directly. Therefore, seven indexes as the utility function of characteristic variables that could be extracted from the urban rail transit network are considered in the destination choice model, including in-vehicle travel time, transfer time, station position relationship, and matching degree of land-use types. The seven variables are mainly used to characterize three categories of explanatory attributes, namely, the accessibility of the destination, the attractiveness of the destination, and matching degree of O-D stations, through which the choice behavior mechanism of passengers can be characterized.According to the choice behavior characteristics of the one-way ticket and the public transportation card passengers, and through the multiple calibration experience of the model, the utility functionsVijone and Vijptc of the destination choice model are constructed, as shown in equations (6) and (7), respectively:(6)Vijone=β1Dj+β2Zij+β3Tijtrain3600+β4Nijtrans3600+β5Gij+β6Sij+β7Lj,(7)Vijptc=β8Dj+β9Zij+β10Tijtrain3600+β11Nijtrans3600+β12Gij+β13Sij,where β1−β13 is the parameter to be calibrated for each variable; Dj is the exit passenger flow of destination station j, ten thousand person trips; Zij is the matching degree of land-use type; Tijtrain is the in-vehicle travel time from the origin station i to the destination station j, second; Nijtrans is the transfer time from the origin station i to the destination station j, second; Gij is a dummy variable, and if the sum of trip generation at origin station i and the attraction at destination station j is larger than a specific scale, the value is 1; Sij is a dummy variable, and if the origin station i and destination station j are in the same line, the value is 1; Lj is a dummy variable, and if the land-use type of destination station j is scenic, commercial, or hub, the value is 1.For one thing, these variables are introduced to facilitate data acquisition, and for another, the characteristics of holidays are considered so as to improve the interpretability and prediction effect of the model further. It should be noted that the travel cost is a sensitive variable to influence the choice behavior, which was included in the variable sets at the beginning. However, when the variables are checked for multicollinearity, the travel cost shows a strong correlation with the travel time. Therefore, the travel cost was eliminated in the utility functions. Compared to one-way ticket passengers, the public transportation card utility functions do not have the variableLj, as adding this variable would reduce the model’s accuracy.Moreover, the acquisition of the matching degree of land-use typesZij and the scenic destination station variables Lj need to be additionally explained. The distribution of passenger flow between stations is closely related to land-use nature around the station, especially the significant difference between holidays and normal days. It is necessary to quantify the impact of land-use interaction. Therefore, Zij is constructed to describe the degree of attraction between different types of stations. Based on this, the metro stations need to be clustered to determine the category of the station first.Due to the land-use properties are a relatively stable indicator and it usually shows a certain relationship with the passenger flow characteristics, theK-means clustering method is used to classify the stations of the whole network of Guangzhou Metro. K-means is a vector quantization method that is popular for cluster analysis in data mining [27]. Through the analysis of passenger flow characteristics, the morning and evening peak flow has a greater correlation with the nature of land-use around stations. And the proportion of one-way tickets and all-day passenger flow at comprehensive transportation hubs is usually larger, while the passenger flow at commercial and scenic stations tends to increase significantly during holidays. Therefore, the five variables are used as inputs for clustering as shown in Table 2. In the clustering research of metro stations, the stations are usually divided into five categories according to weekday travel data [28, 29]. However, since the research scenarios are aimed at holidays, we set eight cluster numbers as preset categories according to the land-use and application requirements of the model. The clustering results are shown in Table 3 (figures in brackets denote the sum number of clustering stations), and they are representative and matched with the preset types.Table 2
The variables forK-means.
VariablesDescriptionMorning peak hour factorThe passenger flow of morning peak hour (7 : 00–9:00) divided by all-day passenger flowEvening peak hour factorThe passenger flow of evening peak hour (17 : 00–19 : 00) divided by all-day passenger flowProportion of one-way ticketThe proportion of passengers using one-way ticketAll-day passenger flowThe all-day passenger flow in the stationsPassenger flow growth rateThe passenger flow of the holiday divided by the weekdays before the holidayTable 3
Station types’ clustering results based on the surrounding area’s land-use.
TypeAttributeDescriptionClustering resultsType 1ResidentialThe station is surrounded by residential areasNanpu, Sanxi, Dongpu, etc. (30)Type 2The majority of residential areaThe station is surrounded by majority of residential areasShiqiao, Meihuay, Xicun, etc. (25)Type 3OfficeThe station is surrounded by office areasHaizhuguagnc, Quzhuang, etc. (20)Type 4The majority of office areaThe station is surrounded by majority of office areasDonghu, Ximenkou, etc. (21)Type 5ComprehensiveThe station is surrounded by various types of land-useShibi, Fangcun, Shiergong, etc. (28)Type 6CommercialThe station is surrounded by commercial areasJinzhou, Jinronggaoxinqu, etc. (14)Type 7ScenicThe station is close to scenic spotDiyong, Guangzhouta, etc. (14)Type 8Hub centerThe station functions as transportation hub centerGuagnzhou South, Airport South, etc. (5)Therefore, the value ofLj can be obtained directly through the clustering results. Besides, the matching degree of land-use type Zij needs further processing. Based on the above clustering results, the average O-D passenger flow with different cluster types could be calculated. Then, the logarithm function is used to normalize the values of various types to differentiate passenger flow better. The formula is as follows:(8)Zij=lnQij−lnmini,jQijlnmaxi,jQij−lnmini,jQij,where Zij is land matching degree from type i to type j; Qij is the average O-D passenger flow of the stations from type i to type j.A case result ofZij is shown in Table 4 (the vertical column indicates the type of the origin station, and the horizontal row indicates the type of the destination station), where the value from Type1 to Type 1 is zero. This means that the passenger flow is the lowest of all type pairs, mainly because the attraction between residential stations is less during holidays in all type pairs. In contrast, the connections between transportation hubs are strengthened, reflected in the maximum value from Type 8 to Type 8.Table 4
Land matching degree values of different types of O-D stations.
Type 1Type 2Type 3Type 4Type 5Type 6Type 7Type 8Type 10.000.080.240.080.100.180.280.55Type 20.090.150.280.150.160.240.290.63Type 30.090.170.350.180.180.200.270.61Type 40.220.250.280.290.220.220.290.64Type 50.110.150.240.160.220.220.360.60Type 60.170.230.250.180.230.140.260.59Type 70.280.260.250.190.340.220.390.59Type 80.510.590.610.550.570.560.581.00


### 3.3. Parameter Estimation

For the parametersβ in equation (1), the personal travel survey is generally performed by the simple random sampling method to obtain the disaggregate type data of the individual choice, thereby using the maximum likelihood estimation method to calibrate the parameters. However, in this paper, the aggregate data obtained by the AFC should be transformed into the disaggregate form for application in the destination choice model. When being applied, it needs methods to deal with the original aggregate data. Yao and Takayuki [30] proposed an integrated model that combines estimation across multiple data sources such as SP, RP, and aggregate data. Therefore, the maximum likelihood estimation method is improved by introducing a weight factor to realize the application of AFC data in the destination choice model’ calibration.Manski and Lerman [31] proposed a weighted exogenous sampling maximum likelihood (WESML) method, introducing weights into log-likelihood functions to calibrate the bias between the sample and population data. It can be expressed as follows:(9)Lθ=∑iεAn∑nδinwilnPin,(10)wi=QiHi,iεC,where δin is 1 if the passenger n chooses selected branch i as destination and 0 otherwise; wi is weights; Qi is the proportion of the selected branch i in the population; Hi is the proportion of i in the sample.To improve the practicability of the method, Cosslett’s research [32] proves that it can be transformed as follows:(11)wi=QiNi/N,where Ni is the data amount of the selected branch i; N is the sum of the data amounts of the respective selected branch.However, in terms of urban rail transit, passengers with the same origin and destination station have the same characteristics; that is, they all make the same choice for the destination. Thus, the amount of O-D passenger flow can be expressed as the selection result of individuals. The weight factor is suited for adjusting the likelihood function of the dataset. Therefore, according to the characteristics of the data that can be extracted, equation (11) is corrected as follows:(12)wi=qi∑qi⋅R,where qi is the O-D passenger flow in the selected branch i; R is the number of individuals, that is, the sum of O-D station pairs.


## 3.1. Model Structure

The theory of random utility maximization refers to the alternatives in which traffic behavior decision-makers choose the most effective ones in their choice sets under certain conditions. If the destination choice sets of passengers from stationi are Ai and the utility of the alternative n is Uin, the requirement that the passengers select the destination j from Ai is Uij>Uin. Among them, the utility function U has divided into two parts: a deterministic term Vij and an error term εij. Therefore, the utility function Uij can be formulated as follows:(1)Uij=Vij+εij=∑βkXijk+εij,where βk is an estimable parameter of attribute k; Xijk is an observable attribute as the explanatory variable; εij is the error term that is used to address the unobserved factors that influence the choices taken by the passengers.The researcher observes some attributes of the alternatives as faced by the decision maker, labeledXij, and can specify a function that relates these observed factors to the decision maker’s utility [24]. The term εij is treated as random, and it captures the factors that affect utility but are not included in Vij. When the error term εij obeys the independent Gumbel distribution, multinomial logit (MNL) models can be derived. For the origin station i, the probability for choosing j is calculated as follows:(2)Pij=expVij∑nεAiexpVin,jεAi.Equation (2) is the destination choice model. The probability that a passenger chooses another station as the destination can be calculated. The production trips from each station are then distributed to all other stations based on the choice of probability destination. That is, the passenger flow distribution qij from the origin station i to the destination station j is computed. The formula is shown as follows:(3)qij=Qi⋅Pij,where Qi is the entrance passenger flow in station i.Considering the different levels of sensitivity of travel characteristics of different types of passengers in the particularity of holidays, two utility functions in the proposed model are constructed with passengers who use one-way tickets and public transportation cards for representing local and nonlocal passengers. The trip distribution is applied separately for each ticket type of passengers who have characteristic travel behavior, with different model parameters. Then, the distribution results of the two ticket types are added together. The formula is shown as follows:(4)qij=qijone+qijptc,where qijone is the one-way ticket passengers’ distribution prediction; qijptc is the public transportation card passengers’ distribution prediction.Equation (4) is the forecasting model of passenger flow distribution. However, it is a singly constrained model so far. There is no guarantee that the sum of the passenger flow from each station to the destination station j is equal to the attracted trips of station j. Therefore, it is necessary to modify the travel flow to enforce constraints between total origins and destinations. The Fratar method is widely used in distribution adjustment due to its fast convergence speed and high calculation accuracy. The idea of the Fratar method is a distribution of horizon year trips from a zone that is proportional to the base year trip distribution pattern modified by the growth factors of the zones under consideration [25, 26]. Therefore, this paper uses the Fratar method for equalization processing. The approach is shown as follows:(5)qijm+1=qijm·FOim·FDjm·Li+Lj2,Li=Oim∑jqijm·FDjm,Lj=Djm∑iqijm·FOim,where qij is the passenger flow of station i to station j; FOi is the growth rate of the entrance passenger flow in station i; FDj is the growth rate of the exit passenger flow in station j; Li is the adjustment coefficient of station i; Lj is the adjustment coefficient of station j; Oi is the entrance passenger flow in station i; Dj is the exit passenger flow in station j; m is the m-th iteration.


## 3.2. Model Specifications

Although personal characteristics affect destination choice, it is unable to obtain personal attributes data from the AFC directly. Therefore, seven indexes as the utility function of characteristic variables that could be extracted from the urban rail transit network are considered in the destination choice model, including in-vehicle travel time, transfer time, station position relationship, and matching degree of land-use types. The seven variables are mainly used to characterize three categories of explanatory attributes, namely, the accessibility of the destination, the attractiveness of the destination, and matching degree of O-D stations, through which the choice behavior mechanism of passengers can be characterized.According to the choice behavior characteristics of the one-way ticket and the public transportation card passengers, and through the multiple calibration experience of the model, the utility functionsVijone and Vijptc of the destination choice model are constructed, as shown in equations (6) and (7), respectively:(6)Vijone=β1Dj+β2Zij+β3Tijtrain3600+β4Nijtrans3600+β5Gij+β6Sij+β7Lj,(7)Vijptc=β8Dj+β9Zij+β10Tijtrain3600+β11Nijtrans3600+β12Gij+β13Sij,where β1−β13 is the parameter to be calibrated for each variable; Dj is the exit passenger flow of destination station j, ten thousand person trips; Zij is the matching degree of land-use type; Tijtrain is the in-vehicle travel time from the origin station i to the destination station j, second; Nijtrans is the transfer time from the origin station i to the destination station j, second; Gij is a dummy variable, and if the sum of trip generation at origin station i and the attraction at destination station j is larger than a specific scale, the value is 1; Sij is a dummy variable, and if the origin station i and destination station j are in the same line, the value is 1; Lj is a dummy variable, and if the land-use type of destination station j is scenic, commercial, or hub, the value is 1.For one thing, these variables are introduced to facilitate data acquisition, and for another, the characteristics of holidays are considered so as to improve the interpretability and prediction effect of the model further. It should be noted that the travel cost is a sensitive variable to influence the choice behavior, which was included in the variable sets at the beginning. However, when the variables are checked for multicollinearity, the travel cost shows a strong correlation with the travel time. Therefore, the travel cost was eliminated in the utility functions. Compared to one-way ticket passengers, the public transportation card utility functions do not have the variableLj, as adding this variable would reduce the model’s accuracy.Moreover, the acquisition of the matching degree of land-use typesZij and the scenic destination station variables Lj need to be additionally explained. The distribution of passenger flow between stations is closely related to land-use nature around the station, especially the significant difference between holidays and normal days. It is necessary to quantify the impact of land-use interaction. Therefore, Zij is constructed to describe the degree of attraction between different types of stations. Based on this, the metro stations need to be clustered to determine the category of the station first.Due to the land-use properties are a relatively stable indicator and it usually shows a certain relationship with the passenger flow characteristics, theK-means clustering method is used to classify the stations of the whole network of Guangzhou Metro. K-means is a vector quantization method that is popular for cluster analysis in data mining [27]. Through the analysis of passenger flow characteristics, the morning and evening peak flow has a greater correlation with the nature of land-use around stations. And the proportion of one-way tickets and all-day passenger flow at comprehensive transportation hubs is usually larger, while the passenger flow at commercial and scenic stations tends to increase significantly during holidays. Therefore, the five variables are used as inputs for clustering as shown in Table 2. In the clustering research of metro stations, the stations are usually divided into five categories according to weekday travel data [28, 29]. However, since the research scenarios are aimed at holidays, we set eight cluster numbers as preset categories according to the land-use and application requirements of the model. The clustering results are shown in Table 3 (figures in brackets denote the sum number of clustering stations), and they are representative and matched with the preset types.Table 2
The variables forK-means.
VariablesDescriptionMorning peak hour factorThe passenger flow of morning peak hour (7 : 00–9:00) divided by all-day passenger flowEvening peak hour factorThe passenger flow of evening peak hour (17 : 00–19 : 00) divided by all-day passenger flowProportion of one-way ticketThe proportion of passengers using one-way ticketAll-day passenger flowThe all-day passenger flow in the stationsPassenger flow growth rateThe passenger flow of the holiday divided by the weekdays before the holidayTable 3
Station types’ clustering results based on the surrounding area’s land-use.
TypeAttributeDescriptionClustering resultsType 1ResidentialThe station is surrounded by residential areasNanpu, Sanxi, Dongpu, etc. (30)Type 2The majority of residential areaThe station is surrounded by majority of residential areasShiqiao, Meihuay, Xicun, etc. (25)Type 3OfficeThe station is surrounded by office areasHaizhuguagnc, Quzhuang, etc. (20)Type 4The majority of office areaThe station is surrounded by majority of office areasDonghu, Ximenkou, etc. (21)Type 5ComprehensiveThe station is surrounded by various types of land-useShibi, Fangcun, Shiergong, etc. (28)Type 6CommercialThe station is surrounded by commercial areasJinzhou, Jinronggaoxinqu, etc. (14)Type 7ScenicThe station is close to scenic spotDiyong, Guangzhouta, etc. (14)Type 8Hub centerThe station functions as transportation hub centerGuagnzhou South, Airport South, etc. (5)Therefore, the value ofLj can be obtained directly through the clustering results. Besides, the matching degree of land-use type Zij needs further processing. Based on the above clustering results, the average O-D passenger flow with different cluster types could be calculated. Then, the logarithm function is used to normalize the values of various types to differentiate passenger flow better. The formula is as follows:(8)Zij=lnQij−lnmini,jQijlnmaxi,jQij−lnmini,jQij,where Zij is land matching degree from type i to type j; Qij is the average O-D passenger flow of the stations from type i to type j.A case result ofZij is shown in Table 4 (the vertical column indicates the type of the origin station, and the horizontal row indicates the type of the destination station), where the value from Type1 to Type 1 is zero. This means that the passenger flow is the lowest of all type pairs, mainly because the attraction between residential stations is less during holidays in all type pairs. In contrast, the connections between transportation hubs are strengthened, reflected in the maximum value from Type 8 to Type 8.Table 4
Land matching degree values of different types of O-D stations.
Type 1Type 2Type 3Type 4Type 5Type 6Type 7Type 8Type 10.000.080.240.080.100.180.280.55Type 20.090.150.280.150.160.240.290.63Type 30.090.170.350.180.180.200.270.61Type 40.220.250.280.290.220.220.290.64Type 50.110.150.240.160.220.220.360.60Type 60.170.230.250.180.230.140.260.59Type 70.280.260.250.190.340.220.390.59Type 80.510.590.610.550.570.560.581.00


## 3.3. Parameter Estimation

For the parametersβ in equation (1), the personal travel survey is generally performed by the simple random sampling method to obtain the disaggregate type data of the individual choice, thereby using the maximum likelihood estimation method to calibrate the parameters. However, in this paper, the aggregate data obtained by the AFC should be transformed into the disaggregate form for application in the destination choice model. When being applied, it needs methods to deal with the original aggregate data. Yao and Takayuki [30] proposed an integrated model that combines estimation across multiple data sources such as SP, RP, and aggregate data. Therefore, the maximum likelihood estimation method is improved by introducing a weight factor to realize the application of AFC data in the destination choice model’ calibration.Manski and Lerman [31] proposed a weighted exogenous sampling maximum likelihood (WESML) method, introducing weights into log-likelihood functions to calibrate the bias between the sample and population data. It can be expressed as follows:(9)Lθ=∑iεAn∑nδinwilnPin,(10)wi=QiHi,iεC,where δin is 1 if the passenger n chooses selected branch i as destination and 0 otherwise; wi is weights; Qi is the proportion of the selected branch i in the population; Hi is the proportion of i in the sample.To improve the practicability of the method, Cosslett’s research [32] proves that it can be transformed as follows:(11)wi=QiNi/N,where Ni is the data amount of the selected branch i; N is the sum of the data amounts of the respective selected branch.However, in terms of urban rail transit, passengers with the same origin and destination station have the same characteristics; that is, they all make the same choice for the destination. Thus, the amount of O-D passenger flow can be expressed as the selection result of individuals. The weight factor is suited for adjusting the likelihood function of the dataset. Therefore, according to the characteristics of the data that can be extracted, equation (11) is corrected as follows:(12)wi=qi∑qi⋅R,where qi is the O-D passenger flow in the selected branch i; R is the number of individuals, that is, the sum of O-D station pairs.


## 4. Results and Analysis

### 4.1. Model Estimation and Analysis

In the construction of the selection set, there are 140 stations in the 2016 New Year’s Day. That is to say, 139 stations should be put into the alternative set except for the real choice of each traveler. However, for general disaggregate models, the size of the alternatives is too large, which would affect the speed of model estimation and is not conducive to application. Ben-Akiva and Lerman [33] demonstrated that the consistency of model parameters is not lost when extracting subselective branches for parameter estimation in the selection set. Therefore, this paper constructed the subselection set by randomly extracting nine stations from the alternative set. It could reduce the difficulty of calibration and increase the operability while ensuring the consistency of the model’s calibrated parameters.In the process of parameter calibration, the values of seven variables are obtained in combination with the network topology and train operation plan of Guangzhou Urban Rail Transit. By using the parameter estimation method described in the section before, the undetermined parameters of the utility function are calibrated. Especially, after several tests, the scale dummy variableGij was set to 1 if it exceeds 7,000 person trips. The calibration results of the New Year’s Day are shown in Table 5 as a study case. All absolute t-values are greater than 1.96, indicating statistical significance and variables’ validation. Moreover, the adjusted ρ2 of this model is over 0.2, which can be regarded as a satisfactory goodness-of-fit [34].Table 5
Model estimation results.
Characteristic variableCase1: the New Year’s DayCase2: the National DayOne-way ticketPublic transport cardOne-way ticketPublic transport cardβit-valueβit-valueβit-valueβit-valueDestination attraction (Dj)0.30137.9890.08426.8180.29038.7910.21128.646Land matching degree (Zij)0.3113.6410.4246.8020.2572.3670.5328.481Collinear variable (Sij)0.53318.1900.54918.7590.49317.1790.55318.812Scale variable (Gij)0.63829.1060.53323.8350.62929.5190.51723.696Travel time (Tijtrain)−0.815−18.286−1.172−25.162−0.508−11.884−1.094−23.556Transfer time (Nijtrans)−5.507−18.324−6.449−20.833−5.975−20.316−6.766−21.519Scenic variables (Lij)0.0843.971——0.0923.350——Model summaryObservations17954183141753417747Lθmax−32640.37−33441.36−31654.83−32615.35L0−41340.61−42169.54−40373.53−40863.98Adjustedρ20.2100.2070.2160.202The estimated parameters are provided with practical significance and expected signs in the sense of explaining passenger destination choice behavior in either the one-way ticket model or public transportation card model. An obvious example is that the parameter of destination attraction variable is positive, indicating that the greater attraction of destination station is, the more passengers choose.As for the negative parameters of travel time and transfer time, the longer the travel time and transfer times are, the less probability of destination station would be chosen, which is consistent with common sense and inversely proportional to destination choice preference. Moreover, the units are the same, but the estimated parameters are not close, which means the travelers have different perceptions. The trade-off between travel and transfer time shows that an increase of 10 minutes in transfer time is equivalent to an increase of 68 minutes in travel time for one-way ticket passengers and 55 minutes for public transportation card passengers in the case of New Year’s Day. It reveals that travelers have a significant negative impact on lengthy transfer times. For public transportation card passengers, the absolute parameters of travel time and transfer time are both larger than the one-way ticket passengers, indicating that the passengers who used the card care more about the time when other variables remain unchanged.Besides, the land matching degree’s parameter is positive, which indicates that when the relationship between O-D station’s land-use types is strong, the destination stations will be more likely to be chosen. The scale and collinear variable’s parameters are positive, revealing that when the origin and destination stations’ travel scale is more extensive, or the O-D station stands on the same line, the probability of the destination station being chosen is greater.For the scenic variable in the one-way ticket model, its parameter is positive. It is also in line with the characteristics of passengers traveling on holidays because there are plenty of tourists who use the one-way tickets. In general, the estimated results are statistically significance and can explain the choice behavior mechanism on the New Year’s Day to some degree. However, it is worth emphasizing that the parameters should be recalibrated so as to regain the travel behaviors when applying other different holidays.


### 4.2. Model Application and Comparison

To test the predictive effect of the proposed forecasting model, the calibrated results are used to predict the New Year’s Day of Guangzhou Metro on January 1, 2017, where the data of the predicted year are used as the test-set and do not participate in the calibration. There are seventeen new stations and three new lines connected to the network. Meanwhile, the singly constrained gravity (SCG) model in the traditional statistical model, the support vector machine (SVM), the back propagation (BP) neural network, and radial basis function (RBF) neural network in machine learning model are selected for comparison under the same data source and conditions. And the traffic impedance function in the form of the exponential function is used in the gravity model, as shown in equation (13). The least-square method is used to transform it into a linear form for parameter estimation [35]:(13)fij=exp−μTij−τnijTij−γ,where Tij and nij are travel time and transfer time from the origin station i to the destination station j, respectively; μ, τ, and γ are the coefficients to be determined.As shown in Figure4(a)–4(e), the predicted values are compared with the actual passenger travel data, and the prediction deviation graph is drawn. The error fluctuation of the singly constrained gravity model and the other three machine learning models is larger than the proposed forecasting model established in this paper. The mean absolute error of the whole network in the gravity model is 130.2 person trips, the SVM model is 140.9, the BP neural network is 139.1, and the RBF neural network is 157.3, while the proposed model is 54.6 that is far better.Figure 4
Prediction deviation of the proposed model and the comparison models on the New Year’s Day. (a) The proposed model. (b) The gravity model. (c) The support vector machine model. (d) The back propagation neural network model. (e) The radial basis function neural network model.
(a)(b)(c)(d)(e)Furthermore, the detailed prediction error statistics of the five models, in this case, are shown in Table6. Compared with the other four models, the mean absolute error of the proposed model is reduced by 58.05%, 61.21%, 60.72%, and 65.26%, respectively. The proportion of absolute errors of the proposed model under 50 person trips reaches 73.1%, and the relative error less than 50% is 66.83%, where the errors are better than that of the other four models.Table 6
Statistics of model deviation in the New Year’s Day.
Case1: the New Year’s DaySCGSVMBPRBFThe proposed modelMaximum of absolute error (person trips)50716099624059322506Mean absolute error (person trips)130.22140.86139.08157.2754.63Proportion of absolute errors over 50 trips (%)50.1356.1257.5766.326.90Proportion of absolute errors over 100 trips (%)31.3131.8335.7139.2914.78Proportion of absolute errors over 200 trips (%)16.2715.1714.7417.155.90Proportion of relative error over 20% (%)84.6085.1184.0085.9562.74Proportion of relative error over 50% (%)66.7864.3464.0868.3733.17Proportion of relative error over 100% (%)40.4537.5545.7046.0716.39A detailed comparison of absolute error and its cumulative percentage can be seen in Figure5. The statistics also show that the proposed model accuracy is better than the conventional gravity model, SVM, and the two neural network models as a whole. However, the proposed model has a slightly weak performance in terms of relative error, mainly because there are many O-D stations with small basic flow, leading to a large relative error. For example, the proportion of relative error more than 200% is 6.78%, where the average absolute error is 41.0 person trips. Moreover, the proportion of relative error more than 500% is 1.70%, where the average absolute error is 35.40 person trips, which is below the total average absolute error. Therefore, it does not mean that the poorer the relative error, the larger the absolute error, and the worse the prediction performance. The prediction effect of the proposed model can still be guaranteed.Figure 5
Comparison of absolute error and cumulative percentage.Besides that, the error results of different categories between new lines and existing lines in the models are shown in Table7. The proposed model’s mean absolute error results are relatively low when predicting the new line, namely, only 23.14 and 23.26 person trips. In the prediction performance of the existing line to existing line, the error is relatively larger than that of others, mainly because of the large basic flow between existing stations.Table 7
Mean absolute error of prediction results.
CategoryMean absolute error (person trips)SCGSVMBPRBFThe proposed modelExisting to new lines49.9299.8167.2682.9623.14New line to existing line48.0776.62119.80105.6423.26New line to new line90.03141.7296.56131.5541.30Existing line to existing line154.94152.50152.12171.6864.10Whole network130.22140.86139.08157.2754.63In this case, the holiday of New Year’s Day is chosen for analysis. However, other holidays might be a little longer in time, and passenger flow patterns and choice behavior would be different in some ways. The proposed destination choice model could be used to reflect the choice behavior characteristics and passenger flow rules, so the methodology applies to all holidays. Considering the validation and portability of the proposed method, this study supplemented a case of the National Day (seven-day holiday) for a relatively comprehensive experimental design. One day of the National Day in 2014 was randomly selected for model estimation (that is, October 2, 2014), and the proposed method was used to predict the passenger flow distribution on the same day of next year.There is one small difference in the calibrated parameters as shown in Table5 above, which reflects the slight distinction of the travel characteristics in different holidays. However, all absolute t-values are still greater than 1.96, and the adjusted ρ2 is over 0.2, which indicates that the model is still applicable and reliable. The prediction deviation graph is also drawn to show the overall error, as shown in Figure 6. For the convenience of reading, the scatter plot is given as shown in Figure 7, which is consistent with the meaning expressed in Figure 6. The graph plots values for the modeled prediction along the Y-axis and the corresponding actual count along the X-axis. If all of the predictions match the actual value exactly, the points on the graph would match up with the red line (45 degree line) drawn in the graph. The prediction results of the proposed model are mostly close to the red line, illustrating that the prediction performs well. The National Day’s comparison models’ error statistics are shown in Table 8. In summary, the prediction effect and accuracy are still ideal than the other models. The validation and applicability in other holiday scenarios can still be guaranteed. And it can be more effectively applied to practical engineering.Figure 6
Prediction deviation of the proposed model on the National Day.Figure 7
Scatter plot of predicted and actual value result presentation.Table 8
Statistics of model deviation in the National Day.
Case2: the National DaySCGSVMBPRBFThe proposed modelMaximum of absolute error (person trips)56818931673043202467Mean absolute error (person trips)129.07110.29109.2579.5851.63Proportion of absolute errors over 50 trips (%)51.5843.6348.3437.5323.49Proportion of absolute errors over 100 trips (%)32.4426.1626.9920.6812.55Proportion of absolute errors over 200 trips (%)16.5312.5812.409.705.47Proportion of relative error over 20% (%)81.1084.6682.4573.0665.15Proportion of relative error over 50% (%)55.4062.9359.8043.6631.61Proportion of relative error over 100% (%)31.8635.7338.5226.5614.06


## 4.1. Model Estimation and Analysis

In the construction of the selection set, there are 140 stations in the 2016 New Year’s Day. That is to say, 139 stations should be put into the alternative set except for the real choice of each traveler. However, for general disaggregate models, the size of the alternatives is too large, which would affect the speed of model estimation and is not conducive to application. Ben-Akiva and Lerman [33] demonstrated that the consistency of model parameters is not lost when extracting subselective branches for parameter estimation in the selection set. Therefore, this paper constructed the subselection set by randomly extracting nine stations from the alternative set. It could reduce the difficulty of calibration and increase the operability while ensuring the consistency of the model’s calibrated parameters.In the process of parameter calibration, the values of seven variables are obtained in combination with the network topology and train operation plan of Guangzhou Urban Rail Transit. By using the parameter estimation method described in the section before, the undetermined parameters of the utility function are calibrated. Especially, after several tests, the scale dummy variableGij was set to 1 if it exceeds 7,000 person trips. The calibration results of the New Year’s Day are shown in Table 5 as a study case. All absolute t-values are greater than 1.96, indicating statistical significance and variables’ validation. Moreover, the adjusted ρ2 of this model is over 0.2, which can be regarded as a satisfactory goodness-of-fit [34].Table 5
Model estimation results.
Characteristic variableCase1: the New Year’s DayCase2: the National DayOne-way ticketPublic transport cardOne-way ticketPublic transport cardβit-valueβit-valueβit-valueβit-valueDestination attraction (Dj)0.30137.9890.08426.8180.29038.7910.21128.646Land matching degree (Zij)0.3113.6410.4246.8020.2572.3670.5328.481Collinear variable (Sij)0.53318.1900.54918.7590.49317.1790.55318.812Scale variable (Gij)0.63829.1060.53323.8350.62929.5190.51723.696Travel time (Tijtrain)−0.815−18.286−1.172−25.162−0.508−11.884−1.094−23.556Transfer time (Nijtrans)−5.507−18.324−6.449−20.833−5.975−20.316−6.766−21.519Scenic variables (Lij)0.0843.971——0.0923.350——Model summaryObservations17954183141753417747Lθmax−32640.37−33441.36−31654.83−32615.35L0−41340.61−42169.54−40373.53−40863.98Adjustedρ20.2100.2070.2160.202The estimated parameters are provided with practical significance and expected signs in the sense of explaining passenger destination choice behavior in either the one-way ticket model or public transportation card model. An obvious example is that the parameter of destination attraction variable is positive, indicating that the greater attraction of destination station is, the more passengers choose.As for the negative parameters of travel time and transfer time, the longer the travel time and transfer times are, the less probability of destination station would be chosen, which is consistent with common sense and inversely proportional to destination choice preference. Moreover, the units are the same, but the estimated parameters are not close, which means the travelers have different perceptions. The trade-off between travel and transfer time shows that an increase of 10 minutes in transfer time is equivalent to an increase of 68 minutes in travel time for one-way ticket passengers and 55 minutes for public transportation card passengers in the case of New Year’s Day. It reveals that travelers have a significant negative impact on lengthy transfer times. For public transportation card passengers, the absolute parameters of travel time and transfer time are both larger than the one-way ticket passengers, indicating that the passengers who used the card care more about the time when other variables remain unchanged.Besides, the land matching degree’s parameter is positive, which indicates that when the relationship between O-D station’s land-use types is strong, the destination stations will be more likely to be chosen. The scale and collinear variable’s parameters are positive, revealing that when the origin and destination stations’ travel scale is more extensive, or the O-D station stands on the same line, the probability of the destination station being chosen is greater.For the scenic variable in the one-way ticket model, its parameter is positive. It is also in line with the characteristics of passengers traveling on holidays because there are plenty of tourists who use the one-way tickets. In general, the estimated results are statistically significance and can explain the choice behavior mechanism on the New Year’s Day to some degree. However, it is worth emphasizing that the parameters should be recalibrated so as to regain the travel behaviors when applying other different holidays.


## 4.2. Model Application and Comparison

To test the predictive effect of the proposed forecasting model, the calibrated results are used to predict the New Year’s Day of Guangzhou Metro on January 1, 2017, where the data of the predicted year are used as the test-set and do not participate in the calibration. There are seventeen new stations and three new lines connected to the network. Meanwhile, the singly constrained gravity (SCG) model in the traditional statistical model, the support vector machine (SVM), the back propagation (BP) neural network, and radial basis function (RBF) neural network in machine learning model are selected for comparison under the same data source and conditions. And the traffic impedance function in the form of the exponential function is used in the gravity model, as shown in equation (13). The least-square method is used to transform it into a linear form for parameter estimation [35]:(13)fij=exp−μTij−τnijTij−γ,where Tij and nij are travel time and transfer time from the origin station i to the destination station j, respectively; μ, τ, and γ are the coefficients to be determined.As shown in Figure4(a)–4(e), the predicted values are compared with the actual passenger travel data, and the prediction deviation graph is drawn. The error fluctuation of the singly constrained gravity model and the other three machine learning models is larger than the proposed forecasting model established in this paper. The mean absolute error of the whole network in the gravity model is 130.2 person trips, the SVM model is 140.9, the BP neural network is 139.1, and the RBF neural network is 157.3, while the proposed model is 54.6 that is far better.Figure 4
Prediction deviation of the proposed model and the comparison models on the New Year’s Day. (a) The proposed model. (b) The gravity model. (c) The support vector machine model. (d) The back propagation neural network model. (e) The radial basis function neural network model.
(a)(b)(c)(d)(e)Furthermore, the detailed prediction error statistics of the five models, in this case, are shown in Table6. Compared with the other four models, the mean absolute error of the proposed model is reduced by 58.05%, 61.21%, 60.72%, and 65.26%, respectively. The proportion of absolute errors of the proposed model under 50 person trips reaches 73.1%, and the relative error less than 50% is 66.83%, where the errors are better than that of the other four models.Table 6
Statistics of model deviation in the New Year’s Day.
Case1: the New Year’s DaySCGSVMBPRBFThe proposed modelMaximum of absolute error (person trips)50716099624059322506Mean absolute error (person trips)130.22140.86139.08157.2754.63Proportion of absolute errors over 50 trips (%)50.1356.1257.5766.326.90Proportion of absolute errors over 100 trips (%)31.3131.8335.7139.2914.78Proportion of absolute errors over 200 trips (%)16.2715.1714.7417.155.90Proportion of relative error over 20% (%)84.6085.1184.0085.9562.74Proportion of relative error over 50% (%)66.7864.3464.0868.3733.17Proportion of relative error over 100% (%)40.4537.5545.7046.0716.39A detailed comparison of absolute error and its cumulative percentage can be seen in Figure5. The statistics also show that the proposed model accuracy is better than the conventional gravity model, SVM, and the two neural network models as a whole. However, the proposed model has a slightly weak performance in terms of relative error, mainly because there are many O-D stations with small basic flow, leading to a large relative error. For example, the proportion of relative error more than 200% is 6.78%, where the average absolute error is 41.0 person trips. Moreover, the proportion of relative error more than 500% is 1.70%, where the average absolute error is 35.40 person trips, which is below the total average absolute error. Therefore, it does not mean that the poorer the relative error, the larger the absolute error, and the worse the prediction performance. The prediction effect of the proposed model can still be guaranteed.Figure 5
Comparison of absolute error and cumulative percentage.Besides that, the error results of different categories between new lines and existing lines in the models are shown in Table7. The proposed model’s mean absolute error results are relatively low when predicting the new line, namely, only 23.14 and 23.26 person trips. In the prediction performance of the existing line to existing line, the error is relatively larger than that of others, mainly because of the large basic flow between existing stations.Table 7
Mean absolute error of prediction results.
CategoryMean absolute error (person trips)SCGSVMBPRBFThe proposed modelExisting to new lines49.9299.8167.2682.9623.14New line to existing line48.0776.62119.80105.6423.26New line to new line90.03141.7296.56131.5541.30Existing line to existing line154.94152.50152.12171.6864.10Whole network130.22140.86139.08157.2754.63In this case, the holiday of New Year’s Day is chosen for analysis. However, other holidays might be a little longer in time, and passenger flow patterns and choice behavior would be different in some ways. The proposed destination choice model could be used to reflect the choice behavior characteristics and passenger flow rules, so the methodology applies to all holidays. Considering the validation and portability of the proposed method, this study supplemented a case of the National Day (seven-day holiday) for a relatively comprehensive experimental design. One day of the National Day in 2014 was randomly selected for model estimation (that is, October 2, 2014), and the proposed method was used to predict the passenger flow distribution on the same day of next year.There is one small difference in the calibrated parameters as shown in Table5 above, which reflects the slight distinction of the travel characteristics in different holidays. However, all absolute t-values are still greater than 1.96, and the adjusted ρ2 is over 0.2, which indicates that the model is still applicable and reliable. The prediction deviation graph is also drawn to show the overall error, as shown in Figure 6. For the convenience of reading, the scatter plot is given as shown in Figure 7, which is consistent with the meaning expressed in Figure 6. The graph plots values for the modeled prediction along the Y-axis and the corresponding actual count along the X-axis. If all of the predictions match the actual value exactly, the points on the graph would match up with the red line (45 degree line) drawn in the graph. The prediction results of the proposed model are mostly close to the red line, illustrating that the prediction performs well. The National Day’s comparison models’ error statistics are shown in Table 8. In summary, the prediction effect and accuracy are still ideal than the other models. The validation and applicability in other holiday scenarios can still be guaranteed. And it can be more effectively applied to practical engineering.Figure 6
Prediction deviation of the proposed model on the National Day.Figure 7
Scatter plot of predicted and actual value result presentation.Table 8
Statistics of model deviation in the National Day.
Case2: the National DaySCGSVMBPRBFThe proposed modelMaximum of absolute error (person trips)56818931673043202467Mean absolute error (person trips)129.07110.29109.2579.5851.63Proportion of absolute errors over 50 trips (%)51.5843.6348.3437.5323.49Proportion of absolute errors over 100 trips (%)32.4426.1626.9920.6812.55Proportion of absolute errors over 200 trips (%)16.5312.5812.409.705.47Proportion of relative error over 20% (%)81.1084.6682.4573.0665.15Proportion of relative error over 50% (%)55.4062.9359.8043.6631.61Proportion of relative error over 100% (%)31.8635.7338.5226.5614.06


## 5. Conclusions

This paper utilizes AFC data to propose a forecasting model for passenger flow distribution for urban rail transit, which is suitable for network structure and the unique characteristics of holidays. The weighted exogenous sampling maximum likelihood (WESML) estimation method is used to calibrate the parameters. The aggregate data extracted from AFC are transformed into the disaggregate form, which realizes the valid calibration of the parameters. It reduces the difficulty of data acquisition and enhances the applicability of the model, meanwhile ensuring acceptable accuracy.In the proposed model, the destination choice model defines destination attraction, land matching degree, and others as explanatory variables. This is the main advantage of the model’s interpretability and predictive power. The model presents reasonable performance becauset-values are all greater than 1.96, and the moderately adjusted ρ2 is over 0.2. Moreover, the calibration results show that both travel and transfer time have significant negative effects on passengers’ destination choice, while other variables such as destination attraction and land matching degree have a positive influence. The results also show that the public transportation card passengers care more about both travel and transfer time when other variables remain unchanged. The dummy variables used to describe the attractiveness and accessibility of the destination also have reasonable interpretability and significance. The proposed model is applied to predict two cases of Guangzhou Metro on New Year’s Day and National Day. Compared with the gravity model, SVM, BP, and RBF models, the proposed model’s error is greatly reduced, which proves the validation and applicability of the prediction model in different holiday scenarios with network changes.As more cities rely on metro systems, accurately forecasted holiday passenger flow distribution could provide important primary data for the metro operation management department to develop a useful organization scheme before the holiday period, which is conducive to easing congestion and improving holiday emergency response capabilities.Since it is difficult to obtain real land-use data around stations, this paper clusters the stations with similar passenger flow characteristics and defines new variables describing the land-use connection into the model. Nonetheless, the impact of significant land-use changes on passenger flow is hard to capture accurately. Furthermore, the dynamic characteristics of traffic flow distribution could be an extending study, which has not yet been considered in this paper. In future research, more land-use attributes and dynamic traffic distribution could be taken into account to develop the distribution forecasting model.



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*Source: 9922660-2021-09-24.xml*