- Email: [email protected]
Bus timetabling considering passenger satisfaction: An empirical study in Beijing
Accepted Manuscript Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing Hua-Yan Shang, Hai-Jun Huang, Wen-Xiang Wu PII: DOI: Reference:
S0360-8352(19)30069-5 https://doi.org/10.1016/j.cie.2019.01.057 CAIE 5683
To appear in:
Computers & Industrial Engineering
Received Date: Revised Date: Accepted Date:
16 December 2017 4 December 2018 27 January 2019
Please cite this article as: Shang, H-Y., Huang, H-J., Wu, W-X., Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing, Computers & Industrial Engineering (2019), doi: https://doi.org/ 10.1016/j.cie.2019.01.057
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing
Hua-Yan Shanga,, Hai-Jun Huangb, Wen-Xiang Wuc a
Information College, Capital University of Economics and Business, Beijing 100070, China
b
School of Economics and Management, Beihang University, Beijing 100191, China and Key Lab of
Complex System Analysis Management and Decision, Ministry of Education, China c
Beijing Key Lab of Urban Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China
Corresponding author. E-mail address: shanghuayan@126. com (H. Y. Shang) 1
Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing
Abstract: Public transport is the key component in sustainable transportation. In China, large subsidies are provided by the national and local governments to encourage the use of public transport systems. However, high commuting demand leads to such incredible phenomenon that passengers have to climb windows for riding in buses during peak hours. Thus, a case study was conducted in a Beijing’s transport hub which covers 116 bus lines and ten stations. The existing bus timetabling is surprisingly manually made and 26.53% of the bus supply undertakes 59.19% of the bus demand, which results in unbearable long waiting time and on-board crowding. To find a bus timetabling method which is practical and applicable in China, three procedures are carried out. Firstly, the passenger satisfaction and the bus transit efficiency are simplified and formulated. Secondly, a preliminary bus timetabling method with consideration of passenger satisfaction is proposed for optimizing the bus frequency and headway. Thirdly, the bus timetabling is optimized by embodying a balance between the passenger satisfaction and the bus transit efficiency, subject to the constraints of load factor. This method is verified by field data and the results demonstrate that it has the advantage of reducing waiting time and lessening on-board discomfort. Keywords: Public transport; Bus timetabling; Waiting time; Congestion effect
1. Introduction Population growth exerts considerable pressure on infrastructure and natural resources in urban regions. For example, China has 102 extra large cities which have populations of more than ten million. By 2016, its urbanization level has risen to 56.1%. One of the most obvious problems in daily life is the transportation system, including environmental pollution, road accidents, and road congestions. How additional transportation demand will be served in growing urban regions is an important issue for achieving sustainability. Indeed, the relationship between the transportation system, urban form, trip demand, and energy use is paramount in addressing the challenges presented by urban growth. This may be attributed to considerable economic inefficiency and environmental degradation associated with excessive private vehicle travel. Thus, public transportation is recognized as a key component in the management and planning of urban regions (Otto and Boysen, 2014). With rapid economic growth of China, traffic congestion can be found everywhere in 2
China’s large cities. To alleviate traffic congestion, the Chinese government is insistently and constantly constructing a comprehensive transportation system with the use of a policy priority to public transport. The policy of vigorously developing the public transportation has been listed in The 13th Five-year Plan for National Economy and Social Development, and issued by the State Council (13th Five-Year Plan, 2015–2020). The general objective of this policy is to build a modern public transport system for each city so as to provide people fast, efficient, safe, green, and economical services. Accordingly, large subsidies are provided by the national and local governments to encourage the use of public transport systems. In Beijing, China, the government subsidies have grown by seven times from 2006 to 2013. The welfare was 3,672 million yuan (US$ 530 million) in 2006, and increased to 250,000 million yuan (US$ 3,600 million) in 2013. In 2014, Beijing government tried to adjust the bus fare, but the fare was still defined well below the system cost. The government bears over 60% of the total cost of public transport now (Statistical Yearbook, 2017). Unfortunately, the current public transport systems in most Chinese cities are not satisfactory. Low speed, low punctuality, poor comfort, inconvenient transferring, and low coverage, all these are problems being faced by the Chinese public transportation systems. Thus, we have conducted a series of field surveys to gain an in-depth understanding of the bus operations in real traffic, including a survey on public transport in Guomao Bridge transport hub (Shang et al., 2014). Nearly 1,500 buses are dispatched from this hub or pass by it with stopping during evening peak hours (17:00-19:30) and the bus fleet is called the world’s largest fleet by Chinese netizens. However, it has a large number of passengers queue at bus stops (see Fig. 1a). Some passengers even have to climb up the bus windows for riding in a bus (see Fig. 1b). Guomao Bridge hub is a classic transit-oriented transport hub. It is located at a central business district (CBD) of Beijing. A variety of public transportation services (e.g., metro trains, urban and suburban bus services) are provided. Tidal-traffic patterns and suburban bus services are prominent. Yanjiao Town is a large residential district in the suburbs. Only one corridor, named Beijing-Tongzhou Expressway, connects the work zone and the home zone (Fig. 2). On each weekday morning, over 300,000 commuters leave homes from Yanjiao Town and travel to Guomao Bridge along the corridor, and return in the afternoon. The suburban bus routes are operated in the region between Guomao Bridge hub and Yanjiao Town district, with fixed routes and a unique route number/name (e.g. Line 813). These routes are very important for the suburban commuters with stable passenger flows. Although they operate similarly with urban bus routes, this paper only focuses on the headway design of these trunk bus routes. 3
The objective of this paper is to find a bus timetabling method which is practical and applicable in China. This method relies heavily on the research background of Guomao Bridge transport hub (detailed in Section 3). Three procedures are carried out: Step 1: Formulate the passenger satisfaction and the bus transit efficiency. There are various important attributes that cannot easily be quantified and measured (Ceder, 2016). For simplicity, waiting time and bus comfort are considered to be the main attributes of the passenger satisfaction according to our survey data. Step 2: Develop a preliminary bus timetabling. The max load method is used to determine the frequencies and headways with smooth transitions are proposed. Step 3: Optimize the bus timetabling. An optimization model is developed with regard to the trade-off between the passenger satisfaction and the bus transit efficiency, subject to the constraints of load factor. In this way, the scheduler will be in a position not only to expedite manual/semi-manual tasks, but also to compare procedures and methods in regard to the trade-off between the passengers’ comfort and the operating efficiency. The rest of the paper is organized as follows: In the next section, a literature review of bus scheduling and passenger satisfaction is provided. The survey and some analyses are presented in Section 3. In Section 4, we formulate the passenger satisfaction and develop the new bus timetabling method. The practical application of the method is illustrated in Section 5. Section 6 concludes the paper.
2. Literature review In the last decades, a fruitful development of models and solution techniques were addressed in bus transport systems. Earlier researches included the design and evaluation of vehicle holding strategies (Osuna and Newell, 1972; Barnett and Kleitman, 1973; Barnett, 1974). Models proposed in these studies aimed to minimize the number of buses required under rather restrictive conditions. At that time, there were not good computational techniques to solve these models and survey data to verify them. Afterwards, the research interest was extended to investigate other strategies such as stop skipping, signal priority, reduction of bus dispatch uncertainty, short-turning, and headway control (Turnquist and Bowman, 1980; Furth and Wilson, 1981; Abkowitz and Engelstein,1984; Wilson et al., 1992; Khasnabis et al., 1999). These studies were empirically validated with data from actual transit operations. For example, Turnquist and Bowman (1980) utilized the data from a bus route in Evanston of Illinois, and Abkowitz and Engelstein (1984) employed the data from Los Angeles of California. It was generally supposed that the strategies proposed were expected to be 4
effective in reality as they were examined by real data (Strathman et al., 2002). Later, passenger waiting time at a bus station and load factor were paid much attention and deeply studied (Rajbhandari et al., 2003; Mishalani, 2006; Badami and Haider, 2007; Toledo et al., 2010; Ceder, 2013). Timetable synchronization is regarded as a useful strategy utilized to reduce passenger waiting time and improve service connectivity. Fonseca et al. (2018) studied the integration of timetabling and vehicle scheduling to reduce passenger-associated costs and operating costs. However, most of the studies on timetable synchronization design focused only on minimizing the transfer waiting time (Liu and Ceder, 2017). Load factor was widely used for frequency and vehicle-size determination. Max-load method is still popular now. It is a general agreement that the in-vehicle and out-of-vehicle times cannot be equally treated since the out-of-vehicle time is much more onerous for determination (Ei-Geneidy et al., 2006). Thus, the load factor can be regarded as an un-direct variable affecting passenger waiting time. These studies consciously inferred that high load factor could reduce waiting time. However, they ignored that higher load factor means higher level of on-board crowding and lower passenger satisfaction. The global public transit problem is computationally intractable and can hardly be tackled at once. Desaulniers and Hickman (2007) divided it into a set of sub-problems that were usually solved sequentially at various stages of the planning process (strategic, tactical, and operational) and during operations (real-time control). They provided a systematic way of reviewing state-of-the-art models and approaches for solving the public transit problems. Ibarra-Rojas et al. (2015) followed this classification. Guihaire and Hao (2008) presented a global review of the crucial strategic and tactical steps of transit planning: the design and scheduling of the network. They followed a five-step planning process including network design, frequencies setting, timetable development, bus scheduling, and driver scheduling (Ceder, 2016). Some studies aim to get a bus schedule which can implement “fewer buses, no waiting time” (Ceder, 2016), but congestion cost or crowding effects have not been fully elucidated (Prud’homme et al, 2012; Tirachini et al. 2013). From the perspective of a transit provider, optimal transit service can be characterized by predictable passenger activity and few service reliability problems. Passengers expect that buses arrive promptly at stops that access, egress, and waiting times are minimized. Also, they seek to minimize their combined in-vehicle and out-of-vehicle travel times. Thus, many studies tried to reveal the quality paradox between service supply and passenger satisfaction (Michaelis and Schöbel, 2009; Friman and Fellesson, 2009; Lai and Chen, 2011). These works mainly focused on such aspects as qualitatively evaluating the reliability, frequency, travel time, fare, comfort, cleanliness, network coverage, safety, and the information released to passengers (Friman and Fellesson, 2009). However, for 5
passenger satisfaction, there are too many quality-based attributes and the importance of attributes being negatively or positively perceived by individual passengers depends on their preferences. It is hard to quantify passenger satisfaction thus qualitative analyses are preferred. In all the attributes of passenger satisfaction, congestion/crowding effects in transit systems have attracted much attention. Congestion leads to on-board discomfort, denied boarding, and low service reliability. Kurauchi et al. (2003) considered the failure-to-board probability and Schmöcker et al. (2008) developed a quasi-dynamic frequency-based model. In addition to capacity constraints, the on-board discomfort effect is presented in Trozzi et al. (2013). Sumalee et al. (2009) and Schmöcker et al. (2011) introduced fail-to-sit probability to satisfy the set of priority rules and the seat capacity constraint. In-vehicle seat priorities were also incorporated by Leurent et al. (2014). Tirachini (2013, 2014) identified and analyzed the interplay between congestion and crowding externalities in the design of urban bus systems. Nuzzolo et al. (2012) and Pel et al. (2014) proposed models that estimate on-board discomfort based on average crowding levels (e.g. volume/capacity or load/seats ratios). These models would underestimate the congestion effect since compared to less crowded vehicles, passengers experienced more discomfort in overcrowded vehicles. Cats et al. (2016) took three distinct congestion effects into account: on-board discomfort, denied boarding, and irregular vehicle arrivals. However, they focused on modeling these effects and the bus timetabling was not considered in their paper. On the other hand, the bunching phenomenon became the most noticeable phenomenon (Cats et al., 2016) and He (2015) suggested an anti-bunching strategy to improve bus schedule and headway reliability by using available accurate information. And yet, up to date, there has not been an explicit function which is calibrated by survey data and can be used to measure the passengers’ discomfort cost caused by crowding in vehicle. Huang et al. (2007) and Tian et al. (2007) quantitatively considered the congestion cost which was formulated as a function of congestion degree and travel time. They conducted a survey at a subway station in Beijing. However, they assumed that the function was linear for deriving an analytical solution. The impact of congestion/crowding effects has seldom been considered in scheduling bus timetable. To our knowledge, discomfort due to crowding in vehicle is usually neglected in the objective functions. Especially, long travel time due to long distance in a crowding vehicle always causes additional psychological discomfort. Jiang et al. (2014) proposed an optimization model to reach the minimization of the waiting time cost, the crowding cost, and the operating cost. But the passenger demand was assumed to be relatively low. With rapid urbanization in China, many transport hubs have sprung up to serve the transportation between CBD and outskirts, similar to Guomao Bridge hub. A variety of public 6
transportation services are provided, among which the suburban bus services account for a large proportion. However, different from those traditional suburban ones, the demands for these outskirt bus services are high. They operate similarly with the urban bus routes, but the trip times are usually long. Thus, passengers expect more efficient service (e.g., high bus frequency) to reduce the waiting time and improve the in-vehicle comfort. In contrast, bus companies are unwilling to operate the routes with low ridership. They always expect a longer headway to reduce operating costs. Moreover, since the passenger flow decreases from downtown to outskirts, bus companies expect higher ridership at the departure stops. Hence, it is important to balance the interests of both passengers and bus companies. In this paper, our model tries to reach the balance of the passenger satisfaction and the bus transit efficiency. The waiting time cost, the discomfort due to crowding in vehicle, and the load factor are considered. The objective of this paper is to find a bus timetabling method which is practical and applicable in China. Thus, some simplified formulations are selected and a quantified modeling approach is adopted to account for the on-board crowding effects.
3. Survey In this section we first introduce the survey on public transport in Guomao Bridge hub and then address the initial findings related to our studies. This section is the model basis of Section 4 and the data source of Section 5. 3.1. Data collection Guomao Bridge transport hub of Beijing was selected for data collection during the evening peak hours (17:00-19:30). Fig. 3 shows the map of this hub with 1.1 square kilometers. All the parking lots, subways, bus stops, and surrounding buildings within this hub are our objects for investigation. We recorded the passenger flows generated from these sites. The operations of 116 bus lines at ten stations, including passenger arrival rates, bus arrival time intervals, passenger waiting times, and queuing lengths, were observed and statically analyzed. The survey lasted for three months from April 2012 to June 2012, and 60 undergraduate students were recruited. Direct observation and video tape recording were simultaneously employed. All field works were finished on weekdays with good weather conditions. 3.2. Initial findings (1) About 80,000 commuters go home during the peak hours of each workday in this hub,, 7
among which 5,857 are transported by private car or taxi, 27,660 by subway, and 42,238 by bus. 1,500 buses of 116 lines serve the commuters from ten stations. (2) 19 bus lines (16.38% of the total lines) serve on suburban bus routes. They dispatch 398 buses (26.53% of the total bus supply) during evening peak hours while transport nearly 25,000 passengers (59.19% of the total bus demand), which means 26.53% of the bus supply undertakes 59.19% of the bus demand. Thus, overload is inevitable. (3) 97 bus lines (83.62%) served on the urban bus routes. 1102 buses of these lines pass by Guomao Bridge transport hub with low bus loads. (4) The special geographical condition leaves the suburban bus commuters with no choice. The sketch map of the suburban bus routes is shown in Fig. 4. These routes depart from Guomao Bridge hub. Each has an independent bus line and a unique route number/name. The passenger flow decreases from the hub to the home zone. So, optimal timetable at the departure stops in the hub is highly important. (5) All vehicles of the suburban bus lines seem to be scheduled manually. Total number of
buses is basically constant but headways fluctuate largely for each line. Bunched and delayed bus arrivals are common. Fig. 5 shows the bus headways for Line 807 in the direction of vertical axis (in minutes), whereas the horizon axis represents the bus order from the first vehicle to the last one. The average headway was three minutes during the surveyed periods. However, the vehicles did not arrive evenly. A vehicle might be late for over ten minutes while other headways might be less than one minute (delayed arrivals vs. bunched arrivals in Fig. 5).
Consequently, vehicles’ uneven arrivals lead to long passengers’ waiting times.
(6) There are significant differences among actual, perceived, and tolerable waiting times for riding in the suburban buses1, as shown in Table 1. The average tolerable waiting time is nearly half an hour because the suburban passengers have no other choice but to wait. The average perceived waiting time is much larger than the actual one, i.e., the passengers over-evaluate their waiting times. In other words, long actual waiting times make the passengers anxious and cause higher perceived waiting times. 1
S0360-8352(19)30069-5 https://doi.org/10.1016/j.cie.2019.01.057 CAIE 5683
To appear in:
Computers & Industrial Engineering
Received Date: Revised Date: Accepted Date:
16 December 2017 4 December 2018 27 January 2019
Please cite this article as: Shang, H-Y., Huang, H-J., Wu, W-X., Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing, Computers & Industrial Engineering (2019), doi: https://doi.org/ 10.1016/j.cie.2019.01.057
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing
Hua-Yan Shanga,, Hai-Jun Huangb, Wen-Xiang Wuc a
Information College, Capital University of Economics and Business, Beijing 100070, China
b
School of Economics and Management, Beihang University, Beijing 100191, China and Key Lab of
Complex System Analysis Management and Decision, Ministry of Education, China c
Beijing Key Lab of Urban Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China
Corresponding author. E-mail address: shanghuayan@126. com (H. Y. Shang) 1
Bus Timetabling Considering Passenger Satisfaction: an Empirical Study in Beijing
Abstract: Public transport is the key component in sustainable transportation. In China, large subsidies are provided by the national and local governments to encourage the use of public transport systems. However, high commuting demand leads to such incredible phenomenon that passengers have to climb windows for riding in buses during peak hours. Thus, a case study was conducted in a Beijing’s transport hub which covers 116 bus lines and ten stations. The existing bus timetabling is surprisingly manually made and 26.53% of the bus supply undertakes 59.19% of the bus demand, which results in unbearable long waiting time and on-board crowding. To find a bus timetabling method which is practical and applicable in China, three procedures are carried out. Firstly, the passenger satisfaction and the bus transit efficiency are simplified and formulated. Secondly, a preliminary bus timetabling method with consideration of passenger satisfaction is proposed for optimizing the bus frequency and headway. Thirdly, the bus timetabling is optimized by embodying a balance between the passenger satisfaction and the bus transit efficiency, subject to the constraints of load factor. This method is verified by field data and the results demonstrate that it has the advantage of reducing waiting time and lessening on-board discomfort. Keywords: Public transport; Bus timetabling; Waiting time; Congestion effect
1. Introduction Population growth exerts considerable pressure on infrastructure and natural resources in urban regions. For example, China has 102 extra large cities which have populations of more than ten million. By 2016, its urbanization level has risen to 56.1%. One of the most obvious problems in daily life is the transportation system, including environmental pollution, road accidents, and road congestions. How additional transportation demand will be served in growing urban regions is an important issue for achieving sustainability. Indeed, the relationship between the transportation system, urban form, trip demand, and energy use is paramount in addressing the challenges presented by urban growth. This may be attributed to considerable economic inefficiency and environmental degradation associated with excessive private vehicle travel. Thus, public transportation is recognized as a key component in the management and planning of urban regions (Otto and Boysen, 2014). With rapid economic growth of China, traffic congestion can be found everywhere in 2
China’s large cities. To alleviate traffic congestion, the Chinese government is insistently and constantly constructing a comprehensive transportation system with the use of a policy priority to public transport. The policy of vigorously developing the public transportation has been listed in The 13th Five-year Plan for National Economy and Social Development, and issued by the State Council (13th Five-Year Plan, 2015–2020). The general objective of this policy is to build a modern public transport system for each city so as to provide people fast, efficient, safe, green, and economical services. Accordingly, large subsidies are provided by the national and local governments to encourage the use of public transport systems. In Beijing, China, the government subsidies have grown by seven times from 2006 to 2013. The welfare was 3,672 million yuan (US$ 530 million) in 2006, and increased to 250,000 million yuan (US$ 3,600 million) in 2013. In 2014, Beijing government tried to adjust the bus fare, but the fare was still defined well below the system cost. The government bears over 60% of the total cost of public transport now (Statistical Yearbook, 2017). Unfortunately, the current public transport systems in most Chinese cities are not satisfactory. Low speed, low punctuality, poor comfort, inconvenient transferring, and low coverage, all these are problems being faced by the Chinese public transportation systems. Thus, we have conducted a series of field surveys to gain an in-depth understanding of the bus operations in real traffic, including a survey on public transport in Guomao Bridge transport hub (Shang et al., 2014). Nearly 1,500 buses are dispatched from this hub or pass by it with stopping during evening peak hours (17:00-19:30) and the bus fleet is called the world’s largest fleet by Chinese netizens. However, it has a large number of passengers queue at bus stops (see Fig. 1a). Some passengers even have to climb up the bus windows for riding in a bus (see Fig. 1b).
2. Literature review In the last decades, a fruitful development of models and solution techniques were addressed in bus transport systems. Earlier researches included the design and evaluation of vehicle holding strategies (Osuna and Newell, 1972; Barnett and Kleitman, 1973; Barnett, 1974). Models proposed in these studies aimed to minimize the number of buses required under rather restrictive conditions. At that time, there were not good computational techniques to solve these models and survey data to verify them. Afterwards, the research interest was extended to investigate other strategies such as stop skipping, signal priority, reduction of bus dispatch uncertainty, short-turning, and headway control (Turnquist and Bowman, 1980; Furth and Wilson, 1981; Abkowitz and Engelstein,1984; Wilson et al., 1992; Khasnabis et al., 1999). These studies were empirically validated with data from actual transit operations. For example, Turnquist and Bowman (1980) utilized the data from a bus route in Evanston of Illinois, and Abkowitz and Engelstein (1984) employed the data from Los Angeles of California. It was generally supposed that the strategies proposed were expected to be 4
effective in reality as they were examined by real data (Strathman et al., 2002). Later, passenger waiting time at a bus station and load factor were paid much attention and deeply studied (Rajbhandari et al., 2003; Mishalani, 2006; Badami and Haider, 2007; Toledo et al., 2010; Ceder, 2013). Timetable synchronization is regarded as a useful strategy utilized to reduce passenger waiting time and improve service connectivity. Fonseca et al. (2018) studied the integration of timetabling and vehicle scheduling to reduce passenger-associated costs and operating costs. However, most of the studies on timetable synchronization design focused only on minimizing the transfer waiting time (Liu and Ceder, 2017). Load factor was widely used for frequency and vehicle-size determination. Max-load method is still popular now. It is a general agreement that the in-vehicle and out-of-vehicle times cannot be equally treated since the out-of-vehicle time is much more onerous for determination (Ei-Geneidy et al., 2006). Thus, the load factor can be regarded as an un-direct variable affecting passenger waiting time. These studies consciously inferred that high load factor could reduce waiting time. However, they ignored that higher load factor means higher level of on-board crowding and lower passenger satisfaction. The global public transit problem is computationally intractable and can hardly be tackled at once. Desaulniers and Hickman (2007) divided it into a set of sub-problems that were usually solved sequentially at various stages of the planning process (strategic, tactical, and operational) and during operations (real-time control). They provided a systematic way of reviewing state-of-the-art models and approaches for solving the public transit problems. Ibarra-Rojas et al. (2015) followed this classification. Guihaire and Hao (2008) presented a global review of the crucial strategic and tactical steps of transit planning: the design and scheduling of the network. They followed a five-step planning process including network design, frequencies setting, timetable development, bus scheduling, and driver scheduling (Ceder, 2016). Some studies aim to get a bus schedule which can implement “fewer buses, no waiting time” (Ceder, 2016), but congestion cost or crowding effects have not been fully elucidated (Prud’homme et al, 2012; Tirachini et al. 2013). From the perspective of a transit provider, optimal transit service can be characterized by predictable passenger activity and few service reliability problems. Passengers expect that buses arrive promptly at stops that access, egress, and waiting times are minimized. Also, they seek to minimize their combined in-vehicle and out-of-vehicle travel times. Thus, many studies tried to reveal the quality paradox between service supply and passenger satisfaction (Michaelis and Schöbel, 2009; Friman and Fellesson, 2009; Lai and Chen, 2011). These works mainly focused on such aspects as qualitatively evaluating the reliability, frequency, travel time, fare, comfort, cleanliness, network coverage, safety, and the information released to passengers (Friman and Fellesson, 2009). However, for 5
passenger satisfaction, there are too many quality-based attributes and the importance of attributes being negatively or positively perceived by individual passengers depends on their preferences. It is hard to quantify passenger satisfaction thus qualitative analyses are preferred. In all the attributes of passenger satisfaction, congestion/crowding effects in transit systems have attracted much attention. Congestion leads to on-board discomfort, denied boarding, and low service reliability. Kurauchi et al. (2003) considered the failure-to-board probability and Schmöcker et al. (2008) developed a quasi-dynamic frequency-based model. In addition to capacity constraints, the on-board discomfort effect is presented in Trozzi et al. (2013). Sumalee et al. (2009) and Schmöcker et al. (2011) introduced fail-to-sit probability to satisfy the set of priority rules and the seat capacity constraint. In-vehicle seat priorities were also incorporated by Leurent et al. (2014). Tirachini (2013, 2014) identified and analyzed the interplay between congestion and crowding externalities in the design of urban bus systems. Nuzzolo et al. (2012) and Pel et al. (2014) proposed models that estimate on-board discomfort based on average crowding levels (e.g. volume/capacity or load/seats ratios). These models would underestimate the congestion effect since compared to less crowded vehicles, passengers experienced more discomfort in overcrowded vehicles. Cats et al. (2016) took three distinct congestion effects into account: on-board discomfort, denied boarding, and irregular vehicle arrivals. However, they focused on modeling these effects and the bus timetabling was not considered in their paper. On the other hand, the bunching phenomenon became the most noticeable phenomenon (Cats et al., 2016) and He (2015) suggested an anti-bunching strategy to improve bus schedule and headway reliability by using available accurate information. And yet, up to date, there has not been an explicit function which is calibrated by survey data and can be used to measure the passengers’ discomfort cost caused by crowding in vehicle. Huang et al. (2007) and Tian et al. (2007) quantitatively considered the congestion cost which was formulated as a function of congestion degree and travel time. They conducted a survey at a subway station in Beijing. However, they assumed that the function was linear for deriving an analytical solution. The impact of congestion/crowding effects has seldom been considered in scheduling bus timetable. To our knowledge, discomfort due to crowding in vehicle is usually neglected in the objective functions. Especially, long travel time due to long distance in a crowding vehicle always causes additional psychological discomfort. Jiang et al. (2014) proposed an optimization model to reach the minimization of the waiting time cost, the crowding cost, and the operating cost. But the passenger demand was assumed to be relatively low. With rapid urbanization in China, many transport hubs have sprung up to serve the transportation between CBD and outskirts, similar to Guomao Bridge hub. A variety of public 6
transportation services are provided, among which the suburban bus services account for a large proportion. However, different from those traditional suburban ones, the demands for these outskirt bus services are high. They operate similarly with the urban bus routes, but the trip times are usually long. Thus, passengers expect more efficient service (e.g., high bus frequency) to reduce the waiting time and improve the in-vehicle comfort. In contrast, bus companies are unwilling to operate the routes with low ridership. They always expect a longer headway to reduce operating costs. Moreover, since the passenger flow decreases from downtown to outskirts, bus companies expect higher ridership at the departure stops. Hence, it is important to balance the interests of both passengers and bus companies. In this paper, our model tries to reach the balance of the passenger satisfaction and the bus transit efficiency. The waiting time cost, the discomfort due to crowding in vehicle, and the load factor are considered. The objective of this paper is to find a bus timetabling method which is practical and applicable in China. Thus, some simplified formulations are selected and a quantified modeling approach is adopted to account for the on-board crowding effects.
3. Survey In this section we first introduce the survey on public transport in Guomao Bridge hub and then address the initial findings related to our studies. This section is the model basis of Section 4 and the data source of Section 5. 3.1. Data collection Guomao Bridge transport hub of Beijing was selected for data collection during the evening peak hours (17:00-19:30). Fig. 3 shows the map of this hub with 1.1 square kilometers. All the parking lots, subways, bus stops, and surrounding buildings within this hub are our objects for investigation. We recorded the passenger flows generated from these sites. The operations of 116 bus lines at ten stations, including passenger arrival rates, bus arrival time intervals, passenger waiting times, and queuing lengths, were observed and statically analyzed. The survey lasted for three months from April 2012 to June 2012, and 60 undergraduate students were recruited. Direct observation and video tape recording were simultaneously employed. All field works were finished on weekdays with good weather conditions.
among which 5,857 are transported by private car or taxi, 27,660 by subway, and 42,238 by bus. 1,500 buses of 116 lines serve the commuters from ten stations. (2) 19 bus lines (16.38% of the total lines) serve on suburban bus routes. They dispatch 398 buses (26.53% of the total bus supply) during evening peak hours while transport nearly 25,000 passengers (59.19% of the total bus demand), which means 26.53% of the bus supply undertakes 59.19% of the bus demand. Thus, overload is inevitable. (3) 97 bus lines (83.62%) served on the urban bus routes. 1102 buses of these lines pass by Guomao Bridge transport hub with low bus loads. (4) The special geographical condition leaves the suburban bus commuters with no choice. The sketch map of the suburban bus routes is shown in Fig. 4. These routes depart from Guomao Bridge hub. Each has an independent bus line and a unique route number/name. The passenger flow decreases from the hub to the home zone. So, optimal timetable at the departure stops in the hub is highly important.
buses is basically constant but headways fluctuate largely for each line. Bunched and delayed bus arrivals are common. Fig. 5 shows the bus headways for Line 807 in the direction of vertical axis (in minutes), whereas the horizon axis represents the bus order from the first vehicle to the last one. The average headway was three minutes during the surveyed periods. However, the vehicles did not arrive evenly. A vehicle might be late for over ten minutes while other headways might be less than one minute (delayed arrivals vs. bunched arrivals in Fig. 5).
Consequently, vehicles’ uneven arrivals lead to long passengers’ waiting times.
(6) There are significant differences among actual, perceived, and tolerable waiting times for riding in the suburban buses1, as shown in Table 1. The average tolerable waiting time is nearly half an hour because the suburban passengers have no other choice but to wait. The average perceived waiting time is much larger than the actual one, i.e., the passengers over-evaluate their waiting times. In other words, long actual waiting times make the passengers anxious and cause higher perceived waiting times.