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FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING
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Specialization: Transport Engineering and Logistics
Report number: 2013.TEL.7809
Title:
Bus Bunching
Author:
T. Boontjes
Title (in Dutch) Het vormen van paren van bussen op een bus lijn
Assignment: literature assignment
Confidential: no
Initiator (university): Dr. F. Corman Supervisor: Dr. F. Corman
Delft University of Technology
FACULTY OF MECHANICAL, MARITIME AND MATERIALS ENGINEERING
Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
Student: T. Boontjes Assignment type: Literature
Supervisor: Dr. F Corman Report number: 2013.TEL.7809
Specialization: TEL Confidential: no
Creditpoints (EC): 10
Subject: Bus Bunching
Have you ever waited so long for a bus, and then two buses of the same line appear together one after each other? The phenomenon is called bus bunching and is an almost unavoidable result of uncontrolled systems dynamic in public transport networks. This phenomenon is also observed in other transport and logistics systems, if (discrete) vehicles are considered, with a fixed service time and a given arrival frequency of the goods/passengers to be moved.
This literature assignment is to study the phenomenon of bus bunching, making an overview of the different studies aiming at modeling it from a theoretical (closed-form) point of view, and simulation approaches. The similarities with analogous phenomena in other kind of transport networks should be discussed, as well as the approaches currently proposed to minimize such phenomenon during operations. The research in this assignment should cover the following:
Formally define the bus bunching phenomenon, the boundary condition for this phenomenon to arise, and the modeling approaches proposed in the literature
Study related phenomena arising in different transport contexts
Classify and compare control approaches that aim at limiting bus bunching phenomena Identify open issues in the literature
This report should be arranged in such a way that all data is structurally presented in graphs, tables, and lists with belonging descriptions and explanations in text.
The report should comply with the guidelines of the section. Details can be found on the website. The mentor,
Table of Contents
1. Introduction ... 1
2. Literature overview ... 2
Models describing the phenomenon ... 2
Early Literature ... 2 Holding Strategies ... 2 Stop Skipping ... 3 Short Turning ... 3 Deadheading ... 3 Signal Priority ... 3 Recent Literature ... 4 Holding strategies ... 4 Stop Skipping ... 4 Deadheading ... 5 Other strategies ... 5 Comparing Studies ... 5
Other means of transport, similar phenomena ... 7
3. Conclusions ... 7
1. Introduction
The phenomenon of bus bunching (also referred to in literature using many different names like Bus platooning, Vehicle Pairing, Headway Instability and Bus Clumping (Moreira-Matias, Ferreira, Gama, Mendes-Moreira, & de Sousa, 2012)) is already known for over 50 years (Newell & Potts, 1964). The phenomenon occurs due to instability in the bus line service. Consider two buses driving the same route. If the first bus has to dwell longer at a stop because of a lot of passengers boarding and alighting, the bus will lag behind schedule. In the meantime more passengers will have arrived at the next stop, and that will slow down the bus even more. The gap between the bus and the following bus will decrease and by that the amount of passenger for the second bus will also decrease, making the gap or headway between the busses even smaller. This will result in the buses clustering together or bunching. The reason that the first bus lags behind schedule, and by that creating the initial
instability, can also be traffic congestion, the boarding of disabled people or other disturbances. Figure 1 gives an illustration of the phenomena.
Figure 1 Buses d and c are considered, driving form the left to the right (a). Bus c is slowed down due to many passengers at stop Xi+2. The headway between both buses then reaches an instable
headway (b). This results in both buses following each other with almost zero headway (c). (Gerhenson & Pineda, 2009)
This report will give an overview on literature aiming at both defining the problem of bus bunching and finding solutions for the problem.
The literature overview will be divided in four parts. The first part will give a short overview of literature aiming at modelling and understanding the bunching problem, the second part contains an overview of the early research done on finding solutions. The third part will discuss more recent literature on solutions for the problem. This recent literature is different form the early research because of the introduction of both automated vehicle location (AVL) and automated passenger counting (APC) technologies. The last part of the literature overview describes research into bunching problems in other means of transportation besides buses
2. Literature overview
Models describing the phenomenon
As mentioned in the introduction bus bunching is already known of for a long time. Newell and Potts (1964) researched the implications to the following buses of delaying a bus at a stop. This paper is seen as the landmark paper for research into the bus bunching problem. Chapman and Michel (1978) modeled a transit line in an analytical model. Their model neglected the alighting of passengers and the capacity of the buses. The result of their research was an expression linking the bunching of vehicles to the number of stops it occurs. Nagatani (2001a) proposes an analytical model linking the speed of the buses to the headway and passengers waiting to board at a stop. He also studied the bunching effect when taking into account different behavior form the driver like skipping stops or speeding up when trying to catch up. This model is further extended for more buses in Nagatani (2002). The research resulted in three phases along the bus route: regular, bunching and oscillatory, and showed that the transfer between these phases depends on an amplification factor for the velocity and the number of bus stops.
More recently Bellei and Gkoumas (2010) developed a stochastic simulations, taking into account dwell time at the stops, capacity contains of the buses and arrival of passengers at the stops during the dwell time. The goal of the study was to show the relation between irregularities in the headway distribution and the bus bunching problem. Following up on this study Moreira-Matias et al. (2012) use ALV data for a more realistic model. They analyze the data by the use of sequence mining1 to identify the causes of the phenomenon. The main results of the paper are that bus bunching often starts at the initial bus stations, and that a high correlations exists between the headway variation at a certain stop and the following stops.
Early Literature
The literature focusses on different solutions for the bus bunching problem. The most commonly used strategy are the so called holding strategies, in which a bus is hold at the station to create a certain headway with the busses in front or behind (headway-based holding) or to adjust to a schedule (schedule-based holding. There are also other strategies focusing at letting buses skip stops and giving buses priority at intersections.
Holding Strategies
Research in vehicle holding strategies started with the research of Osuna and Newell (1972). Their analytical model was further improved the next years (Barnett, 1974) (Barnett & Kleitman, 1978) (Barnett, 1978). These models were simple using only a simple service loop with only one bus. So these models are were not yet applicable for real use. The models derive an optimal value for the threshold or headway as headway-based holding strategies do.
The previous holding strategies were using one specific control point, but the work of Turnquist and Blume (1980) showed that the highest benefit of an holding strategy can be achieved at the stop were the headway deviation is already significant, the amount of passengers in the vehicle is low, and the amount of passengers at the downstream stop is high. This shows that the stop were the control has to be executed can vary.
The results from these earlier studies can be summarized in the following points (Strathman, Kimpel, & Dueker, 2001):
Holding increases travel time for passengers already on the bus. Holding increases running time of the transit operation.
Holding is most effective when the amount of passengers in the bus is low, the amount of passengers at the stop is low and the amount of passengers on the downstream stop is high. Holding is most effective on the stops after the control point.
Headway variability increases again following control.
1 Sequential Pattern mining is a topic of concerned with finding statistically relevant patterns between data examples where the values are delivered in a sequence.
As described earlier in the literature on holding strategies two different holding strategies exist; headway-based holding and schedule-based holding. A lot of research has gone into determining which of these strategies is the most efficient. These studies use heuristics and Monte Carlo
simulations because of the complexity of describing transit routes analytically for instance the studies of Abkowitz and Engelstein (1984), Senevirante (1990). These models use a random pattern of passenger arrivals, and a binominal distribution for the number of passengers leaving the bus at a stop. The conclusion of these studies is that both headway-based holding and schedule-based holding are an improvement, but the headway-based holding has the largest impact.
Newer research on holding strategies focus again on analytical models, making use of more detailed transit models. The models determine, by the use of quadratic programming, an optimal holding time at the dispatch point of the bus route, or on a control point. Hickman (2001) describes an analytical stochastic model to determine the optimal vehicle holding time. The model describes both the service running times and the passenger boarding and alighting as stochastic processes, which is closer to reality. The model still contains some shortcomings:
The vehicle capacity is assumed infinite. The holding time is only solved for one vehicle.
The boarding and alighting time is assumed to be linear to the amount of passengers, this might not occur in some cases when handling passengers with special needs for instance. Passengers traveling in groups (arriving at the stop together and alighting the bus together)
are not taken into account.
Stop Skipping
As the name already states, stop skipping is a strategy in which the buses are allowed to skip a stop to avoid lateness of the bus. Although skipping stops increases the travel speed of the bus, decreases the waiting time of the on-board passengers and the passengers on the downstream stops, it
increases the waiting time for the passengers at the skipped stop and might discourage the passengers of the skipped stop to use the transit system (Lin, Liang, Schonfeld, & Larson, 1995).
Short Turning
Short turning involves a bus turning around before it reaches the end-point of the route, and by this reducing the headway variance in the opposite direction. Furth and Day (1984) describe the
advantages and disadvantages of short turning as well as the most favorable conditions for the strategy to have an impact. The ideal scenario for short-turning is low bus speeds, and a small amount of passengers in the bus. The short-turning strategy still has to coop with the fact that passengers are left standing at the skipped stops. Most early models focus on finding the right stop to start the short turning (Furth P. G., 1987) (Vijayaraghavan & Anantharamaiah, 1995).
Deadheading
Deadheading is comparable to both short turning and stop skipping. The vehicle is allowed to skip some stops, but does so empty. One main disadvantage of deadheading is that all passengers have to alight at a particular stop although it might not be their destination stop (Furth & Day, 1984). Other early literature on deadheading does exist, but focusses mainly on reducing the amount of vehicles used to sustain the transit operation (Furth P. , 1985) (Ceder & Stern, Deficit function bus scheduling with deadheading trip insertion for fleet size reduction, 1981) (Ceder, 2003) (Ceder, 2004).
Signal Priority
A small part of literature focusses on reducing delays in the transit system based on giving buses priority at intersections. This strategy is described by Lin et al. (1995). In comparison with the holding strategy reduces the waiting time for the passengers on the bus and increases the vehicle speed of the buses. The system does need real-time information on traffic densities, and also influences other traffic and intersecting bus lines.
Recent Literature
More recent literature is defined as literature in which modern technology such as AVL and APC make it possible to use real-time data about the position of the buses.
Holding strategies
Daganzo (2009a) proposes a control strategy using dynamic holding times, based on real-time
headway information. The model uses more control points to assure that the headway is closest to the desired headway, and no large corrections are needed. The fact that buses in this study can only react to disturbances ahead, and not behind makes this model not very suitable when disturbances are large. To overcome this problem Daganzo and Pilachowski (2011) and Daganzo (2009b) propose a model with cooperative control in which the bus speed is regulated based on the expected demand and the spacing between the current bus and both the bus in front of and behind it. In this way the model can react more easily to large disturbances. Xuan, Argote and Daganzo (2011) continue with the work of Daganzo (2009a) and introduce a virtual schedule into the model, which has as an advantage that it can be applied to transit lines with both short and long headways, due to the fact that the buses are then able to stick to a schedule.
The literature previously mentioned does not take into account the capacity of each bus. Delgado et al. (2009) use a combination of vehicle holding and boarding limits, even when the bus is not yet at capacity to increase operating speed. The objective of the model is to minimize de total time of the passengers in the system, from the moment they arrive at the stop until they reach their destination. Later this model was improved by Delgado et al. (2012). They made is possible for the model to use a holding only strategy when boarding limits were not wished for and compared the model of Delgado et al.(2009) to the new model of Delgado et al.(2012). They concluded that a combination of holding and boarding limits has a significant advantage over holding only when used on a transit line with a high passenger load and short headways. The most recent paper discusses in this report, is the paper from Chen et al. (2012). The paper also considers holding but then in combination with boarding at the same time, this is different from earlier papers. It uses a simulation case study with real-time bus operation data from the Chicago Transit Authority (many of the recent papers use this data to
evaluate their models). Although the results in this paper are compared with other papers from almost 10 years ago, it shows some promising results with regard to the fast algorithm used, and the use of boarding while holding out-performs the older models with holding only.
Bartholdi and Eisenstein (2011) use a different approach compared with the work mentioned above. Their method uses neither a schedule nor a desired headway. Their model focusses on dynamically self-equalizing the headway of the buses. The buses do not need intervention from the management or even the drivers. The system tries to converge to the smallest possible headway given the capacity and the load on the transit line. If a bus reaches the control point, a snapshot is taken form the positions of the buses on the line, and the bus is held at the control point to achieve a regular headway. The system was tested at a bus-line on the campus of the Georgia institute of technology, and results showed that it, in that case, performed better than systems using a target headway or target schedule.
Stop Skipping
The literature mentioned in this chapter so far all focus on holding strategies, and although earlier literature did not show the benefits of stop-skipping, research in this field has continued. Sun and Hickman (2005) investigate the implementation of a stop-skipping control model. To overcome one of the mayor drawbacks of stop-skipping they investigated the stop-skipping with the possibility to still drop of passengers at skipped stops. The decision whether to skip a stop or not is made real-time. They conclude that letting passengers still alight at a stop which is to be skipped, has, in most cases, an advantage over the basic stop skipping. Saez et al. (2012) investigate a hybrid predictive controller in which both holding and stop-skipping are considered. The decision on what to do is made when a bus arrives at the stop. A predictive controller then decides, based on minimizing the passengers’ total travel time. Although this research has shown some good results further research is still
recommended by the authors to obtain an optimal policy for the strategy by looking into the prediction horizon and the weight parameters of the model.
Deadheading
Eberlein and Wilson (1998) claim to be the first have the first model for a deadheading strategy in which data from AVL and APC are fully available. It has to be noted that their model was applied in a case study on the Green Line (MBTA)2 which is a light rail system, and because of that, other traffic will have less influence on the operation of the system. More recently Yu et al. (2012) developed a deadheading strategy in which the bus is not obligated to follow the exact route of the bus line when in the deadheading part.
Other strategies
Erath (2013) did a research on a specific line in Singapore where bus bunching was is large problem. Since bus bunching tends to become more of a problem along a longer line, it is proposed to simply cut the line in two shorter lines. Simulations have shown that the solution service reliability might be improved by 35%. The downside of this strategy is that passengers which used to travel the whole line have now to switch buses somewhere along the line. The question remains how many of the passengers actually use the whole length of the line, and by that will be affected by this problem.
Comparing Studies
Several papers are written to compare the different strategies with each other. The paper of Munoz et al. (2012) compares the holding strategies from both the study of Delgado et al. (2012) and Saez et al. (2012). The former makes decisions by solving a long-term deterministic prediction model, while the latter uses a hybrid predictive control methodology on a shorter horizon. The paper designs 8 different scenarios by varying the capacities of the buses, headway and passenger load. Results show that the hybrid predictive control strategy shows better results when capacity limits of the bus are never reached, but when they do, deterministic prediction performs better. The reason given for these results is that deterministic control has a long term horizon and can react earlier to prevent the buses from reaching capacity. The shorter prediction horizon of the hybrid prediction model lets the model react more precise and also the model uses a term for regulating headway and by that, the model performs better when the maximum capacity is not reached.
To get a more structured overview of the different recent studies, Table 1 is presented. The table groups the different studies in 3 parts, the first two represent comparable studies, and last one contains studies which cannot directly be linked together. The table sums up the different strategies used in the papers, what data they require, what the goal of the model is, whether bus capacity is taken into account or not, and in some cases the application suggested by the authors.
Table 1 Overview of recent literature
Paper Year Strategy Data Goal
Bus
Capacity Applicable
Daganzo 2009a Headway-based holding Headway with bus in front Target headway Unlimited Daganzo 2009b Headway-based holding and adjusting speed Headway with bus in front and behind (cooperative) Target headway Unlimited Daganzo and
Pilachowski 2011
Headway-based holding and adjusting speed
Headway with bus in front and
behind (cooperative) Target headway Unlimited
Xuan, Argote and
Daganzo 2011 Schedule-based holding Information of the bus in front
Minimizing total time in the system
of passengers Unlimited
Delgado et al. 2009 Headway-based holding and Boarding limits Real-time state of the system Minimizing total time in the system of passengers Constrained High frequency, low headway Delgado et al. 2012
Headway-based holding (only)
and Boarding limits Real-time state of the system
Minimizing total time in the system of passengers
Constraine d
High frequency, low headway
Bartholdi and
Eisenstein 2012 Headway-based holding Headway with the bus behind Variable headway Shuttle or temporary service Sun and Hickman 2005 Stop Skipping Real-time state of the system
Minimizing total time in the system
of passengers Unlimited
Saez et al. 2012 Stop Skipping and Holding Real-time state of the system Minimizing total time in the system of passengers Constrained
Chen et al. 2012 Headway-based holding while boarding Real-time state of the system Minimizing total time in the system of passengers Unlimited Short headway Yu et al. 2012 Deadheading Real-time state of the system
Minimize average passenger waiting time
Constraine d
High variation in passenger load
Other means of transport, similar phenomena
Although the work of van Oort, Wilson and van Nes (2010) and van Oort, Boterman and van Nes (2012) does not really focus on the bunching or platooning of transit vehicles, their work is still worth mentioning in this report due to its research on holding strategies, applied in a case study on a tramline (Tram Line 9 in Den Hague) instead of buses. The first research focusses on a short-headway service, and compares both a headway- and a schedule-based holding strategy. The difference with other research in the field of holding that in this case a maximum holding time is implemented as a variable. The maximum holding time is introduces because both passengers and drivers might not accept holding times longer than a certain value. The conclusions of this research are that when a maximum holding time is applied, a headway-based holding strategy is the most effective, while when no maximum holding time is specified, schedule based holding is the most effective. The second research compares using a schedule-based holding to not using holding at all on a long-headway service. Results are similar to results of other studies on holding strategies; Holding is better than no holding, and the best location for holding depends on the distribution of passengers.
In general research on rail systems is different from the research on busses because of the fact that rail networks are less influenced by other traffic, which means that in the case of bunching, it might be attractive to also try and speed up buses lagging behind, to reduce headway or catch up the lost time on the schedule.
3. Conclusions
There is an enormous amount of research done on the topic of improving bus-services in general. The reason for that can be the large amount of possible situations in which bus lines are used. Every line has different properties of the traffic situation, passenger distribution and passenger demand. The different papers are often based on a specific line, so the research is often applicable to a certain line or lines with comparable specifications.
Research on other means of transport show the same results as on busses with as main difference the absence of traffic, which makes speeding up the vehicle to regain time on the schedule a possibility. Most research has still only been done on relatively simple lines, without taking into account a whole network of lines which is often found in major cities. The influence of large transfer points is often mentioned in the papers as a direction for further research.
On the part of the passenger behavior, most models assume the passengers to arrive on their own randomly, but more realistic is when passenger arrive in groups, and also go through the system in groups although this might be difficult to model.
In general the bus bunching problem can be solved two ways. By speeding up the bus that is falling behind by using stop-skipping or short turning. Or slowing down the bus in front by the use of holding strategies. The first way can be hard to sustain in a busy city center because of traffic and
congestions. The holding strategies on the other hand do add extra time to the passenger on board, but overall the waiting time of the passengers in the system can be greatly improved. In some cases a combination of both might even be the best solution.
It can be concluded that what strategy is chosen for the bus bunching problem, depends on the application. And it is recommended to focus further research on more complicated networks.
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