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A Multi-Method Simulation of a High-Frequency Bus Line Using Anylogic

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A Multi-Method Simulation of a High-Frequency Bus Line Using Anylogic A multi-method simulation of a high-frequency bus line using AnyLogic Thierry van der Spek Name Two LIACS, Leiden University LIACS, Leiden University [email protected] [email protected] ABSTRACT able approach to visualize this bus line and create a better In this work a mixed agent-based and discrete event simula- comprehension of frequently occurring problems. One of the tion model is developed for a high frequency bus route in the external factors, the number of passengers, is modelled and Netherlands. With this model, different passenger growth can be configured to analyse several passenger growth sce- scenarios can be easily evaluated. This simulation model narios. The effect of these scenarios is illustrated by several helps policy makers to predict changes that have to be made key performance indicators (KPIs), determined by Arriva. to bus routes and planned travel times before problems oc- This paper is structured as follows: In Section 2, common cur. The model is validated using several performance indi- domain terminology is introduced to gain a better under- cators, showing that under some model assumptions, it can standing of the problems occurring. In Section 3, the prob- realistically simulate real-life situations. The simulation's lems occurring are described by formulating our KPIs. In workings are illustrated by two use cases. Section 4, we look into related work in this domain, and also at other agent-based and discrete-event simulation models. 1. INTRODUCTION Section 5 discusses the data that is considered and the data sets that are used. Also, the preprocessing of data that In all metropolitan areas, people rely on buses as a means is needed to generate our model is discussed. Thereafter, of transportation. Commuters increasingly use public trans- in Section 6, the modelling choices that are made are dis- port to get to or go from their work or study location in these cussed. In Section 7, the discussed model is validated using areas. This puts a high strain on bus companies to pro- the defined KPIs and two use cases of passenger growth are vide a reliable and frequent service, especially during rush discussed. Finally, in Section 8, we conclude this work and hours. The procession of buses is easily disrupted by dif- possible future perspectives are briefly discussed. ferent factors such as congestion, traffic lights, open bridges and passengers boarding or alighting. This causes delays, which again may cause bus bunching. Bus bunching, the 2. BACKGROUND INFORMATION uneven spacing of buses over a route, causes uneven load- In this section, we go over some basic definitions that are ing of passengers and therefore inefficient usage of material. needed to gain a better understanding of the problem defini- Furthermore, passenger satisfaction may be lower due to full tion and the proposed model. Furthermore, common charac- buses. teristics for service quality and reliability that the proposed In the Randstad megalopolis in central-western Nether- model provides insight into are defined. lands, several high-frequency bus lines are created to inter- connect cities. Such a high-frequency line provides a quick 2.1 Preliminaries connection between places, but inherently is challenged by In this section, notation needed to define the bus route these disruptive influences. This work aims to create insight and terminology used in the field of public transport are into these factors and their effect on travel time on one of given. Some definitions might be common knowledge, but these high-frequency bus lines between the cities of Leiden others are less known outside this discipline. arXiv:1704.05692v1 [cs.AI] 19 Apr 2017 and Zoetermeer, exploited by the Arriva bus company. A group of bus lines can be seen as a graph G = We show that a combination of agent-based and discrete- (V; E), which is a combination of a set of stops V = 1 event models using the AnyLogic simulation tool are a suit- fv0; v1; v2; : : : ; vng and a set of route segments E ⊆ V × V . A stop vi is a designated place at which passengers can alight 1 Anylogic Multimethod Simulation, http://anylogic.com/, Vis- or board the bus. ited: Feb 17, 2017 We define P to be the set of all possible bus trips: P = fv0; : : : ; vn j 80 ≤ i < n :(vi; vi+1) 2 E; (1) 80 ≤ h < i ≤ n : vh = vi =) (h; i) = (0; n)g A bus trip p 2 P of length n can then be seen as an This student paper is the result of an academic computer science research ordered sequence of n + 1 stops, where there exists a route project. Permission to make digital or hard copies of all or part of this work segment ei 2 E from every stop vi to its subsequent stop for personal or classroom use is granted without fee provided that copies are v . not made or distributed for profit or commercial advantage and that copies i+1 bear this notice on the first page. We call stops v0 and vn terminals. At these stops, the bus changes trips. Figure 1 shows a schematic overview of TTi DTi v0 v1 vi−1 vi vi+1 vn Figure 1: Schematic overview of bus stops along one direction of a bus line with n + 1 stops. The arrow indicates the direction in which the bus is travelling. Dots indicate possible other stops on the route. Stops 0 and n are terminal stops. a trip. they are part of the R-net concept2, which only allows these Between stops, the bus drives these specific route seg- specific buses to drive designated routes. ments. The time that each segment ei takes is called travel To create a reliable bus line there are some important fac- time (TTi). Travel time can be measured between stop de- tors that have to be optimized. In this work, the R-net 400 partures, between departure at stop vi and arrival at stop bus line is simulated, whilst giving insight into some of these vi+1 or vice versa. We define travel time (TTi) between stop factors. Two main components of customer satisfaction are vi−1 and vi as the time between departure at stop vi−1 and waiting time and seat availability [14]. We discuss both of arrival at stop vi, which is the time it takes to travel seg- them below. ment ei. We note that when we talk about travel time, we talk about the time that it takes to travel a route segment Waiting time towards a stop from its preceding stop, therefore e0 is not Waiting time is mainly determined by bus punctuality and defined. regularity. Bus lines can either consist of a single trip in which the start terminal is the same as the end terminal v = v , or 0 n • Punctuality: punctuality is usually seen as being on two trips in roughly opposite directions v0 6= vn. For the first case we have a circular bus line, which is more common time. Punctuality shifts are caused by any deviation in urban areas. In the latter case most bus stops are usually from the scheduled arrival time at a stop. In this in opposite sides of the road to allow passengers to travel in paper, the term punctuality is used as the inverse, both directions of the route. so that an increase in punctuality defines a larger Furthermore, stops are defined by a GPS radius. This deviation from the schedule. This can be calculated GPS radius is roughly 35 metres. The time the bus spends for a single stop, or all stops of a line. For a stop vi, we can for example calculate the average (departure) within the radius of stop vi is known as dwell time of stop punctuality Q¯i on a trip p as follows: vi (DTi). Within this GPS radius the bus stops to let pas- sengers board or alight the bus. Doors open within a stop's GPS radius. The time that the bus' doors are open within ki the radius of stop vi is defined as door open time (DOTi). P act sched Di;j − Di;j Bus operators have a specific itinerary of trips that they j=1 Q¯i = (2) drive during the day, this is called the operators' run R ⊂ P . ki A run implies that operators possibly have to switch buses where: at terminals. Buses also have a specific itinerary of trips C ⊂ P which called the bus' circulation. A bus circulation ki: number of buses departing from stop i sched could be on the same line, but a bus may also switch lines, Di;j : scheduled departure time at stop i of vehicle j thus changing routes. act Buses can also enter or leave the system at terminals. Di;j : actual departure time at stop i of vehicle j Some parts of the day (off-peak hours) may have longer headways, which is the time between one bus and the next bus on the same trip. This means total bus capacity is re- The formulation in Equation 2 has the downside that duced and some buses return to the garage to be stored. it does not indicate if vehicles depart too early or too The drive from and to the garage is not indicated as a trip, late, but compensates departures that are too early but is called deadhead. This happens at the start and end with departures that are too late. One solution is to of a bus' circulation. A bus can have multiple circulations take the absolute value of the difference, but then trips during the day thus also having multiple deadheads.
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