Evaluation of passenger delays under different levels of information using a large-scale adaptive route choice model

Abstract

One thing about public transport is certain; it is uncertain. This study proposes a methodology that allows determining realistic door-to-door passenger delays incurred on the basis of such uncertainties. By combining Automated Vehicle Location (AVL) data for bus and train services with an adaptive route choice model, we test the influence of obtaining information about current delays by allowing four levels of adaptivity. The model is evaluated using more than 800,000 daily trips for 65 realised timetables of the large-scale multi-modal public transport network of the Metropolitan Area of Copenhagen. The model shows that adapting routes can heavily reduce incurred delays of passengers, even more so when updating routes during trips. 7 Keywords: 8 Passenger Delays, Public Transport Assignment, Agent-Based Simulation, Adaptive Route Choice, AVL Data, 9 Passenger Information

10 1. Introduction

11 Public transport services are rarely fully punctual, and as such its passengers will often get higher or lower travel 12 times than expected. Even when knowing the delays of all public transport services, the corresponding passenger 13 delays are difficult to determine as they depend on the exact routes of passengers – routes that might change during 14 the trip as passengers miss connections or discover that betters alternatives have arisen. Developing a model allowing 15 the calculation of such passenger delays while taking into account that passengers adapt to delays of the system is the 16 aim of this study. 17 Determining passenger delays are a lot easier if personal, trackable data is available, as shown by e.g. Jiang et al. 18 (2012); Sun et al. (2016a,b); Antos and Eichler (2016) for smart card data and Carrel et al. (2015) for smart phone 19 data. However, such data are rarely available, and obtaining permission to use such data can be tedious due to the 20 juridical aspect of dealing with sensitive personal data.

∗ Corresponding author

Email address: madsp@dtu.dk (Mads Paulsen)

Submitted to the 9th Symposium of the European Association for Research in Transportation (hEART), Lyon, 2020 February 1, 2020

21 Models for passenger delays without additional personal information have existed for small networks since Hick22 man and Bernstein (1997). A medium sized railway network was handled by Nielsen et al. (2009), who also evaluated 23 the impact of when to start looking for other alternatives. 24 Leng et al. (2018) used an agent-based approach to model passenger adaptation to a railway disruption, but as25 sumed either agents with a unrealistically low level of adaptation or knowledge about future delay. The same can 26 be said about Paulsen et al. (2018), which furthermore had two additional shortcomings. Firstly, the method was a 27 cumbersome iterative approach which also meant that the model could not handle the entire population in a metropoli28 tan area. Secondly, only railway delays were included in the study. The above mentioned shortcomings have been 29 addressed in the current study. 30 Zhu and Goverde (2019) introduced a dynamic passenger assignment model for major railway disruptions that 31 incorporates passenger responses to information given to passengers. However, it was only applied to a small network 32 with 17 stations, and only considering a single disruption. 33 Khani (2019) proposed a model, that theoretically could be used for modelling passenger delays, as it allows 34 modelling uncertain travel times whilst taking the probability of missing a transfer into account. However, it lacks the 35 ability to include correlation between delays across departures, and is not suitable for evaluating several days of AVL 36 data, as the computation time would scales with the number of included days to the power three. 37 Finally, some studies deal with the managing the operational side to minimise passenger delays, e.g. Dollevoet 38 et al. (2012); Zhen and Jing (2016); Corman et al. (2017); Ghaemi et al. (2018), but it is beyond the scope of this short 39 paper to go into a detailed review of those. 40 We contribute to the literature by proposing an adaptive route choice model for large-scale multi-modal public 41 transport networks that allows en-route decisions of its agents. Dynamic changes to the routes are allowed on-the-go, 42 and is dependent on the level of information the agent receives, ranging from no information to receiving information 43 about new optimal paths every two and a half minutes based on the current delays of vehicles in the public transport 44 system. 45 The remainder of the paper is structured as follows. Section 2 describes the proposed adaptive route choice model 46 in brief. Section 3 introduces the data used in the study, and tests the methodology on a large-scale case study of 47 Metropolitan Area of Copenhagen while investigating the impact of different levels of passenger information. Section 48 4 summarises the findings and discuss limitations and future work related to the study.

49 2. Model

50 We propose a dynamic public transport assignment model, that starts by obtaining initially planned routes of agents 51 determined by searching for the shortest path in the planned timetable. As time progresses, agents move through the 52 system either by foot or in a public transport service. At some moments in time, t = nτ, n ∈ N with τ = 150s, the 53 agents may search for the shortest path from their current location to their destination in a partially realised timetable

54 that includes delays up to that time and constantly extrapolated delays beyond. If a better alternative exists, the agent 55 changes its route and starts to pursue this instead of the previous. 56 By restricting every agent to search at the same time (multiples of τ), their partial realised timetables are equal, 57 why we only need to create realised timetables and corresponding RAPTOR (Delling et al., 2015) for these moments 58 in time. Searching in a RAPTOR graph is very fast, and since its construction time is also manageable, this approach 59 causes the entire model to be rather fast. We have used the version of RAPTOR proposed by and implemented in 60 JAVA by Rieser et al. (2018), which is both fast and easily configurable. For agents onboard public transport services, 61 a slightly modified search is performed. Firstly, the search is done from the next stop of that service, H ∗ , at the time the 62 service reaches that stop, t∗ – however based on the delay information up until time t like all other agents. Secondly, 63 no boarding penalty is incurred if the new search causes the agent to board the service he/she is actually already in. 64 Fully realised timetables are used to secure that boarding and alightings only takes place when vehicles actually 65 arrived/departed at/from stops. By traversing the day chronologically and keeping track of the locations of agents 66 and locations and delays of public transport vehicles, a one-shot assignment can be performed, dramatically reducing 67 the computation time compared to iterative approaches. This allows the model to be applied to larger networks and 68 population than iterative approaches within the same computation time. 69 We propose four different configurations of the model, characterised by different situations in which the agents are 70 assumed to search for new paths. As better alternatives can only arise if new information is available, the setups can 71 also be interpreted as levels of information provided to the passenger. The rigid setup does not allow any alterations 72 to the list of stops that needs to be visited, whereas the non-adaptive setup allows agents to search for a route at the 73 beginning of their trip (rigid after that). In both cases, if a route becomes infeasible because they are at a stop that is no 74 longer connected to their next intended stop, they simple give up and the trip is incomplete. In the semi-adaptive setup 75 agents furthermore search for a new route when they are waiting at stops/stations. In the full-adaptive setup a shortest 76 path search can also be performed whilst walking or onboard public transport services. Behaviourally, this may seem 77 very tedious, but is achievable if thought of as an app doing searches and providing notifications to passengers when 78 better alternatives emerge.

79 3. Case Study

80 3.1. Data

81 3.1.1. Automated Vehicle Location Data 82 The AVL data used in this study are provided by the national railway manager in Denmark, Rail Net Denmark, and 83 the regional bus agency, Movia, for every weekday (Monday-Friday) of the fall (September, October, and November) 84 2014 – a total of 65 days. 85 Delay data was not available for local train and metro lines, but are otherwise predominantly available for all 86 departures on the remaining train network, see Figure 2. Luckily, the effect of lack of data from local train and metro

87 lines will most likely be limited as the local trains have a low demand (only 4.3% of trips use them, see Figure 3) and 88 the metro has a high frequency down to two minutes headway in peak hours. A total of 4,414,922 observations of a 89 train arriving or departing at a station were available in the data, corresponding to approximately 67,922 observations 90 per day. The average delay was 10.6 seconds, see Table 1 and Figure 4 for additional descriptive statistics. 91 For buses, delay information is spread across the entire model area but is less complete than the train data, as the 92 bus company only collected AVL data for a sample of their vehicles. A total of 60,400,126 observations were present 93 in the dataset, corresponding to roughly 929,232 observations per day.

Trains Buses N 2,207,329 30,200,063 Mean [min.] 0.18 1.97 Mode [min.] -0.67 0.70 2.5% quantile [min.] -1.65 -1.78 Median [min.] -0.28 1.33 97.5% quantile [min.] 5.13 9.83 Std. dev. of mean [min.] 0.98 6.35 Coverage 93.99%1 48.57%

Table 1: Key statistical measures vehicle arrivals for trains and buses.

94 The data was initially cleaned in order to secure consistency in the AVL data. The criteria used for consistency 95 were that realised times for each service are non-decreasing from stop to stop, and that the time difference between 96 two consecutive elements (i.e. a stop arrival or a stop departure) cannot exceed two hours. For each departure, if 97 at least one inconsistency is found, this observation as well as the previous and next observation is updated using 98 linear interpolation of the delays based on their corresponding planned times. If extrapolation is needed, constant 99 extrapolation of delays is used. This eventually causes no inconsistencies or all of the delays to be undefined. In 100 the latter case, the observations were deemed too noisy to fix, and in lack of further information, the departure was 101 assumed to follow the published timetable for all stops. The numbers reported in Table 1 are based on the cleaned 102 dataset. Departures assumed to operate according to the schedule (either due to lack of data or too noisy data) are 103 those causing the coverage to drop below 100%.

1 56.61 % if including local trains (8.734 daily arrivals) and metro (15,128 daily arrivals) in the calculation of coverage.

Tracks Tracks S Bus S Bus DelaySD DelaySD 0 - 60 0 - 60 60 - 120 60 - 120 120 - 300 120 - 300 300 - 600 300 - 600 600 - ∞ 600 - ∞

Figure 1: Standard deviation of arrival delays at bus stops. Figure 2: Standard deviation of arrival delays at train stations.

104 3.1.2. Demand 105 The demand used for the study is based on the Copenhagen Model for Person Activity Scheduling (COMPAS) 106 (Prato et al., 2013), and consists of 387,511 agents having a total of 812,359 public transport trips. Trips not using 107 public transport were ignored in the study. 108 The time use of walking, waiting, and for each of the submodes as well as number of boardings are visualised 109 in Figure 3. It can be seen that about 10% find it most suitable to walk the entire trip in the base scenario, roughly 110 two thirds use bus, 45% use S-trains, barely 20% use metro, regional and InterCity-trains account for roughly 12.5%, 111 whereas less than 5% use local trains. The walking time distribution is fairly wide, but with about 60% of trips having 112 between five and 20 minutes walk. Less than 5% of the trips boards more than three vehicles, whereas both one and 113 two boardings account for roughly 35% of trips each.