In this paper, we present a discrete event simulation model of the Viennese subway network with capacity constraints and time-dependent demand. Demand, passenger transfer and travel times as well as vehicle travel and turning maneuver times are stochastic. Capacity restrictions apply to the number of waiting passengers on a platform and within a vehicle. Passenger generation is a time-dependent Poisson process which uses hourly origin-destination-matrices based on mobile phone data. A statistical analysis of vehicle data revealed that vehicle inter-station travel times are not time- but direction-dependent. The purpose of this model is to support strategic decision making by performing what-if-scenarios to gain managerial insights. Such decisions involve how many vehicles may be needed to achieve certain headways and what are the consequences. There are trade-offs between customer satisfaction (e.g. travel time) and the transportation system provider’s view (e.g. mileage). First results allow for a bottleneck and a sensitivity analysis.
The Viennese subway network has 5 lines and consists of 90 physical stations, 10 of which are crossing stations where 2 or – in one single case – 3 lines meet. Table 1 contains some facts and figures on the subway system. Figure 1 depicts a stretched schematic plan of the Viennese subway network. Since this paper is going to look into the details of certain stations, three have been marked with icons representing a respective close-by landmark. marks Stephansplatz (i.e. the city center) and its renowned landmark St. Stephen’s Cathedral. marks Praterstern and its landmark the Viennese ferris wheel. is a highly frequented train station called Westbahnhof. All three stations are highly frequented crossing stations.
Headway optimization is a significant subject in urban public transportation. Population growth – a prognosis expects the Viennese population (currently 1.78 millions) to break the 2 million mark by 2027 (Hanika 2015) – and reasons (efforts to reduce carbon emissions, improve the quality of life, tourism, etc.) call for frequent re-evaluations whether provisions are – now or in future – indispensable. Economic factors – namely, capital and operational expenditure (including infrastructure preservation and potential expansion) – are contrary to the goal of passenger satisfaction (i.e. service level). This joint project is dedicated to solve these conflicting goals by determining the optimal hourly headways for each line.
This paper is structured as follows: Section 2 explains the problem of headway optimization. In Section 3 we describe the modeling approach, the detailed structure of the model and its entities. Section 4 discusses preliminary results, before Section 5 concludes the paper and presents future work.
Figure 1: Stretched schematic plan of the Viennese subway network (as of 2012).
According to Liebchen (2008), the planning process in public transportation comprises:
- network design;
- line planning;
- vehicle scheduling;
- duty scheduling;
- crew rostering.
The result of an earlier planning stage serves as an input for the subsequent tasks. Headway optimization is part of the task timetabling and one of three procedures of creating a schedule (Ceder 2001). Since a rapid transportation system like a subway system usually has a headway well below 10 minutes (especially during peak hours), passengers tend to ignore the schedule (Mandl 1980).
In order to model such a complex service system, origin-destination-matrices are needed. To the best of our knowledge, related contributions use count data (Ceder 1984), smart card data (Pelletier et al. 2009) and mobile phone data (Friedrich et al. 2010).
Another obstacle is modeling passenger behavior, especially how they decide which route they take (Agard et al. 2007). Raveau et al. (2014) show that there are also regional differences. For a study on various technologies used in pedestrian counting and tracking see Bauer et al. (2009).
The goals of this case study are to gain insights into the system’s boundaries: First, whether there is room to improve present day system’s performance by headway alterations and what are consequences in terms of number of vehicles, mileage and passenger satisfaction (passenger times). Second, future-oriented questions, namely: How many additional passengers can be handled under the current headway setting? In both cases, it is important to examine how certain key performance indicators (e.g. passenger times) interact. But there are of course conflicting goals: While passengers prefer tight headways which lead – up to a certain point – to reduced waiting and thereby a lower passenger travel time as well as low utilization, the Viennese public transportation provider has to operate in a resource-efficient way. To be able to answer those questions and derive strategic (and also tactical) actions, a decision support tool had to be developed as part of a joint project with the transportation network provider. That decision support tool is based on a model of the real world system.
Since the service system under consideration contains many stochastic elements (time-dependent Poisson processes, passenger as well as vehicle times) that preclude the application of analytic methods like Jackson networks (Jackson 1963) and its extensions, we resort to a simulation model.
The simulation model was implemented in AnyLogic (version 7.0.3) and uses JGraphT (version 0.9.1).
Figure 2: Schematic example of two intersecting lines.