A combined discrete-continuous simulation model for analyzing train-pedestrian interactions

Computer simulation has defined itself as a reliable method for the analysis of stochastic and dynamic complex systems in both academic and practical applications. This is largely attributed to the advent and evolution of several simulation taxonomies, such as, Discrete Event Simulation, Continuous Simulation, System Dynamics, Agent-Based Modeling, and hybrid approaches, e.g., combined discrete-continuous simulation, etc. Each of these simulation methods works best for certain types of problems. In this paper, a discrete-continuous simulation approach is described for studying train and pedestrian traffic interactions for purposes of decision support. A practical operations problem related to commodity train operation within two small towns in Alberta, Canada, is then used to demonstrate the implementation of the approach within the Simphony.NET simulation system. Simulation results generated are presented.

Train tracks constructed and operated on grade often intersect with other transportation modes such as vehicular and pedestrian transportation. Vehicular transportation refers to cars, trucks, e.t.c., on roads, while pedestrian transportation refers to people walking or running. Such intersections are typically left uncontrolled until such a time that traffic volumes increase, the nuisance from train whistles is intolerable, or there is an occurrence of incidents. Controls are installed to ensure continued operation of each transportation mode with minimal interference. In both controlled and uncontrolled intersections, higher priority is normally given to the mode which would be affected the most by frequent stops, wait times, etc. For pedestrian-train intersections, trains are prioritized.

Pedestrian simulation

Schematic layout summarizing possible pedestrian behavior

Formal studies are inevitable in arriving at the decision that relate to the need to install formal control devices at such intersections because of the capital and running costs involved. Such studies rely on the concept of warrants which is predominantly used in traffic management of intersections (Roess, Prassas, and McShane 2010). Such studies are either carried out empirically, using simulation-based approaches, or using a combination of both. Simulation-based approached or a mixed approach would be considered more favorable because either approach facilitates inexpensive ways of experimenting with different scenarios. Consequently, a combined approach was adapted for the study presented in this paper.

In the mixed approach, i.e., empirical-simulation-based approach, the empirical component was used to ground truth the state of the system being studied through observation of traffic arrival patterns, the geography of the site, etc. Data collected served as basic inputs for the simulation model building process. On the other hand, the simulation component was dedicated to explicitly emulating the traffic interactions within a computer-based virtual environment. Coupling numerical or analytical methods, other than simulation, with empirical studies would have been ineffective because they cannot handle uncertainty and stochasticity as well as simulation-based methods. Constructs in transportation are generally characterized by uncertainty and stochasticity hence the mixed empirical and simulation-based approach was deemed appropriate.

Computer simulation

Several taxonomies of computer simulation exist today. This is partly due to the advances made in the computing science domain and the increasing complex nature of problems that have to be analyzed using simulation. Examples of simulation taxonomies include: Monte Carlo simulation, Discrete Event Simulation (DES), Continuous Simulation (CS), System Dynamics (SD), Agent-Based Modeling (ABM), e.t.c. Monte Carlo simulation is a simulation method that to a large extent relies on random deviates drawn from a model, for the performance of computations (Law and Kelton 1991). Most Monte Carlo simulations are static in nature but also dynamic ones exist. Discrete event simulation is a dynamic type of simulation that is used in the emulation of systems through the scheduling and processing of events at specific points in time. On the other hand, in continuous simulation, the system being emulated on computer is scanned every time step (typically each in size) and decisions made on whether events get triggered (Pritsker 1986). In most situations, the state variables of the system are tightly coupled with time and hence continuously change. Finite difference numeric algorithms are utilized in the process of updating these state variables. Examples of continuous simulation languages include: SLAM II (Pritsker 1986), ACSL and CSSL-IV (Pratt 1987), SIMSCRIPT II.5 (Fayek 1988), and SIMAN (Sturrock and Pegden 1989). Contemporary simulation systems that support continuous simulation include: Simphony (Hajjar and AbouRizk 1999), AnyLogic (The AnyLogic Company), and Vensim (Ventana Systems® 1988), e.t.c.

System Dynamics is a high level type of simulation that utilizes a continuous simulation implementation scheme together with mathematical modeling techniques. This simulation paradigm was created in the mid-1950s by Professor Jay Forrester while working at MIT Sloan School of Management (Jay 1971; Radzicki and Taylor 2008). System Dynamics is most suitable for problems that are characterized by non-linear interrelations between state variables. Graphical simulation systems that support SD permit the representation of state variables using stocks, flows, and loops (balancing or reinforcing). The stocks and flows emulate the dynamic change in the variables while the loops facilitate explicit representation of feed and feedback behaviors.

Agent-Based modeling is another high level simulation paradigm that is comprised of automatous or semi-autonomous constructs referred to as agents (Wooldridge 1999). These agents have the ability to communicate with each other and their environment, and can behave in unique ways (Mili & Steiner 2008; Kesaniemi and Terziyan 2011). Environments that support this simulation modeling paradigm, typically provide capabilities for modelers to utilize any of the other simulation types described, i.e., DES, CS, SD, etc., in their model development.

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