Traffic simulation

Traffic simulation or the simulation of transportation systems is the mathematical modeling of transportation systems (e.g., freeway junctions, arterial routes, roundabouts, downtown grid systems, etc.) through the application of computer software to better help plan, design and operate transportation systems. Simulation of transportation systems started over forty years ago, and is an important area of discipline in traffic engineering and transportation planning today. Various national and local transportation agencies, academic institutions and consulting firms use simulation to aid in their management of transportation networks.

Simulation in transportation is important because it can study models too complicated for analytical or numerical treatment, can be used for experimental studies, can study detailed relations that might be lost in analytical or numerical treatment and can produce attractive visual demonstrations of present and future scenarios.

To understand simulation, it is important to understand the concept of system state, which is a set of variables that contains enough information to describe the evolution of the system over time. System state can be either discrete or continuous. Traffic simulation models are classified according to discrete and continuous time, state, and space.

Simulation methods in transportation can employ a selection of theories, including probability and statistics, differential equations and numerical methods.

One of the earliest discrete event simulation models is the Monte Carlo simulation, where a series of random numbers are used to synthesise traffic conditions.

This was followed by the cellular automata model that generates randomness from deterministic rules.

More recent methods use either discrete event simulation or continuous-time simulation. Discrete event simulation models are both (with random components) and dynamic (time is a variable). Single server queues for instance can be modeled very well using discrete event simulation, as servers are usually at a single location and so are discrete (e.g. traffic lights). Continuous time simulation, on the other hand, can solve the shortcoming of discrete event simulation where the model is required to have input, state and output trajectories within a time interval. The method requires the use of differential equations, specifically numerical integration methods. These equations can range from simple methods, such as Euler's method, to higher order Taylor's series methods, such as Heun's method and Runge-Kutta.

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