Traffic simulation

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

• Monte Carlo method

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.[5]

• Cellular automata model

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

• Discrete event and continuous-time simulation

More recent methods use either discrete event simulation or continuous-time simulation. Discrete event simulation models are both stochastic (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.[6] 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.[7]

• Car-following models

A class of microscopic continuous-time models, known as car-following models, are also based on differential equations. Significant models include the Pipes, intelligent driver model and Gipps' model. They model the behavior of each vehicle ("microscopic") to see its implications on the whole traffic system ("macroscopic"). Employing a numerical method with a car-following model (such as Gipps' with Heun's) can generate important information for traffic conditions, such as system delays and identification of bottlenecks.

The methods noted above are generally used to model the behavior of an existing system, and are often focused around specific areas of interest under a range of conditions (such as a change in layout, lane closures, and different levels of traffic flow). Transport planning and forecasting can be used to develop a wider understanding of traffic demands over a broad geographic area, and predicting future traffic levels at different links (sections) in the network, incorporating different growth scenarios, with feedback loops to incorporate the effect of congestion on the distribution of trips.

Map displaying the results of simulating pedestrian traffic at the National September 11 Memorial & Museum site, based on modeling by the Louis Berger Group

Ground transportation for both passenger and goods movement is perhaps the area where simulation is most widely used. Simulation can be carried out at a corridor level, or at a more complex roadway grid network level to analyze planning, design and operations such as delay, pollution, and congestion. Ground transportation models can include all modes of roadway travel, including vehicles, trucks, buses, bicycles and pedestrians. In traditional road traffic models, aggregate representation of traffic is typically used where all vehicles of a particular group obey the same rules of behavior; in micro-simulation, driver behavior and network performance are included so that complete traffic problems (e.g. Intelligent transportation system, shockwaves) can be examined.[9]

Rail is an important mode of travel for both freight and passengers. Modeling railways for freight movement is important to determine the operational efficiency and rationalize planning decisions.[10] Freight simulation can include aspects such as dedicated truck lanes, commodity flow, corridor and system capacity, traffic assignment/network flow, and freight plans that involve travel demand forecasting.[11]

Maritime and air transportation presents two areas that are important for the economy. Maritime simulation primarily includes container terminal modeling, that deals with the logistics of container handling to improve system efficiency. Air transportation simulation primarily involves modeling of the airport terminal operations (baggage handling, security checkpoint), and runway operations.

In addition to simulating individual modes, it is often more important to simulate a multi-modal network, since in reality modes are integrated and represent more complexities that each individual mode can overlook. Inter-modal network simulation can also better understand the impact of a certain network from a comprehensive perspective to more accurately represent its impact in order to realize important policy implications. An example of an inter-modal simulator is Commuter developed by Azalient which introduces both dynamic route and mode choice by agents during simulation - this type of modeling is referred to as nanosimulation as it considers demand and travel at a finer level of detail than traditional microsimulation.

Simulation in transportation can also be integrated with urban environment simulation, where a large urban area is simulated which includes roadway networks, to better understand land use and other planning implications of the traffic network on the urban environment.

The output of a microsimulation model is different from that of the US Federal Highway Capacity Manual (HCM). For example, most HCM procedures assume that the operation of one intersection will not be affected by the conditions of an adjacent roadway (with the exception of HCS 2000 Freeways). 'Rubbernecking' and long queues from one location interfering with another location would contradict this assumption.

The HCM 2010 provides revised guidance on what types of output from traffic simulation software are most suitable for analysis in, and comparison to, the HCM for example vehicle trajectories and raw loop detector output.

In the HCM delay is used to estimate the level of service (LOS) for intersections. However, there are distinct differences between the way microsimulation programs and the HCM define delay. The HCM bases its delay on adjusted flow using mean control delay for the highest 15 minute period within the hour. The distinction between total delay and control delay is important. Control delay is when a signal control causes a group to slow down or stop. It's important to look at the software's documentation to understand how it calculates delay. In order to use microsimulation outputs to find LOS, the delay must be accumulated over 15 minute intervals and averaged over several runs with different random seeds. Because the HCM uses adjusted flow, another way to compare delay is divide the simulation input's 15 minute peak volume by the peak hour factor (PHF) to increase the simulation's volume.

HCM 2000 defines a queue as a line of vehicles, bicycles, or persons waiting to be served by the system in which the flow rate from the front of the queue determines the average speed within the queue. Slowly moving vehicles or people joining the rear of the queue are usually considered part of the queue. These definitions are somewhat relative and can be ambiguous. In most microsimulation programs the queue length cannot exceed the storage capacity for that turn-bay or lane. Overflows into the adjacent link or off the network are usually not accounted for, even though this may affect the results. (If this is the case, a work-around can be to temporarily ignore those effects and extend the network or storage area for the link to include the maximum queue length.)[14]