Traffic simulation or the simulation of transportation systems is the
mathematical modeling
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, b ...
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
Transportation planning is the process of defining future policies, goals, investments, and spatial planning designs to prepare for future needs to move people and goods to destinations. As practiced today, it is a collaborative process that i ...
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
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
* Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a ...
or
continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
. Traffic simulation models are classified according to discrete and continuous time, state, and space.
Theory
Traffic models
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
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determini ...
, where a series of random numbers are used to synthesise traffic conditions.
* Cellular automata model
This was followed by the
cellular automata
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...
model that generates randomness from deterministic rules.
* Discrete event and continuous-time simulation
More recent methods use either
discrete event simulation
A discrete-event simulation (DES) models the operation of a system as a (discrete) sequence of events in time. Each event occurs at a particular instant in time and marks a change of state in the system. Between consecutive events, no change in the ...
or
continuous-time simulation. Discrete event simulation models are both
stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
(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
Traffic lights, traffic signals, or stoplights – known also as robots in South Africa are signalling devices positioned at road intersections, pedestrian crossings, and other locations in order to control flows of traffic.
Traffic light ...
). 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
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
, specifically numerical integration methods. These equations can range from simple methods, such as
Euler's method
In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit met ...
, to higher order
Taylor's series methods, such as
Heun's method In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical p ...
and
Runge-Kutta.
* Car-following models
A class of
microscopic
The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens (optics), lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded a ...
continuous-time models, known as
car-following models, are also based on differential equations. Significant models include the Pipes,
intelligent driver model
In traffic flow modeling, the intelligent driver model (IDM) is a time-continuous car-following model for the simulation of freeway and urban traffic. It was developed by Treiber, Hennecke and Helbing in 2000 to improve upon results provided wit ...
and
Gipps' model
Gipps' model is a mathematical model for describing car-following behaviour by motorists in the United Kingdom.
The model is named after Peter G. Gipps who developed it in the late-1970s under S.R.C. grants at the Transport Operations Research Gr ...
. They model the behavior of each individual vehicle ("microscopic") in order 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.
Systems planning
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.
Applications in transportation engineering
Traffic simulation models are useful from a microscopic, macroscopic and sometimes mesoscopic perspectives. Simulation can be applied to both transportation planning and to transportation design and operations. In transportation planning the simulation models evaluate the impacts of regional urban development patterns on the performance of the transportation infrastructure.
Regional planning organizations use these models to evaluate what-if scenarios in the region, such as air quality to help develop
land use
Land use involves the management and modification of natural environment or wilderness into built environment such as settlements and semi-natural habitats such as arable fields, pastures, and managed woods. Land use by humans has a long h ...
policies that lead to more
sustainable travel. On the other hand, modeling of transportation system operations and design focus on a smaller scale, such as a highway corridor and pinch-points. Lane types, signal timing and other traffic related questions are investigated to improve local system effectiveness and efficiency. While certain simulation models are specialized to model either operations or system planning, certain models have the capability to model both to some degree.
Whether it is for planning or for systems operations, simulations can be used for a variety of
transportation modes.
Roadway and ground transportation
![WTC Pedestrian Modeling](https://upload.wikimedia.org/wikipedia/commons/d/d5/WTC_Pedestrian_Modeling.png)
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.
Rail transportation
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. 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.
Maritime and air transportation
Maritime and air transportation presents two areas that are important for the economy. Maritime simulation primarily includes
container terminal
A container port or container terminal is a facility where cargo containers are transshipped between different transport vehicles, for onward transportation. The transshipment may be between container ships and land vehicles, for example train ...
modeling, that deals with the logistics of container handling to improve system efficiency. Air transportation simulation primarily involves modeling of the
airport terminal
An airport terminal is a building at an airport where passengers transfer between ground transportation and the facilities that allow them to board and disembark from an Fixed-wing aircraft, aircraft.
Within the terminal, passengers purchase ...
operations (baggage handling, security checkpoint), and
runway
According to the International Civil Aviation Organization (ICAO), a runway is a "defined rectangular area on a land aerodrome prepared for the landing and takeoff of aircraft". Runways may be a man-made surface (often asphalt concrete, as ...
operations.
Other
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.
Software programs
Simulation software is getting better in a variety of different ways. With new advancements in mathematics, engineering and computing, simulation software programs are increasingly becoming faster, more powerful, more detail oriented and more realistic.
Transportation models generally can be classified into microscopic, mesoscopic, macroscopic, and metascopic models. Microscopic models study individual elements of transportation systems, such as individual vehicle dynamics and individual traveler behavior. Mesoscopic models analyze transportation elements in small groups, within which elements are considered homogeneous. A typical example is vehicle platoon dynamics and household-level travel behavior. Macroscopic models deal with aggregated characteristics of transportation elements, such as aggregated traffic flow dynamics and zonal-level travel demand analysis.
Microsimulation
Microsimulation models track individual vehicle movements on a second or subsecond basis. Microsimulation relies on random numbers to generate vehicles, select routing decisions, and determine behavior. Because of this variation, it is necessary to run the model several times with different
random number seeds to obtain the desired accuracy. There will be a 'warm-up' period before the system reaches a steady state, and this period should be excluded from the results.
Microsimulation models usually produce two types of results: animated displays, and numerical output in text files. It is important to understand how the software has accumulated and summarized the numerical results to prevent incorrect interpretation. Animation can allow the analyst to quickly assess the performance, however it is limited to qualitative comparisons. The main indication of a problem that can be seen in an animation is the forming of persistent queues.
'Measures of Effectiveness' (MOEs) may be calculated or defined in a manner which is unique to each simulation program. MOEs are the system performance statistics that categorize the degree to which a particular alternative meets the project objectives. The following MOEs are most common when analyzing simulation models:
* 'VMT' (vehicle miles traveled) is computed as a combination of the number of vehicles in the system and the distance they travel.
* 'VHT' (vehicle hours of travel) is computed as the product of the link volume and the link travel time, summed over all links.
* 'Mean system speed' is equal to VMT/VHT.
* 'Total system delay' is one of the most effective ways to evaluate different congestion relieving alternatives and it is usually the MOE that the travelling public notices. Delay can be calculated several ways. Some consider it to be only that delay which is above free flow conditions. Others include the baseline delay which occurs as a result of traffic control devices. Some even include acceleration and deceleration delay, while others include only stopped delay.
Other commonly reported metrics from traffic simulation tools include:
.
* Link road section speeds, flow, density, travel time, delay, stop time
* Intersection turning volumes, delay,
* Journey times
* Loop detector records for speed, occupancy, headway, gap
* Vehicle trajectories and speed vs. distance plots
Comparing simulation results with the US Highway Capacity Manual
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 2010provides 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.
Comparison with HCM delay and level of service
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.
Comparison with HCM Queues
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.)
[http://ops.fhwa.dot.gov/trafficanalysistools/tat_vol3/vol3_guidelines.pdf ]
References
Further reading
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*
*
* {{cite web , url=http://ops.fhwa.dot.gov/trafficanalysistools/tat_vol3/vol3_guidelines.pdf , title=Traffic Analysis Toolbox Volume III: Guidelines for Applying Traffic Microsimulation Modeling Software , publisher=
Federal Highway Administration
The Federal Highway Administration (FHWA) is a division of the United States Department of Transportation that specializes in highway transportation. The agency's major activities are grouped into two programs, the Federal-aid Highway Program a ...
, date=July 2004