# Dynamic Traffic Assignment¶

Traffic assignment is the process that determines how the traffic demand – usually defined in terms of an origin-destination matrix – is loaded onto the network to determine the traffic flows on the network links. The underlying hypothesis is that as vehicles travel from their origin to their destination in the network they try to minimize their individual travel times. That is, drivers chose the routes they perceive as being the shortest under the prevailing traffic conditions.

The advent of intelligent transport systems (ITS), advanced traffic management systems (ATMS), and advanced traffic information systems (ATIS) has prompted the need for models which account for how flow changes over time, that is *dynamic* models that can appropriately describe the time dependencies of traffic demand and the corresponding induced traffic flows. The "dynamic traffic assignment problem" (DTA) can therefore be considered an extension of the traffic assignment problem described by Wardrop and solutions must be able to determine how time-varying link or path flows evolve in time and space in the network (Mahmassani 2001). The approaches proposed to solve the DTA problem fall into two classes: mathematical formulations looking for analytical solutions, and simulation models looking for approximate heuristic solutions. General simulation-based approaches (Tong and Wong 2000, Lo and Szeto 2002, Varia and Dingra 2004, Liu et al. 2005) explicitly or implicitly split the process into two components: a route choice mechanism determining how the time-dependent path flow rates are assigned to available paths at each time step; and a method to determine how these flows propagate in the network. A systematic approach based on these two components was proposed by Florian et al. 2001 and 2002. Simulation models, especially at the level of microsimulation, tend to focus on the description of the dynamics of traffic flows, while traffic assignment processes are not always modeled in accordance with the corresponding dynamic version of J.G. Wardrop’s first principle Friesz et al. 1993, Smith 1993, Ran and Boyce 1996 based on the concept of user equilibrium "the journey times on all routes actually used are equal and are not greater than those which would be experienced by a single vehicle on any unused route."

Consequently these simulation models cannot guarantee full network optimization. In these cases the route choice algorithms try to optimize route decisions based on currently available information, using either discrete choice theory or other probabilistic approaches (Mahmassani 2001). These approaches can be considered to be dynamic traffic assignment procedures but do not qualify as a dynamic user equilibrium (DUE) model because they omit the traveler's process of longitudinal learning through repeated journeys.

## DTA in Aimsun Next¶

Aimsun Next therefore utilizes a sophisticated set of route choice algorithms which include: static assignment based on Wardrop's equilibrium; dynamic assignment based on network conditions; and information supplied through ITS, to achieve a DUE where drivers react to their experience of the road network.

Aimsun Next provides two Dynamic Traffic Assignment (DTA) algorithms:

**SRC** calculates, at the end of each departure time interval (set by the user) of the running simulation, the least cost path, and distributes the vehicles between this path and the least cost paths calculated in previous intervals with a discrete choice function (Binomial, Proportional, Logit or C-Logit).

The path is assigned to each vehicle when it starts the trip; an option allows defining a proportion of enrouted vehicles, which repeat the route choice process while on-trip every time the costs are updated.

**DUE** is an iterative procedure aiming, for each O/D pair and each departure time interval (set by the user), that travel times experienced by vehicles departing during the same period are equal and minimal.

The progress towards a stable solution is measured by the Relative Gap (RGap), which is the relative difference between the total travel time actually experienced and the total travel time that would have been experienced if all the vehicles had had a travel time equal to that of the current shortest path.

The threshold of RGap that determines the achievement of convergence depends on the size of the network and on the level of congestion reached during the simulation period, but generally can be established between 5% and 10%.

In order to reduce the number of iterations to achieve convergence, and to achieve a better convergence the DUE process should be:

- Started with an input path file produced, for example, with a macroscopic assignment; or
- Run incrementally (i.e. increasing the demand and the number of alternative paths with the iterations).

The different assignment algorithms reproduce different levels of access to travel time information: DUE represents habitual drivers that base their routing decisions on historical knowledge of the conditions without real time information; SRC represents drivers that have access to pre-trip (non-enrouted) or on-trip (enrouted) information.

Aimsun Next allows providing to some of the vehicles in a one-shot simulation paths loaded from an input path file and paths manually defined, thus combining different route choice behaviors in the same simulation.

Which route choice algorithm to use and whether input path files should be calculated and re-used depends on the application of the model, on the amount of routing alternatives available in the modelled area and on observation of vehicle behavior. The table below provides some basic guidelines.

Model Type | Route choice |
---|---|

Single junction or corridor with no route options | Run SRC with fixed paths evaluated in free flow conditions |

Route choice is available in the model but it is uncongested | Run SRC with fixed paths evaluated at the end of the warm-up period |

Route choice is available in the model, there is congestion, recurrent conditions are modelled | Run DUE |

Route choice is available in the model, there is congestion, recurrent conditions are modelled, the study requires to capture routing behavior of drivers who have access to pre-trip or on-trip travel time information | Run DUE and save path file. Run one-shot in which drivers who have no access to travel time information use paths from the path file, drivers who have access to pre-trip information follow SRC paths and drivers who have have access to on-trip information are enrouted |

Route choice is available in the model, there is congestion, non-recurrent conditions are modelled (e.g. accident or construction) | Run DUE with a scenario representing recurrent conditions (e.g. no accident, no construction) and save path file. Run one-shot in which drivers who have no access to travel time information use paths from the path file, drivers who have access to pre-trip information follow SRC paths and drivers who have have access to on-trip information are enrouted. Use traffic management actions to divert vehicles from their habitual path (e.g. because they see a VMS) |

The topics related to Dynamic Traffic Assignment algorithms:

- Stochastic Route Choice (SRC)
- Road Network Representation: How the route choice network is represented
- Link Cost Functions: How the perceived cost of traversing a road section is derived
- Route Paths: How route paths are found
- Path Selection: How vehicles choose their paths through the network, including the effect of information from ITS systems to cause vehicles to update path choice en route.

- Dynamic User Equilibrium (DUE): Builds on the traffic assignment work above and assigns traffic to the road network using driver knowledge derived from previous iterations.