Traffic simulation with FASTLANE","")?> Introduction")?>

Modern simulation models analyse road networks and traffic on a very high level of detail, e.g. every car has its own information about origin and destination - this data is stored in the origin/destination matrix (ODM) - and the departure time.

Wardrop's first principle determines a drivers's route. It says that every driver chooses the route with the lowest costs - taking into account the network state which is of course determined by the decisions of the other drivers. The state in which Wardrop's principle is fulfilled is called user equilibrium. For calculating this equilibrium, it is common practice to neglect the time dependance of the ODM and the network state to simplify the problem.

But in reality the ODM is time dependant. Normally the traffic volume during the rush hours is bigger than at noon. This has to be noticed for route planning. The result is a time dependant user equilibrium, the dynamic user equilibrium.

It is possible to calculate the dynamic user equilibrium from a time dependant ODM by using variational inequality models. On large road networks, nowadays computer performance is insufficient to solve the problem in an appropriate period of time. Therefore, FASTLANE takes another course.

Equilibrium
Calculation")?>

FASTLANE calculates the dynamic user equilibrium (the optimal routes) in a pragmatic way: by iterative simulations. We start with a given time dependent ODM and compute the optimal routes by means of the routelength to fulfill Wardrop's first principle. Now the iteration process begins:

  1. The simulation runs over one day according to the rules of the used car following model.
  2. The network load and the travel times are calculated and with this data
  3. we update the routes, e.g. every driver chooses according to his present experience (travel times per route) a temporal shorter route for the next day (the next iteration).

This process is continued until the travel times are stationary. This state is the dynamic user equilibrium.

On the Wuppertal network, FASTLANE needed 35 iterations to reach the equilibrium. During the first iterations the traffic flow collapsed completely.

Iterational
Problems")?>

The procedure described above normally contains two potential problems:

  1. The iteration process produces oscillations in the route choice or is unstable. For the FASTLANE algorithm the stability can be shown on small example networks.
  2. A simulation based on single vehicles needs enormous computer power. Most of the microscopic car following models are too slow to compute several iterations of daily traffic on an urban road network in an appropriate period of time. Therefore, FASTLANE is based on a more simple car following model, the Queuing Model.

    The
    Queuing
    Model")?>

    For the iterative algorithm described above we need a very fast car following model. One iteration of the Wuppertal network with the already fast Nagel-Schreckenberg-Model using our software PLANSIM-T takes approximately nine hours CPU-time on a 166MHz UltraSPARC processor. To reach the dynamic user equilibrium in this special case we need 35 iterations. The in the Queuing Model described below is 8.6 times faster (while simulating the northrheinwestfalian highway net the factor increases to 85, the bottleneck factor is even 143).

    The network FASTLANE operates on is composed out of LINKs. Every LINK is represented by a queue and described by the characteristics

    When a car reaches a new LINK its travel time on this LINK will be calculated. This travel time is dependent on the LINK-length, the state of the LINK (e.g. number of cars on the LINK) and the desired velocity. Then the car with its calculated arrival time (at the end of the LINK) is put in the queue. If a LINK has several ingoing LINKs and if the number of cars which want to change to this LINK exceeds the capacity (maximal flow), the ingoing LINKs receive proportionate capacity according to their priority. In one time step only a limited number of vehicles can leave a LINK. This number is dependent on the capacity of this LINK, as well as from the car's individual routes and the capacity of the following LINKs.

    Normally NODES are used to implement signalized and unsignalized intersections. In the Queuing Model NODES are not used but they are modelled equivalently by LINK capacities.

    For additional information about the Queuing Model and the other models used in traffic simulation visit our model page.

    Summing Up")?>

    With modern computers and fast car following models the traffic of large road networks can be simulated to a very high level of detail. The accuracy of the simulation depends not only on the car following model but also on the exactness of the origin/destination matrix (ODM) and the routing algorithm.

    Variational inequality models calculate the routes according to special cost functions. But these routes are not user-optimal with respect to the travel times, which is especially problematic in simulations which study the effect of systems like Advanced Traveler Information Systems (ATIS) or Advanced Traffic Management Systems (ATMS) which influence the route choice behaviour.

    FASTLANE solves this problem by calculating optimal routes for a timedependent ODM with respect to a cost function specified by the simulation. Beyond it FASTLANE is able to handle very large networks.

    The Queuing Model speeds up the calculation of the dynamic user equilibrium up to two orders of magnitude compared with the Nagel-Schreckenberg-Model. If the FASTLANE simulation is not detailled enough, the calculated routes can be used as input data for following simulations with the Nagel-Schreckenberg-Model.


    More traffic")?> For detailled information about our traffic simulation please click:

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    Contact:

    ")?> traffic@zpr.uni-koeln.de