Since Dynasmart is assumed as term of reference in this laboratory application, the QDTA model has been calibrated by applying a Particle Swarm Optimization algorithm to determine the parameters of volume-delay functions that better approximate the results provided by Dynasmart on the test network used in this experiment.
z = objective function (OF) as defined in (1), where the simulated traffic measurements are obtained directly by performing the assignment process with Dynasmart (i.e., it is an assignment matrix free method).
Each time the SPSA computes a gradient approximation (5), there is the need to run an assignment by Dynasmart. Since m computations of the gradient approximation are required at each iteration of SPSA (4), the parameter m strongly affects the computational times.
Results obtained introducing the QDTA (Set VIII) are comparable with that obtained by using Dynasmart with DNL mixed with fixed DUE paths (Set VI), since QDTA applies a probabilistic statistic network loading.
In the case of the Dynasmart simulator, not only the measures adopted inside the OFs are reported in the table (i.e., link volume, speed, density, and queue length) but also the other measures that are never used during the O-D estimation, as the outflow and the left-turn movements from each monitored link.
Also when the QDTA is applied, as an approximation of the DTA, the solutions founded confirm the trend of the other assignment criteria and the results obtained in previous studies: the reproduction of traffic measures is good and when link volumes are considered together with speeds and densities, the improvements are comparable with those obtained in the Dynasmart case by adopting an iterative dynamic assignment approach.
In case of adoption of the QDTA model (Set VIII), the optimization algorithm does not find the need to move so far from the starting matrix as it does in Dynasmart simulations in order to reproduce the traffic measures.
Mahmassani, DYNASMART: DYnamic Network Assignment-Simulation Model for Advanced Road Telematics, Working Paper DTFH61-90-C00074-TWP1, Center for Transportation, The University of Texas at Austin, January, 1992.