Two Gradient Estimation Techniques for Average Path Travel Time of Cell-based Traffic Simulation Models

It has been sometime since simulation was adopted in the study of traffic flow and transportation network systems. Although simulation is a strong tool in generating and replicating the traffic patterns and computing the travel times, its mathematical properties are not well understood due to its rule-based and algorithmic nature. In the authors’ view, one major obstacle to discussion about traffic flow simulation properties is the lack of a language by which discussion can occur. The authors seek to overcome this void by defining a set of implicit variables and functions that facilitate the communication process regarding traffic simulation models. One of the properties of traffic simulation models is sensitivity of outputs to inputs. The sensitivities are necessary in capturing marginal effects which is a requirement for improving the convergence ability of simulation-based dynamic traffic assignment and enhancing their application domain to problems such as system optimal traffic assignment and toll design. Estimating each of the derivatives is equivalent to a rerunning of simulation which is computationally very demanding considering the number of input and output variables in the system. This study introduces two novel techniques for calculating the derivatives of each path travel time with respect to each path departing flow in cell-based traffic simulation models without rerunning the simulation. Clearly speaking, the changes in path travel time vector due to slight changes in path departing flow vector is captured. The performance of the techniques is evaluated through comparing their derivative values to the values obtained from brute force method. The techniques have been implemented in a Cell transmission traffic simulation model where the path flows are processed according to a pre-given set of path numbers. According to our evaluation, while the first technique is lower demanding in terms of time and memory and has somehow comparable results, the second technique is more powerful in generating higher levels of accuracy with imposing extra computational requirement. Keywords-Gradient Estimation Techniques; Cell-based Traffic Model; Dynamic Traffic Assignment Models; Marginal Effects; Simulation Laboratory; System Optimal; Toll Design