A Monte Carlo Approach to Simulate the Stochastic Demand in a Continuous Dynamic Traffic Network Loading Problem

Dynamic traffic assignment models are mathematical tools used for traffic management and control. These require a dynamic network load (DNL) model, a route choice model, and a mechanism to ensure the relationship between the submodels. The DNL problem aims to find, on a congested network, dynamic traffic volumes and travel times for a given time period. The DNL problem involves a high computational cost; thus, the model becomes intractable in real time and, often, on offline applications. This paper proposes a discrete event algorithm for the continuous DNL problem based on flow discretizations, instead of time discretizations. These discretizations create homogeneous traffic packets according to their route. The algorithm propagates the packets synchronously across the links. The dynamic mechanism used in the network links are based on a generalization of the whole-link travel time model, which divides the links in the running section and the vertical queue section. The first one is associated with the travel time, and the second one is associated with the capacity. A generalization of the point-queue model is introduced to tackle dynamic link capacities such as signalized intersections. Under certain assumptions, the resulting model satisfies the first in, first out rule, and it is used to obtain a computationally tractable model. It allows stochastic demands to be dealt with a Monte Carlo simulation approach. This scheme is computationally expensive but can be addressed through distributed computing techniques. The method and its implementation by using parallel computing techniques is assessed using the Nguyen-Dupuis and Sioux Falls networks.