Abstract: This article proposes a cell-based multi-class dynamic traffic assignment problem that considers the random evolution of traffic states. Travelers are assumed to select routes based on perceived effective travel time, where effective travel time is the sum of mean travel time and safety margin. The proposed problem is formulated as a fixed point problem, which includes a Monte–Carlo-based stochastic cell transmission model to capture the effect of physical queues and the random evolution of traffic states during flow propagation. The fixed point problem is solved by the self-regulated averaging method. The results illustrate the properties of the problem and the effectiveness of the solution method. The key findings include the following: (1) Reducing perception errors on traffic conditions may not be able to reduce the uncertainty of estimating system performance, (2) Using the self-regulated averaging method can give a much faster rate of convergence in most test cases compared with using the method of successive averages, (3) The combination of the values of the step size parameters highly affects the speed of convergence, (4) A higher demand, a better information quality, or a higher degree of the risk aversion of drivers can lead to a higher computation time, (5) More driver classes do not necessarily result in a longer computation time, and (6) Computation time can be significantly reduced by using small sample sizes in the early stage of solution processes.
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