Solving the multiclass percentile user equilibrium traffic assignment problem

The multiclass percentile user equilibrium (MCPUE) problem discussed in this paper assumes that travelers, subject to uncertainty in a transportation network, strive to minimize reserved travel time (also known as the travel time budget) to ensure a probability of arriving at their destinations on time. An MCPUE, defined as an extension of the Wardrop equilibrium in a probabilistic network, is achieved when no travelers, regardless of their preferred on-time arrival probability, can reduce their reserved travel time by unilaterally changing their routes. Efficient numerical procedures for computing the MCPUE are studied in this paper. Specifically, a proposed new gradient projection algorithm avoids path enumeration through a column generation procedure based on a reliable shortest path algorithm. Implementation details of inner iterations, which are critical to the overall efficiency of the algorithm, are also discussed. Numerical experiments are conducted to test the computational performance of the proposed algorithm.