On Socially Optimal Traffic Flow in the Presence of Random Users

Traffic assignment is an integral part of urban city planning. Roads and freeways are constructed to cater to the expected demands of the commuters between different origin-destination pairs with the overall objective of minimising the travel cost. As compared to static traffic assignment problems where the traffic network is fixed over time, a dynamic traffic network is more realistic where the network's cost parameters change over time due to the presence of random congestion. In this paper, we consider a stochastic version of the traffic assignment problem where the central planner is interested in finding an optimal social flow in the presence of random users. These users are random and cannot be controlled by any central directives. We propose a Frank-Wolfe algorithm based stochastic algorithm to determine the socially optimal flow for the stochastic setting in an online manner. Further, simulation results corroborate the efficacy of the proposed algorithm.