  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.
