The marginal cost pricing under stochastic network

The well-known marginal cost pricing (MCP) has been extensively studied under the case with deterministic travel demand. However, this assumption may not be realistic due to the existence of variability and uncertainty in travel demand from day to day. This paper attempts to investigate the MCP under the stochastic network (SN-MCP) in which demand uncertainties are explicitly considered. We show that the first-best SN-MCP cannot be evaluated by only replacing the link flow and link travel time in the original MCP with their expected values. This naïve calculation will underestimate the external cost incurred by an additional road user's entry on each link. The paper then derives the true first-best SN-MCP which is then compared to naïve formulation. In numerical experiments, the expected total travel time under different MCP schemes is examined. The comparison shows that the more uncertain the travel demand, the higher the gap between the true and naïve SN-MCPs.