Risk-averse toll pricing in a stochastic transportation network

We consider the toll pricing problem under uncertain network conditions resulting in stochastic travel times. Using the conditional value-at-risk (CVaR) as a risk measure on the alternate functions of the random travel times we introduce several travel time reliability-related network performance measures. CVaR is used to control the undesired realisations of random outcomes based on travel times, and consequently, improve the reliability of the transportation system. We characterise the random network parameters, which are in general highly correlated, by a set of scenarios and propose alternate risk-averse toll pricing models. These optimisation models involve decisions of transportation managers aiming to improve the system-wide network reliability and decisions of network users who are assumed to choose routes to minimise their expected total travel costs. We describe a solution method integrating mathematical programming approaches with a genetic algorithm. We also conduct a computational study to illustrate the effectiveness of the proposed approaches.