Risk-Averse Selfish Routing

We consider a nonatomic selfish routing model with independent stochastic travel times for each edge, represented by mean and variance latency functions that depend on edge flows. This model can apply to traffic in the Internet or in a road network. Variability negatively impacts packets or drivers by introducing jitter in transmission delays, which lowers quality of streaming audio or video, or by making it more difficult to predict the arrival time at destination. At equilibrium, agents may select paths that do not minimize the expected latency so as to obtain lower variability. A social planner, who is likely to be more risk neutral than agents because it operates at a longer time scale, quantifies social cost with the total expected delay along routes. From that perspective, agents may make suboptimal decisions that degrade long-term quality. We define the price of risk aversion (PRA) as the worst-case ratio of the social cost at a risk-averse Wardrop equilibrium to that where agents are risk neutral....