Uncertainty in Multi-Commodity Routing Networks: When does it help?

We study the equilibrium quality in a multi commodity selfish routing game with many types of users, where each user type experiences a different level of uncertainty. We consider a new model of uncertainty where each user-type over- or under-estimates their congestion costs by a multiplicative constant. We present a variety of theoretical results showing that when users under-estimate their costs, the network congestion decreases at equilibrium, whereas overestimation of costs leads to increased equilibrium congestion. Motivated by applications in urban transportation networks, we perform simulations consisting of parking users and through traffic on synthetic network topologies. Our results strongly indicate that while users' perception of network costs can significantly impact the equilibrium quality, optimism in the face of uncertainty leads to favorable network conditions.