Inefficiency in Networks with Multiple Sources and Sinks

We study the problem of optimizing traffic in decentralized transportation networks, where the cost of a link depends on its congestion. If users of a transportation network are permitted to choose their own routes, they generally try to minimize their personal travel time. In the absence of centralized coordination, such a behavior can be inefficient for society and even for each individual user. This inefficiency can be quantified by the “price of anarchy”, the ratio of the suboptimal total cost to the socially optimal cost. Here we study the price of anarchy in multi-commodity networks, (i.e., networks where traffic simultaneously flows between different origins and destinations).