Price of Anarchy in network routing with class based capacity guarantees

In this paper, we consider the inefficiency of distributed routing in a network of parallel links with class-based traffic. Network link behavior is modeled by the M/M/1-GPS queue (i.e. when links use General Processor Sharing(GPS) scheduling scheme to serve packets). Each traffic type is guaranteed a minimum capacity rate on each link using GPS scheduling. We show under specific demand conditions that, among multiple equilibria the worst-case Nash equilibrium occurs when each class dispatcher utilizes all the links to fulfill its demand. Using this fact, we give an upper bound on the Price of Anarchy (PoA). Our results also indicate that, while the price of selfish behavior can be unbounded in a specific demand setting, there exist demand regimes where the bound on PoA is reasonable. These results also apply to the resource allocation or load balancing applications in the processor sharing systems.