The Price of Anarchy for a Network of Queues in Heavy Traffic

Abstract

The price of anarchy (POA) in a congestion network refers to the ratio of the individually optimal total cost to the socially optimal total cost. An extensive literature on this subject has focussed mostly on deriving upper bounds on the POA that are independent of the topology of the network and (to a lesser extent) the form of the cost functions at the facilities of the network. This paper considers congestion networks in which the cost functions at the facilities display qualitative characteristics found in the waiting-time function for queue with an infinite waiting room. For a network of parallel M/M/1 queues an explicit expression exists for the POA, which, unlike the bounds in the literature, remains finite in heavy traffic. We show that a similar explicit expression holds in heavy traffic for parallel GI/GI/1 queues and, in some cases, in more general networks as well.KeywordsArrival RateOptimal AllocationHeavy TrafficCongestion NetworkSocial OptimizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.