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.
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Notes
- 1.
This abstract characterization of a network is sufficiently general to include both classical models of networks of queues and road traffic networks, as well as more recent models of communication networks. In queueing-network models (e.g., a Jackson network), each queue (service facility) is modeled as a node, with a directed arc from node j to node k if service at queue j may be followed immediately by service at queue k. In communication-network models it is more common (and more natural) to consider each transmission link as a service facility, with a queue of jobs (messages or packets) at the node (router/server) at the head of the link, waiting to be transmitted. In road traffic networks, both nodes (intersections) and links (road segments between intersections) are service facilities in the sense that they are potential sources of congestion and waiting.
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Stidham, S. (2014). The Price of Anarchy for a Network of Queues in Heavy Traffic. In: Pulat, P., Sarin, S., Uzsoy, R. (eds) Essays in Production, Project Planning and Scheduling. International Series in Operations Research & Management Science, vol 200. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9056-2_5
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