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Price of Anarchy in Non-Cooperative Load Balancing

Summary: Price of Anarchy
in Non-Cooperative Load Balancing
U. Ayesta1,3, O. Brun2, B.J. Prabhu2
1 BCAM, Basque Center for Applied Mathematics, 48160 Derio, Spain
2 CNRS ; LAAS ; 7 avenue du colonel Roche, 31077 Toulouse, France
3 IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
Abstract--We investigate the price of anarchy of a load balanc-
ing game with K dispatchers. The service rates and holding costs
are assumed to depend on the server, and the service discipline is
assumed to be processor-sharing at each server. The performance
criterion is taken to be the weighted mean number of jobs in the
system, or equivalently, the weighted mean sojourn time in the
For this game, we first show that, for a fixed amount of total
incoming traffic, the worst-case Nash equilibrium occurs when
each player routes exactly the same amount of traffic, i.e., when
the game is symmetric. For this symmetric game, we provide the
expression for the loads on the servers at the Nash equilibrium.
Using this result we then show that, for a system with two or
more servers, the price of anarchy, which is the worst-case ratio


Source: Ayesta, Urtzi - Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS


Collections: Engineering