Is the Price of Anarchy the Right Measure for Load-Balancing Games?

Price of anarchy is an oft-used worst-case measure of the inefficiency of noncooperative decentralized architectures. For a noncooperative load-balancing game with two classes of servers and for a finite or infinite number of dispatchers, we show that the price of anarchy is an overly pessimistic measure that does not reflect the performance obtained in most instances of the problem. We explicitly characterize the worst-case traffic conditions for the efficiency of noncooperative load-balancing schemes and show that, contrary to a common belief, the worst inefficiency is in general not achieved in heavy traffic.

[1]  Csaba D. Tóth,et al.  Selfish Load Balancing and Atomic Congestion Games , 2004, SPAA '04.

[2]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[3]  Adam Wierman,et al.  The effect of local scheduling in load balancing designs , 2008, PERV.

[4]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

[5]  Elias Koutsoupias,et al.  The price of anarchy of finite congestion games , 2005, STOC '05.

[6]  Tim Roughgarden,et al.  The price of anarchy in an exponential multi-server , 2007, Oper. Res. Lett..

[7]  S. Stidham,et al.  Individual versus Social Optimization in the Allocation of Customers to Alternative Servers , 1983 .

[8]  L. Shapley,et al.  Potential Games , 1994 .

[9]  Balakrishna J. Prabhu,et al.  On the efficiency of non-cooperative load balancing , 2013, 2013 IFIP Networking Conference.

[10]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[11]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[12]  Tim Roughgarden,et al.  Fully Distributed Algorithms for Convex Optimization Problems , 2007, SIAM J. Optim..

[13]  Balakrishna J. Prabhu,et al.  Price of anarchy in non-cooperative load balancing games , 2011, Perform. Evaluation.

[14]  Ariel Orda,et al.  Architecting noncooperative networks , 1995, Eighteenth Convention of Electrical and Electronics Engineers in Israel.

[15]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[16]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[17]  Ariel Orda,et al.  Achieving network optima using Stackelberg routing strategies , 1997, TNET.