Routing in max-min fair networks: A game theoretic approach

In this paper, we study the problem of routing in networks with max-min fair congestion control at the link level. The goal of each user is to maximize its own bandwidth by selecting its path. The problem is formulated as a non-cooperative game. We first prove the existence of Nash Equilibria. This is important, because at a Nash Equilibrium (NE), no user has the incentive to change its routing strategy. In addition, we investigate how the selfish behavior of the users may affect the performance of the network as a whole. We next introduce a novel concept of observed available bandwidth on each link. It allows a user to find a path with maximum bandwidth under max-min fair congestion control in polynomial time. We then present a game based algorithm to compute an NE and prove that by following the natural game course the network converges to an NE. Extensive experiments show that the network can converge to an NE in less than 10 iterations and also significantly improves the fairness compared with other algorithms. Our results have the implication for the future routing protocol design.

[1]  Ariel Orda,et al.  Bottleneck Routing Games in Communication Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[2]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[3]  Abraham P. Punnen.  A linear time algorithm for the maximum capacity path problem , 1991 .

[4]  Moti Yung,et al.  Approximating max-min fair rates via distributed local scheduling with partial information , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[5]  Dritan Nace,et al.  Computing Optimal Max-Min Fair Resource Allocation for Elastic Flows , 2006, IEEE/ACM Transactions on Networking.

[6]  Scott Shenker,et al.  Analysis and simulation of a fair queueing algorithm , 1989, SIGCOMM '89.

[7]  Martha Steenstrup.  Inter-Domain Policy Routing Protocol Specification: Version 1 , 1993, RFC.

[8]  Lixin Gao,et al.  Stable Internet routing without global coordination , 2000, SIGMETRICS '00.

[9]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[10]  BERNARD M. WAXMAN,et al.  Routing of multipoint connections , 1988, IEEE J. Sel. Areas Commun..

[11]  J. J. Garcia-Luna-Aceves,et al.  Distributed, scalable routing based on link-state vectors , 1994, SIGCOMM.

[12]  Dritan Nace,et al.  Computing optimal max-min fair resource allocation for elastic flows , 2006, TNET.

[13]  Klara Nahrstedt,et al.  Maxmin Fair Routing in Connection-Oriented Networks , 1998 .

[14]  Peter Steenkiste,et al.  Routing high-bandwidth traffic in max-min fair share networks , 1996, SIGCOMM '96.

[15]  Gordon T. Wilfong,et al.  The stable paths problem and interdomain routing , 2002, TNET.

[16]  Raj Jain,et al.  Congestion control with explicit rate indication , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[17]  Gordon T. Wilfong,et al.  A safe path vector protocol , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[18]  Brighten Godfrey,et al.  Incentive compatibility and dynamics of congestion control , 2010, SIGMETRICS '10.

[19]  M. Dufwenberg.  Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[20]  Jeffrey M. Jaffe,et al.  Bottleneck Flow Control , 1981, IEEE Trans. Commun..

[21]  J. J. Garcia-Luna-Aceves,et al.  Distributed, scalable routing based on link-state vectors , 1994, SIGCOMM 1994.