Bottleneck Routing with Elastic Demands

Abstract Bottleneck routing games are a well-studied model to investigate the impact of selfish behavior in communication networks. In this model, each user selects a path in a network for routing her fixed demand. The disutility of a user only depends on the most congested link visited. We extend this model by allowing users to continuously vary the demand rate at which data is sent along the chosen path. As our main result we establish tight conditions for the existence of pure strategy Nash equilibria.

[1]  Donald F. Towsley,et al.  Path Selection and Multipath Congestion Control , 2007, INFOCOM.

[2]  Costas Busch,et al.  Atomic routing games on maximum congestion , 2006, Theor. Comput. Sci..

[3]  Martin Hoefer,et al.  Routing Games With Progressive Filling , 2016, IEEE/ACM Transactions on Networking.

[4]  Yin Zhang,et al.  On selfish routing in internet-like environments , 2006, TNET.

[5]  Rajgopal Kannan,et al.  Bottleneck Routing Games on Grids , 2011, GAMENETS.

[6]  Rajgopal Kannan,et al.  Bottleneck Congestion Games with Logarithmic Price of Anarchy , 2010, SAGT.

[7]  Roberto Cominetti,et al.  Network congestion control with Markovian multipath routing , 2011, International Conference on NETwork Games, Control and Optimization (NetGCooP 2011).

[8]  Max Klimm,et al.  Bottleneck Routing with Elastic Demands , 2015, WINE.

[9]  Xi Fang,et al.  A Game-Theoretic Approach to Stable Routing in Max-Min Fair Networks , 2013, IEEE/ACM Transactions on Networking.

[10]  Athanasios V. Vasilakos,et al.  Optimal Price of Anarchy of Polynomial and Super-Polynomial Bottleneck Congestion Games , 2011, GAMENETS.

[11]  Charles D. Kolstad,et al.  Computing Cournot-Nash Equilibria , 1991, Oper. Res..

[12]  Rolf H. Möhring,et al.  Strong equilibria in games with the lexicographical improvement property , 2013, Int. J. Game Theory.

[13]  R. Srikant,et al.  Multi-Path TCP: A Joint Congestion Control and Routing Scheme to Exploit Path Diversity in the Internet , 2006, IEEE/ACM Transactions on Networking.

[14]  F. Paganini,et al.  A Unified Approach to Congestion Control and Node-Based Multipath Routing , 2009, IEEE/ACM Transactions on Networking.

[15]  N. Kukushkin.  Acyclicity of Improvements in Games with Common Intermediate Objectives ∗ , 2006 .

[16]  Max Klimm,et al.  Equilibria in a class of aggregative location games , 2015 .

[17]  S. Kakutani.  A generalization of Brouwer’s fixed point theorem , 1941 .

[18]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[19]  S. Shenker.  Fundamental Design Issues for the Future Internet , 1995 .

[20]  Rayadurgam Srikant,et al.  The Mathematics of Internet Congestion Control , 2003 .

[21]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[22]  Max Klimm,et al.  Congestion Games with Variable Demands , 2016, Math. Oper. Res..

[23]  Ioannis Caragiannis,et al.  Network Load Games , 2005, ISAAC.

[24]  Ariel Orda,et al.  Bottleneck Routing Games in Communication Networks , 2007, IEEE J. Sel. Areas Commun..

[25]  Martin Hoefer,et al.  Computing Pure Nash and Strong Equilibria in Bottleneck Congestion Games , 2010, ESA.

[26]  Thomas Voice,et al.  Stability of Multi-Path Dual Congestion Control Algorithms , 2006, IEEE/ACM Transactions on Networking.

[27]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[28]  Nikolai S. Kukushkin,et al.  Congestion games revisited , 2007, Int. J. Game Theory.

[29]  Tobias Harks,et al.  Utility Max-Min Fair Congestion Control with Time-Varying Delays , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[30]  A. Khanna,et al.  The revised ARPANET routing metric , 1989, SIGCOMM 1989.

[31]  Aurel A. Lazar,et al.  On the existence of equilibria in noncooperative optimal flow control , 1995, JACM.

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

[33]  Guido Schäfer,et al.  On the Inefficiency of Equilibria in Linear Bottleneck Congestion Games , 2010, SAGT.

[34]  Alexandre Proutière,et al.  Routing games with elastic traffic , 2009, PERV.