On a Non-cooperative Model for Wavelength Assignment in Multifiber Optical Networks

We study path multicoloring games that describe situations in which selfish entities possess communication requests in a multifiber all-optical network. Each player is charged according to the maximum fiber multiplicity that her color (wavelength) choice incurs and the social cost is the maximum player cost. We investigate the price of anarchy of such games and provide two different upper bounds for general graphs--namely the number of wavelengths and the minimum length of a path of maximum disutility, over all worst-case Nash Equilibria--as well as matching lower bounds which hold even for trees; as a corollary we obtain that the price of anarchy in stars is exactly 2. We also prove constant bounds for the price of anarchy in chains and rings in which the number of wavelengths is relatively small compared to the load of the network; in the opposite case we show that the price of anarchy is unbounded.

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

[2]  Steve Chien,et al.  Convergence to approximate Nash equilibria in congestion games , 2007, SODA '07.

[3]  Rahul Simha,et al.  On the wavelength assignment problem in multifiber WDM star and ring networks , 2001, TNET.

[4]  Katerina Potika,et al.  Resource Allocation Problems in Multifiber WDM Tree Networks , 2003, WG.

[5]  Katerina Potika,et al.  Selfish Routing and Path Coloring in All-Optical Networks , 2007, CAAN.

[6]  Paul G. Spirakis,et al.  The structure and complexity of Nash equilibria for a selfish routing game , 2009, Theor. Comput. Sci..

[7]  Janos Simon,et al.  Wavelength Assignment Problem on All-Optical Networks with k Fibres per Link , 2000, ICALP.

[8]  Aris Pagourtzis,et al.  Routing and Path Multi-Coloring , 2001, Inf. Process. Lett..

[9]  Tim Roughgarden,et al.  The Price of Stability for Network Design with Fair Cost Allocation , 2004, FOCS.

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

[11]  Peter Winkler,et al.  Wavelength assignment and generalized interval graph coloring , 2003, SODA '03.

[12]  Dimitris J. Kavvadias,et al.  Nash equilibria in all-optical networks , 2005, Discret. Math..

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

[14]  Lisa Zhang,et al.  Wavelength Assignment in Optical Networks with Fixed Fiber Capacity , 2004, ICALP.

[15]  Lisa Zhang,et al.  Minimizing maximum fiber requirement in optical networks , 2006, J. Comput. Syst. Sci..

[16]  J. Nash.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

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

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

[19]  Tim Roughgarden,et al.  How bad is selfish routing? , 2002, JACM.

[20]  Vittorio Bilò,et al.  The Price of Anarchy in All-Optical Networks , 2004, SIROCCO.

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

[22]  Paul G. Spirakis,et al.  The price of selfish routing , 2001, STOC '01.

[23]  Matthew Andrews,et al.  Complexity of wavelength assignment in optical network optimization , 2009, TNET.

[24]  I. Milchtaich,et al.  Congestion Games with Player-Specific Payoff Functions , 1996 .

[25]  Vittorio Bilò,et al.  On Nash Equilibria in Non-cooperative All-Optical Networks , 2005, STACS.