Heavy Traffic Approximation of Equilibria in Resource Sharing Games

We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the system, and users from different classes act to minimize the sum of their cost for processing delay and payment. As the exact processing time of this system is hard to compute and cannot be characterized in closed form, we introduce the notion of heavy traffic equilibrium as an approximation of the Nash equilibrium, derived by considering the asymptotic regime where the system load approaches capacity. We discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium.

[1]  Urtzi Ayesta,et al.  Heavy traffic analysis of the discriminatory randomorderofservice discipline , 2011, PERV.

[2]  J. Goodman.  Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[3]  Refael Hassin,et al.  To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems , 2002 .

[4]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.

[5]  Kiran M. Rege,et al.  Queue-Length Distribution for the Discriminatory Processor-Sharing Queue , 1996, Oper. Res..

[6]  Yu Wu,et al.  Heavy Traffic Approximation of Equilibria in Resource Sharing Games , 2012, IEEE J. Sel. Areas Commun..

[7]  P. Naor.  The Regulation of Queue Size by Levying Tolls , 1969 .

[8]  Leonard Kleinrock,et al.  Time-shared Systems: a theoretical treatment , 1967, JACM.

[9]  Costis Maglaras,et al.  Design of an Aggregated Marketplace Under Congestion Effects: Asymptotic Analysis and Equilibrium Characterization , 2008 .

[10]  Martin I. Reiman,et al.  Open Queueing Networks in Heavy Traffic , 1984, Math. Oper. Res..

[11]  J. Kingman.  On Queues in Heavy Traffic , 1962 .

[12]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2005, IEEE Trans. Autom. Control..

[13]  Urtzi Ayesta,et al.  Heavy-Traffic Analysis of a Multiple-Phase Network with Discriminatory Processor Sharing , 2009, Oper. Res..

[14]  Itay Gurvich,et al.  Pricing and Dimensioning Competing Large-Scale Service Providers , 2010, Manuf. Serv. Oper. Manag..

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

[16]  van der J Jan Wal,et al.  Equilibrium Strategies for Processor Sharing and Random Queues with Relative Priorities , 1997, Probability in the Engineering and Informational Sciences.

[17]  Patrick Billingsley,et al.  Weak convergence of measures - applications in probability , 1971, CBMS-NSF regional conference series in applied mathematics.

[18]  Leonard Kleinrock,et al.  Theory, Volume 1, Queueing Systems , 1975 .

[19]  Sandeep Juneja,et al.  The concert queueing game: to wait or to be late , 2011, Discret. Event Dyn. Syst..

[20]  Adam Wierman,et al.  Exploiting network effects in the provisioning of large scale systems , 2011, PERV.

[21]  Eitan Altman,et al.  A survey on discriminatory processor sharing , 2006, Queueing Syst. Theory Appl..

[22]  Laurent Massoulié,et al.  Bandwidth sharing and admission control for elastic traffic , 2000, Telecommun. Syst..

[23]  M. Thomas.  Queueing Systems. Volume 1: Theory (Leonard Kleinrock) , 1976 .

[24]  R. J. Williams,et al.  State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy , 2009, 0910.3821.

[25]  Michael V. Mannino,et al.  Optimal incentive-compatible pricing for M/G/1 queues , 2003, Oper. Res. Lett..

[26]  Jean C. Walrand,et al.  Fair end-to-end window-based congestion control , 2000, TNET.

[27]  Haim Mendelson,et al.  Optimal Incentive-Compatible Priority Pricing for the M/M/1 Queue , 1990, Oper. Res..

[28]  Isi Mitrani,et al.  Sharing a Processor Among Many Job Classes , 1980, JACM.

[29]  Refael Hassin,et al.  ?/M/1: On the equilibrium distribution of customer arrivals , 1983 .