Tolls and Welfare Optimization for Multiclass Traffic in Multiqueue Systems

We consider a queueing system with multiple heterogeneous servers serving a multiclass population. The classes are distinguished by the time costs. All customers have i.i.d. service requirements. Arriving customers do not see the instantaneous queue occupancy. Arrivals are randomly routed to one of the servers and the routing probabilities are determined centrally to optimize the expected waiting cost. This is, in general, a difficult optimization problem and we obtain the structure of the routing matrix. Next we consider a system in which each queue charges an admission price. The arrivals are routed randomly to minimize an individual objective function that includes the expected waiting cost and the admission price. Once again, we obtain the structure of the equilibrium routing matrix for this case. Finally, we determine the admission prices to make the equilibrium routing probability matrix equal to a given optimal routing probability matrix.

[1]  Urtzi Ayesta,et al.  Load balancing in processor sharing systems , 2011, Telecommun. Syst..

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

[3]  Sem C. Borst.  Optimal probabilistic allocation of customer types to servers , 1995, SIGMETRICS '95/PERFORMANCE '95.

[4]  Haim Mendelson,et al.  Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure , 2004, Manag. Sci..

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

[6]  S. Rao,et al.  Optimal Pricing of Priority Services , 1998, Oper. Res..

[7]  Richard M. Bradford.  Pricing, routing, and incentive compatibility in multiserver queues , 1996 .

[8]  A. C. Pigou.  Economics of welfare , 1920 .

[9]  Vivek S. Borkar,et al.  Charge-based control of DiffServ-like queues , 2004, Autom..

[10]  Eitan Altman,et al.  Equilibria for multiclass routing in multi-agent networks , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[11]  Ariel Orda,et al.  Competitive routing in multi-user communication networks , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[12]  Andrew M. Odlyzko,et al.  Paris metro pricing for the internet , 1999, EC '99.

[13]  Y. Masuda,et al.  Dynamic Pricing for Network Service: Equilibrium and Stability , 1999 .

[14]  D. Manjunath,et al.  Differential join prices for parallel queues: social optimality, dynamic pricing algorithms and application to Internet pricing , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[15]  S. C. Littlechild,et al.  Optimal arrival rate in a simple queueing system , 1974 .

[16]  Hai Yang,et al.  Principle of marginal-cost pricing : How does it work in a general road network ? , 1998 .

[17]  Mike J. Smith.  The marginal cost taxation of a transportation network , 1979 .

[18]  Ravi Jain,et al.  Analysis of Paris Metro Pricing Strategy for QoS with a Single Service Provider , 2001, IWQoS.

[19]  Balakrishna J. Prabhu,et al.  Price of Anarchy in Non-Cooperative Load Balancing , 2010, 2010 Proceedings IEEE INFOCOM.

[20]  Ariel Orda,et al.  Competitive routing in multiuser communication networks , 1993, TNET.

[21]  M. Haviv,et al.  To Queue or Not to Queue , 2003 .

[22]  Mark S. Squillante,et al.  Optimal stochastic scheduling in multiclass parallel queues , 1999, SIGMETRICS '99.

[23]  K. Balachandran.  Purchasing Priorities in Queues , 1972 .

[24]  D. K. Hildebrand,et al.  Congestion Tolls for Poisson Queuing Processes , 1975 .

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

[26]  D. Manjunath,et al.  Load balancing and routing games with admission price , 2011, IEEE Conference on Decision and Control and European Control Conference.

[27]  D. Manjunath,et al.  On load balancing equilibria in multiqueue systems with multiclass traffic , 2011, International Conference on NETwork Games, Control and Optimization (NetGCooP 2011).

[28]  Ariel Orda,et al.  Capacity allocation under noncooperative routing , 1997, IEEE Trans. Autom. Control..