Dynamic pricing of preemptive service for elastic demand

We consider a service provider that accommodates two classes of users: primary users (PUs) and secondary users (SUs). SU demand is elastic to price whereas PU demand is inelastic. When a PU arrives to the system and finds all channels busy, it preempts an SU unless there are no SUs in the system. Call durations are exponentially distributed and their means are identical. We study the optimal pricing policy of SUs by using dynamic programming to maximize the total expected discounted profit over finite and infinite horizons, and the average profit. Our main contribution is to show that although the system is modeled as a two-dimensional Markov chain, the optimal pricing policy depends only on the total number of users in the system (PUs and SUs), i.e. the total occupancy. We also demonstrate that optimal prices are increasing with the total occupancy. Finally, we describe applications of these results to the special case of admission control and show that the optimal pricing policy structure of the original system is not preserved for systems with elastic PUs.

[1]  Jon M. Peha,et al.  Approaches to spectrum sharing , 2005, IEEE Communications Magazine.

[2]  Susan H. Xu,et al.  Optimal Expulsion Control - A Dual Approach to Admission Control of an Ordered-Entry System , 1993, Oper. Res..

[3]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[4]  Juan A. Garay,et al.  Call preemption in communication networks , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[5]  Steven P. Weber,et al.  Preemption rates for a parallel link loss network , 2009, Perform. Evaluation.

[6]  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.

[7]  Gajf Gido Brouns.  Queueing models with admission and termination control : monotonicity and threshold results , 2003 .

[8]  Janne Riihijärvi,et al.  Flexible and Spectrum Aware Radio Access through Measurements and Modelling in Cognitive Radio Systems FARAMIR Document Number D 6 . 2 Prototype Description and Field Trial Results , 2011 .

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[10]  Apostolos Burnetas,et al.  Admission policies for a two class loss system , 2001 .

[11]  Huseyin Mutlu.  Spot pricing of secondary access to wireless spectrum , 2010 .

[12]  Bruce L. Miller,et al.  A Queueing Reward System with Several Customer Classes , 1969 .

[13]  John N. Tsitsiklis,et al.  Congestion-dependent pricing of network services , 2000, TNET.

[14]  Jan van der Wal,et al.  Optimal threshold policies in a two-class preemptive priority queue with admission and termination control , 2006, Queueing Syst. Theory Appl..

[15]  Walter Helly.  Letter to the Editor—Two Doctrines for the Handling of Two-Priority Traffic by a Group of N Servers , 1962 .

[16]  David Starobinski,et al.  Optimal admission control of secondary users in preemptive cognitive radio networks , 2012, 2012 10th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt).

[17]  David Starobinski,et al.  Spot Pricing of Secondary Spectrum Usage in Wireless Cellular Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[18]  Refik Güllü,et al.  Admission and Termination Control of a Two Class Loss System , 2011 .

[19]  Don Towsley,et al.  On optimal call admission control in cellular networks , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[20]  Noah Gans,et al.  Pricing and Capacity Rationing for Rentals with Uncertain Durations , 2007, Manag. Sci..

[21]  Jean C. Walrand,et al.  An introduction to queueing networks , 1989, Prentice Hall International editions.