Online pricing for bandwidth provisioning in multi-class networks

We consider the problem of pricing for bandwidth provisioning over a single link, where users arrive according to a known stochastic traffic model. The network administrator controls the resource allocation by setting a price at every epoch, and each user's response to the price is governed by a demand function. We formulate this problem as a partially observable Markov decision process (POMDP), and explore two novel pricing schemes--reactive pricing and spot pricing--and compare their performance to appropriately tuned flat pricing. We use a gradient-ascent approach in all the three pricing schemes. We provide methods for computing unbiased estimates of the gradient in an online (incremental) fashion. Our simulation results show that our novel schemes take advantage of the known underlying traffic model and significantly outperform the model-free pricing scheme of flat pricing.

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

[2]  O. Hernández-Lerma,et al.  Error bounds for rolling horizon policies in discrete-time Markov control processes , 1990 .

[3]  Downing StreetCambridge.  Pricing Priority Classes in a Diierentiated Services Network , 1999 .

[4]  Jeffrey K. MacKie-Mason,et al.  A Market-Based Approach to Optimal Resource Allocation in Integrated-Services Connection-Oriented Networks , 2002, Oper. Res..

[5]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[6]  Herbert E. Scarf,et al.  The Computation of Economic Equilibria , 1974 .

[7]  Francesco Mallegni,et al.  The Computation of Economic Equilibria , 1973 .

[8]  Jon M. Peha,et al.  State-Dependent Pricing and Its Economic Implications , 2001, Telecommun. Syst..

[9]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[10]  S.D. Patek,et al.  Pricing of dialup services: an example of congestion-dependent pricing in the Internet , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  Robert Givan,et al.  On-line sampling-based control for network queueing problems , 2001 .

[12]  Xi-Ren Cao,et al.  Internet pricing with a game theoretical approach: concepts and examples , 2002, TNET.

[13]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[14]  Richard J. Gibbens,et al.  Resource pricing and the evolution of congestion control , 1999, at - Automatisierungstechnik.

[15]  Robert Givan,et al.  A framework for simulation-based network control via hindsight optimization , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[16]  E. Chong,et al.  Optimization of queues using an infinitesimal perturbation analysis-based stochastic algorithm with general update times , 1993 .

[17]  John N. Tsitsiklis,et al.  Simulation-based optimization of Markov reward processes , 2001, IEEE Trans. Autom. Control..

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

[19]  Catherine Rosenberg,et al.  A game theoretic framework for bandwidth allocation and pricing in broadband networks , 2000, TNET.

[20]  Pravin Varaiya,et al.  Correction to "A new approach to service provisioning in ATM networks" , 1993, TNET.

[21]  Dimitri P. Bertsekas,et al.  Rollout Algorithms for Stochastic Scheduling Problems , 1999, J. Heuristics.

[22]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[23]  Xi-Ren Cao,et al.  Perturbation analysis of discrete event dynamic systems , 1991 .