Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T20:59:00.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Conditional Sojourn times and the volatility of payment schemes for bandwidth sharing in packet networks

Part of: Mathematical economics Basic methods Operations research and management science Special processes

Published online by Cambridge University Press:  30 March 2016

Fabrice M. Guillemin  and
Ravi R. Mazumdar
Fabrice M. Guillemin*
Affiliation:
Orange Labs
Ravi R. Mazumdar*
Affiliation:
University of Waterloo
*
∗Postal address: Orange Labs, 2 Avenue Pierre Marzin, F-22300 Lannion, France.
∗∗Postal address: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Predictability of revenue and costs to both operators and users is critical for payment schemes. We study the issue of the design of payment schemes in networks with bandwidth sharing. The model we consider is a processor sharing system that is accessed by various classes of users with different processing requirements or file sizes. The users are charged according to a Vickrey–Clarke–Groves mechanism because of its efficiency and fairness when logarithmic utility functions are involved. Subject to a given mean revenue for the operator, we study whether it is preferable for a user to pay upon arrival, depending on the congestion level, or whether the user should opt to pay at the end. This leads to a study of the volatility of payment schemes and we show that opting for prepayment is preferable from a user point of view. The analysis yields new results on the asymptotic behavior of conditional response times for processor sharing systems and connections to associated orthogonal polynomials.

Keywords

PricingM/M/1 processor sharingorthogonal polynomials

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service 80M35: Asymptotic analysis 91B26: Market models (auctions, bargaining, bidding, selling, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 962 - 980
Copyright
Copyright © Applied Probability Trust 2015 

References

[1] Abramowitz, M. and Stegun, I. A. (1964). Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables (Nat. Bureau Standards Appl. Math. Ser. 55). U.S. Government Printing Office, Washington, DC.Google Scholar
[2] Asare, B. K. and Foster, F. G. (1983). Conditional response times in the M/G/1 processor-sharing system. J. Appl. Prob. 20, 910–915.CrossRefGoogle Scholar
[3] Askey, R. and Ismail, M. (1984). Recurrence relations, continued fractions and orthogonal polynomials. Mem. Amer. Math. Soc. 49, No. 300.Google Scholar
[4] Birmiwal, S., Mazumdar, R. R. and Sundaram, S. (2012). Processor sharing and pricing implications. In Proc. ITC 24 (Krakow, Poland).Google Scholar
[5] Bulow, J. and Klemperer, P. (1996). Auctions versus negotiations. Amer. Econom. Rev. 86, 180–194.Google Scholar
[6] Charris, J. A. and Ismail, M. E. H. (1987). On sieved orthogonal polynomials. V. Sieved Pollaczek polynomials. SIAM J. Math. Anal. 18, 1177–1218.CrossRefGoogle Scholar
[7] Guillemin, F. and Boyer, J. (2001). Analysis of the M/M/1 queue with processor sharing via spectral theory. Queueing Systems 39, 377–397.CrossRefGoogle Scholar
[8] Kelly, F. (1997). Charging and rate control for elastic traffic. Europ. Trans. Telecommun. 8, 33–37.CrossRefGoogle Scholar
[9] Kleinrock, L. (1975). Queueing Systems , Vol. II. John Wiley, New York.Google Scholar
[10] Ozdaglar, A. and Srikant, R. (2007). Incentives and pricing in communications networks. In Algorithmic Game Theory , Cambridge University Press, pp. 571–591.CrossRefGoogle Scholar
[11] Reed, M. and Simon, B. (1980). Methods of Modern Mathematical Physics, Vol. II, Fourier Analysis, Selfadjointness. Academic Press, New York.Google Scholar
[12] Robert, P. (2003). Stochastic Networks and Queues (Appl. Math. (New York) 52). Springer, Berlin.CrossRefGoogle Scholar
[13] Roberts, J. W. and Massoulié, L. (2000). Bandwidth sharing and admission control for elastic traffic. Telecommun. Systems 15, 185–201.Google Scholar
[14] Sengupta, B. and Jagerman, D. L. (1985). A conditional response time of the M/M/1 processor-sharing queue. AT&T Tech. J. 64, 409–421.Google Scholar
[15] Vickrey, W. (1961). Counterspeculation, auctions, and competitive sealed tenders. J. Finance 16, 8–37.CrossRefGoogle Scholar
[16] Yaiche, H., Mazumdar, R. R. and Rosenberg, C. (2000). A game theoretic framework for bandwidth allocation and pricing in broadband networks. IEEE/ACM Trans. Networking 8, 667–678.CrossRefGoogle Scholar
[17] Yang, S. and Hajek, B. (2007). VCG-Kelly mechanisms for allocation of divisible goods: adapting VCG mechanisms to one-dimensional signals. IEEE J. Selected Areas Commun. 25, 1237–1243.CrossRefGoogle Scholar