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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: mazum@uwaterloo.ca
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Abstract

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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 

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