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Congestion-dependent pricing in a stochastic service system

Part of: Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Idriss Maoui ,
Hayriye Ayhan  and
Robert D. Foley
Idriss Maoui*
Affiliation:
Georgia Institute of Technology
Hayriye Ayhan*
Affiliation:
Georgia Institute of Technology
Robert D. Foley*
Affiliation:
Georgia Institute of Technology
*
∗ Current address: Lehman Brothers, New York, NY 10019, USA. Email address: imaoui@lehman.com
∗∗ Postal address: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA.
∗∗ Postal address: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA.
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Abstract

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We study a service facility modeled as a queueing system with finite or infinite capacity. Arriving customers enter if there is room in the facility and if they are willing to pay the price posted by the service provider. Customers belong to one of a finite number of classes that have different willingnesses-to-pay. Moreover, there is a penalty for congestion in the facility in the form of state-dependent holding costs. The service provider may advertise class-specific prices that may fluctuate over time. We show the existence of a unique optimal stationary pricing policy in a continuous and unbounded action space that maximizes the long-run average profit per unit time. We determine an expression for this policy under certain conditions. We also analyze the structure and the properties of this policy.

Keywords

Dynamic pricingqueueingMarkov decision processrevenue management

MSC classification

Primary: 90B22: Queues and service
Secondary: 90C40: Markov and semi-Markov decision processes

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007 , pp. 898 - 921
Copyright
Copyright © Applied Probability Trust 2007 

References

Aktaran, T. and Ayhan, H. (2007). Sensitivity of optimal prices to system parameters in a service facility. Working paper.Google Scholar
Ata, B. and Shneorson, S. (2006). Dynamic control of an M/M/1 service system with adjustable arrival and service rates. Manag. Sci. 52, 1778–1791.Google Scholar
Çil, E. B., Karaesmen, F. and Örmeci, E. L. (2007). Sensitivity analysis on a dynamic pricing problem of an M/M/c queuing system. Submitted.Google Scholar
George, J. M. and Harrison, J. M. (2001). Dynamic control of a queue with adjustable service rate. Operat. Res. 49, 720–731.Google Scholar
Hassin, R. (1986). Consumer information in markets with random product quality: the case of queues and balking. Econometrica 54, 1185–1195.CrossRefGoogle Scholar
Knudsen, N. C. (1972). Individual and social optimization in a multiserver queue with a general cost-benefit structure. Econometrica 40, 515–528.CrossRefGoogle Scholar
Larsen, C. (1998). Investigating sensitivity and the impact of information on pricing decisions in an M/M/1/∞ queueing model. Internat. J. Production Econom. 56–57, 365–377.Google Scholar
Lasserre, J.-B. and Hernández-Lerma, O. (1996). Discrete-Time Markov Control Processes. Basic Optimality Criteria. Springer, New York.Google Scholar
Low, D. W. (1974). Optimal dynamic pricing policies for an M/M/s queue. Operat. Res. 22, 545–561.Google Scholar
Low, D. W. (1974). Optimal pricing for an unbounded queue. IBM J. Res. Development 18, 290–302.CrossRefGoogle Scholar
Maoui, I., Ayhan, H. and Foley, R. D. (2007). Optimal static pricing for a service facility with holding costs. To appear in Europ. J. Operat. Res.Google Scholar
Mendelson, H. and Whang, S. (1990). Optimal incentive-compatible priority pricing for the M/M/1 queue. Operat. Res. 38, 870–883.Google Scholar
Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica 37, 15–24.Google Scholar
Paschalidis, I. C. and Tsitsiklis, J. N. (2000). Congestion-dependent pricing of network services. IEEE/ACM Trans. Networking 8, 171–184.Google Scholar
Puterman, M. (1994). Markov Decision Processes. John Wiley, New York.Google Scholar
Stidham, S. (1985). Optimal control of admission to a queueing system. IEEE Trans. Automatic Control 30, 705–713.CrossRefGoogle Scholar
Weber, R. R. and Stidham, S. (1987). Optimal control of service rates in network queues. Adv. Appl. Prob. 19, 202–218.CrossRefGoogle Scholar
Yechiali, U. (1971). On optimal balking rules and toll charges in the G/M/1/s queue. Operat. Res. 19, 349–370.Google Scholar
Ziya, S., Ayhan, H. and Foley, R. D. (2004). Relationships among three assumptions in revenue management. Operat. Res. 52, 804–809.Google Scholar
Ziya, S., Ayhan, H. and Foley, R. D. (2006). Optimal prices for finite capacity queueing systems. Operat. Res. Lett. 34, 214–218.Google Scholar