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

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