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THE OPTIMAL ADMISSION THRESHOLD IN OBSERVABLE QUEUES WITH STATE DEPENDENT PRICING
Published online by Cambridge University Press: 13 December 2013
Abstract
We consider the social welfare model of Naor [20] and revenue-maximization model of Chen and Frank [7], where a single class of delay-sensitive customers seek service from a server with an observable queue, under state dependent pricing. It is known that in this setting both revenue and social welfare can be maximized by a threshold policy, whereby customers are barred from entry once the queue length reaches a certain threshold. However, no explicit expression for this threshold has been found. This paper presents the first derivation of the optimal threshold in closed form, and a surprisingly simple formula for the (maximum) revenue under this optimal threshold. Utilizing properties of the Lambert W function, we also provide explicit scaling results of the optimal threshold as the customer valuation grows. Finally, we present a generalization of our results, allowing for settings with multiple servers.
- Type
- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 28 , Issue 1 , January 2014 , pp. 101 - 119
- Copyright
- Copyright © Cambridge University Press 2013
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