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ISTC-CC Abstract
The Optimal Admission Threshold in Observable Queues with State Dependent Pricing
Probability in the Engineering and Informational Sciences, vol. 28, 2014, pp. 101-119. January 2014.
Christian Borgs, Jennifer T. Chayes, Sherwin Doroudi*, Mor Harchol-Balter^,
Kuang Xu†
Microsoft Research
* Tepper School of Business, Carnegie Mellon University
^ School of Computer Science, Carnegie Mellon University
† Laboratory for Information and Decision Systems, Massachusetts Institute of Technology,
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.
FULL PAPER: pdf