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Optimal admission control for a single-server loss queue

  • Kyle Y. Lin (a1) and Sheldon M. Ross (a2)

Abstract

This paper presents a single-server loss queueing system where customers arrive according to a Poisson process. Upon arrival, the customer presents itself to a gatekeeper who has to decide whether to admit the customer into the system without knowing the busy–idle status of the server. There is a cost if the gatekeeper blocks a customer, and a larger cost if an admitted customer finds the server busy and therefore has to leave the system. The goal of the gatekeeper is to minimize the total expected discounted cost on an infinite time horizon. In the case of an exponential service distribution, we show that a threshold-type policy—block for a time period following each admission and then admit the next customer—is optimal. For general service distributions, we show that a threshold-type policy need not be optimal; we then present a sufficient condition for the existence of an optimal threshold-type policy.

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Corresponding author

Postal address: Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, USA. Email address: kylin@vt.edu
∗∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.

References

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Lin, K. Y., and Ross, S. M. (2003). Admission control with incomplete information of a queueing system. Operat. Res. 51, 645654.
Ross, S. M. (1983). Introduction to Stochastic Dynamic Programming. Academic Press, New York.
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.
Stidham, S. Jr. (1985). Optimal control of admission to a queueing system, IEEE Trans. Automatic Control 30, 705713.

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