Deterministic Retrial Times are Optimal in Queues with Forbidden States

INFOR, Vol. 27, No. 3, pp. 374-386, August 1989

14 Pages Posted: 20 Feb 2009 Last revised: 19 Oct 2010

See all articles by V. G. Kulkarni

V. G. Kulkarni

University of North Carolina (UNC) at Chapel Hill

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: February 16, 2009

Abstract

Consider a customer X, who wishes to obtain service at a queueing system. When X arrives at this system, he has three possible courses of action to choose from, i) join the system; ii) not to join the system now, but return later after a random amount of time; or iii) to leave without obtaining service. Suppose that the system has a set of forbidden states and when X, upon arrival, finds the system in one of these forbidden states, he has no choice but to return later. Otherwise, he joins the system. The problem addressed in this paper is the following: Given that every unsuccessful retrial costs a certain amount and every unit of time spent waiting outside the system costs a certain amount, then after how long a period, possibly random, should X try his luck again? We show that under the assumption that all forbidden states are regenerative, there are deterministic (i.e. non-random) optimal retrial times that minimize the expected cost of getting served. Several applications are discussed.

Keywords: Optimal Retrial Times, Queueing, Regenerative States, Retrial queues

JEL Classification: M11, C61

Suggested Citation

Kulkarni, V. G. and Sethi, Suresh, Deterministic Retrial Times are Optimal in Queues with Forbidden States (February 16, 2009). INFOR, Vol. 27, No. 3, pp. 374-386, August 1989. Available at SSRN: https://ssrn.com/abstract=1344468

V. G. Kulkarni

University of North Carolina (UNC) at Chapel Hill ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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