Optimal Dynamic Assignment of Customers to Heterogeneous Servers in Parallel

Susan H. Xu, Rhonda Righter and J. George Shanthikumar
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Susan H. Xu: Pennsylvania State University, University Park, Pennsylvania
Rhonda Righter: Santa Clara University, Santa Clara, California
J. George Shanthikumar: University of California, Berkeley, California

Operations Research, 1992, vol. 40, issue 6, 1126-1138

Abstract: The system under consideration comprises two classes of customers to be served by two stations, with parallel servers in each station. While class-1 customers can only receive service from station 1, class-2 customers can be served by either station. Arrival processes of customers form two mutually independent Poisson processes. The service time of a customer at either station is exponentially distributed with a common rate. A class- i customer, while present in the system, will incur a holding cost h i with h 1 ≥ h 2 . The objective is to dynamically assign customers to idle servers so that the expected discounted (or the long-run average) holding cost is minimized. We show that a class- j customer should be assigned to an idle server in station j , j = 1, 2, whenever possible, and a class-2 customer should be assigned to an idle server in station 1 only if (no class-1 customers are waiting, and) the length of queue 2 exceeds a critical number. Moreover, the critical number is monotonically increasing in the number of busy servers in station 1. The numerical results for some test cases are reported.

Keywords: dynamic programming/optimal control: infinite state Markov model; manufacturing: strategy in automated manufacturing (search for similar items in EconPapers)
Date: 1992
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