OPTIMAL DYNAMIC ASSIGNMENT OF CUSTOMERS TO HETEROGENEOUS SERVERS IN PARALLEL

• 成果类型: Article
• 署名作者: XU, SH; RIGHTER, R; SHANTHIKUMAR, JG
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.40.6.1126
• 发表日期: 1992
• 页码: 1126-1138

摘要

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 h1 greater-than-or-equal-to h2. 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.