Asymptotically optimal routing and service rate allocation in a multiserver queueing system
成果类型：
Article
署名作者：
Shanthikumar, JG; Xu, SH
署名单位：
Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.45.3.464
发表日期：
1997
页码：
464-469
关键词：
摘要：
We consider a single stage queueing system with c heterogeneous servers. Customers arrive at this system according to a renewal process with mean 1/lambda and squared coefficient of variation (scv) C-a(2). An incoming customer is routed to server i with probability theta(i), Sigma(i=1)(c) theta(i) = 1. The service times at servier i are i.i.d random variables mean 1/mu(i) and scv C-Si(2). The holding cost rate of queue i is h, per customer. i = 1,2,...,c. The problems of interest are twofold: (a) for a fixed service rate allocation mu(i), Sigma(i=1)(c) mu(1) = mu, find the routing probabilities, theta(i)*, Sigma(i=1)(c) theta(i)* = 1, that minimize the average total holding cost: and (b) for fixed routing probabilities theta(i), Sigma(i=1)(c) theta(i), and total service rate CL, find the service rate allocation mu(i)* = mu delta(i)*, Sigma(i=1)(c) delta(i)* = 1, that minimizes the average total holding cost of the system. For each problem, we characterize the optimal policy under heavy traffic conditions. We also derive the routing probabilities, <(theta)over cap>(i), (proportions <(delta)over cap>(i)). i = 1,...,c, that are strongly asymptotically optimal. That is, the difference between the average total holding costs under <(theta)over cap>(i), i = 1,...,c, and theta(i)*, i = 1,...,c (<(delta)over cap>(i), i = 1,...,c, and delta(i)*, i = 1,...,c) is bounded by a fixed constant independent of the routing probabilities (proportions) and the arrival rate. In addition, ws discuss the necessity and sufficiency of the accurate knowledge of the means and sns of the interarrival and service times in obtaining asymptotically optimal policies.