ASYMPTOTICALLY OPTIMAL ROUTING AND SERVICE RATE ALLOCATION IN A MULTISERVER QUEUING SYSTEM

Citation
Jg. Shanthikumar et Sh. Xu, ASYMPTOTICALLY OPTIMAL ROUTING AND SERVICE RATE ALLOCATION IN A MULTISERVER QUEUING SYSTEM, Operations research, 45(3), 1997, pp. 464-469
Citations number
19
Categorie Soggetti
Management,"Operatione Research & Management Science","Operatione Research & Management Science
Journal title
ISSN journal
0030364X
Volume
45
Issue
3
Year of publication
1997
Pages
464 - 469
Database
ISI
SICI code
0030-364X(1997)45:3<464:AORASR>2.0.ZU;2-K
Abstract
We consider a single stage queueing system with c heterogeneous server s. Customers arrive at this system according to a renewal process with mean 1/lambda and squared coefficient of variation (scv) C-a(2). An i ncoming customer is routed to server i with probability theta(i), Sigm a(i=1)(c) theta(i) = 1. The service times at servier i are i.i.d rando m variables mean 1/mu(i) and scv C-Si(2). The holding cost rate of que ue i is h, per customer. i = 1,2,...,c. The problems of interest are t wofold: (a) for a fixed service rate allocation mu(i), Sigma(i=1)(c) m u(1) = mu, find the routing probabilities, theta(i), Sigma(i=1)(c) th eta(i) = 1, that minimize the average total holding cost: and (b) for fixed routing probabilities theta(i), Sigma(i=1)(c) theta(i), and tot al 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 ho lding cost of the system. For each problem, we characterize the optima l policy under heavy traffic conditions. We also derive the routing pr obabilities, <(theta)over cap>(i), (proportions <(delta)over cap>(i)). i = 1,...,c, that are strongly asymptotically optimal. That is, the d ifference between the average total holding costs under <(theta)over c ap>(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 consta nt independent of the routing probabilities (proportions) and the arri val rate. In addition, ws discuss the necessity and sufficiency of the accurate knowledge of the means and sns of the interarrival and servi ce times in obtaining asymptotically optimal policies.