NDLI: Asymptotic Expansions of Moments of the Waiting Time in a Shared-Processor of an Interactive System

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Morrison, J. A. Mitra, Debasis
Copyright Year	1983
Abstract	An interactive computer system service is characterized by the random waiting (or response) time perceived by users. This paper presents a novel solution to the problem of efficiently computing the second moment of the waiting time of a class of large interactive systems. The physical system consists of a bank of terminals, each of which asynchronously alternates between thinking and waiting for service from a CPU which operates under the processor-sharing discipline. The problem of obtaining higher order waiting time moments is quite different from that of obtaining CPU queue statistics. Only the first moment of the waiting time is obtainable from the CPU queue statistics.The technique for arriving at the second moment of the waiting time consists of developing an asymptotic expansion in inverse powers of the number of terminals. Hence, as the system grows, quite fortuitously, fewer terms of the series require computation to achieve the desired accuracy. Beside its numerical advantages, the results give new insight since the leading terms of the series, which contain most of the information, are obtained explicitly. The novelty also rests on the fact that instead of solving matrix equations, the problem is turned into one of solving a second order differential equation. A simple two-dimensional recursion yields all the terms of the asymptotic expansion.
Starting Page	789
Ending Page	802
Page Count	14
File Format	PDF
ISSN	00975397
DOI	10.1137/0212054
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	12
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	queueing theory asymptotic expansions waiting time moments queueing networks
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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