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Storage allocation under processor sharing II: Further asymptotic results

Published online by Cambridge University Press:  30 November 2010

EUNJU SOHN  and
CHARLES KNESSL
EUNJU SOHN
Affiliation:
Department of Mathematics, Boyd Graduate Studies Research Center, University of Georgia, Athens, GA 30602, USA email: esohn@math.uga.edu
CHARLES KNESSL
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA email: knessl@uic.edu
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Abstract

We consider a processor-sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items. All of the spaces are numbered and ordered. An arriving customer takes the lowest available space. Dynamic storage allocation and the fragmentation of computer memory are well-known applications of this model. We define the traffic intensity ρ to be λ/μ, where λ is the customers' arrival rate and μ is the service rate of the processor. We study the joint probability distribution of the numbers of occupied primary and secondary spaces. We study the problem in two asymptotic limits: (1) m → ∞ with a fixed ρ < 1, and (2) ρ ↑ 1, m → ∞ with m(1-ρ) = O(1). The asymptotics yield insight into how many secondary spaces tend to be needed, and into the sample paths leading to the occupation of the two types of spaces. We show that the asymptotics lead to accurate numerical approximations.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 1 , February 2011 , pp. 45 - 82
Copyright
Copyright © Cambridge University Press 2010

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