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Storage allocation under processor sharing II: Further asymptotic results

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journal contribution
posted on 20.08.2012, 00:00 by Eunju Sohn, Charles Knessl
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 wellknown 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. 1 Introduction


This work was partly supported by NSF grant DMS 05-03745 and NSA grant H 98230- 08-1-0102.


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© Cambridge University Press 2010. The original version is available through Cambridge University Press at DOI: 10.1017/S0956792510000306


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