A Stochastic Model of Fragmentation in Dynamic Storage Allocation

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dc.contributor.authorCoffman, E. G
dc.contributor.authorKadota, T. T
dc.contributor.authorShepp, Larry A
dc.date2023-05-17T15:08:58.000
dc.date.accessioned2023-05-23T03:36:18Z
dc.date.available2023-05-23T03:36:18Z
dc.date.issued1985-05-01
dc.date.submitted2016-07-27T07:17:03-07:00
dc.description.abstractWe study a model of dynamic storage allocation in which requests for single units of memory arrive in a Poisson stream at rate λ and are accommodated by the first available location found in a linear scan of memory. Immediately after this first-fit assignment, an occupied location commences an exponential delay with rate parameter μ, after which the location again becomes available. The set of occupied locations (identified by their numbers) at time t forms a random subset St of {1,2, . . .}. The extent of the fragmentation in St, i.e. the alternating holes and occupied regions of memory, is measured by (St) - |St |. In equilibrium, the number of occupied locations, |S|, is known to be Poisson distributed with mean ρ = λ/μ. We obtain an explicit formula for the stationary distribution of max (S), the last occupied location, and by independent arguments we show that (E max (S) - E|S|)/E|S| → 0 as the traffic intensity ρ → ∞. Moreover, we verify numerically that for any ρ the expected number of wasted locations in equilibrium is never more than 1/3 the expected number of occupied locations. Our model applies to studies of fragmentation in paged computer systems, and to containerization problems in industrial storage applications. Finally, our model can be regarded as a simple concrete model of interacting particles [Adv. Math., 5 (1970), pp. 246–290].
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/47791
dc.legacy.articleid1192
dc.legacy.fields10.1137/0214032
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1192&context=statistics_papers&unstamped=1
dc.rights<p>Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.</p>
dc.source.beginpage416
dc.source.endpage425
dc.source.issue408
dc.source.issue2
dc.source.journalStatistics Papers
dc.source.journaltitleSIAM Journal on Computing
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume14
dc.subject.otherdynamic storage allocation
dc.subject.othercheckerboarding
dc.subject.otherM/M/∞ queue
dc.subject.othermemory allocation
dc.subject.otherComputer Sciences
dc.subject.otherStatistics and Probability
dc.titleA Stochastic Model of Fragmentation in Dynamic Storage Allocation
dc.typeArticle
digcom.contributor.authorCoffman, E. G
digcom.contributor.authorKadota, T. T
digcom.contributor.authorShepp, Larry A
digcom.identifierstatistics_papers/408
digcom.identifier.contextkey8885183
digcom.identifier.submissionpathstatistics_papers/408
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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