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Stochastic Models of Queue Storage

Lookup NU author(s): Emeritus Professor Isi Mitrani


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We study a model of queue storage in which items (requests for single units of storage) arrive in a Poisson stream and are accommodated by the first available location in a linear scan of storage. The processing times of items are independent, exponentially distributed random variables. The set of occupied locations (identified by their indices) at time t forms a random subset Si, of [1,2,.…]. The extent of the fragmentation in Si, i.e., the alternating holes and occupied regions of storage, is measured by Wt, = max St, – |St|.

Publication metadata

Author(s): Coffman EG, Flatto L, Knessl C, Mitrani I, Shepp LA

Publication type: Article

Publication status: Published

Journal: Probability in the Engineering and Informational Sciences

Year: 1988

Volume: 2

Issue: 1

Pages: 75-93

ISSN (print): 0269-9648

ISSN (electronic): 1469-8951

Publisher: Cambridge University Press


DOI: 10.1017/S0269964800000644


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