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Stochastic Models of Queue Storage

Published online by Cambridge University Press:  27 July 2009

E. G. Coffman Jr ,
L. Flatto ,
I. Mitrani ,
L. A. Shepp  and
C. Knessl
E. G. Coffman Jr
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey 07974
L. Flatto
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey 07974
I. Mitrani
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey 07974
L. A. Shepp
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey 07974
C. Knessl
Affiliation:
The Technological Institute Northwestern University Evanston, Illinois 60201
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Abstract

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|.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 75 - 93
Copyright
Copyright © Cambridge University Press 1988

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