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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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References

Aldous, D., Some interesting processes arising as heavy-traffic limits in a M/M/∞ storage process, Stochastic Process Applications (to appear).Google Scholar
Coffman, E.G. Jr, Kadota, T.T. & Shepp, L.A. (1985). A stochastic model of fragmentation in dynamic storage allocation. SIAM Journal Computation 14: 416–425.CrossRefGoogle Scholar
Coffman, E.G. Jr & Leighton, F.T. (1986). A provably efficient algorithm for dynamic storage allocation. Proceedings of the 18th ACM Symposium on Theoretical Computation, pp. 77–90.CrossRefGoogle Scholar
Feller, W. (1950). An introduction to probability theory and its applications, vol. 1, 2nd edition. New York: John Wiley.Google Scholar
Knuth, D.E. (1973). Fundamental algorithms, vol. 1, 2nd edition, Reading, Massachusetts:Addison–Wesley. (See Sect. 2.5, p. 435ff).Google Scholar
Kosten, L. (1937). Uber Sperrungswahrscheinlichkeiten bei Staffelschaltungen. Electra Nachrichten-Technik 14: 5–12.Google Scholar
Newell, G.F. (1984). The M/M/∞ service system with ranked servers in heavy traffic. New York:Springer-Verlag.CrossRefGoogle Scholar