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New results in the theory of repeated orders queueing systems

Published online by Cambridge University Press:  14 July 2016

Qui Hoon Choo  and
Brian Conolly
Qui Hoon Choo*
Affiliation:
Chelsea College, University of London
Brian Conolly*
Affiliation:
Chelsea College, University of London
*
∗ Postal address: Department of Mathematics, Chelsea College, Manresa Road, London SW3 6LX, U.K.
∗ Postal address: Department of Mathematics, Chelsea College, Manresa Road, London SW3 6LX, U.K.
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Abstract

The repeated orders queueing system (ROO) permits no waiting or queue in the normal sense. Instead customers who find the service (or device, to use an engineering term) busy make reapplications at random intervals and in random order until their needs are met. Thus a second demand stream supplements the basic first arrival stream. Familiar examples are provided in a telephone communication setting, in particular in the context of a multiaccess computing system. Cohen [3] and Aleksandrov [1] made the first contributions to the theory of ROO. This paper complements their work with a steady-state analysis of system time (waiting time including service of a new arrival), of service idle time, and of system busy period.

Keywords

DEVICE BUSY PERIODBLOCKED DEVICEWAITING TIME IN ORBITCAR PARK FULL
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 631 - 640
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Aleksandrov, A. M. (1974) A queueing system with repeated orders. Izv. Akad. Nauk SSSR Tehn. Kibernet. 2, 86–89.Google Scholar
[2] Choo, Q. H. (1978) The Interaction of Theory and Simulation in Queueing Analysis. Ph.D. Thesis, Chelsea College, University of London.Google Scholar
[3] Cohen, J. W. (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommunication Rev. 18, no. 2.Google Scholar
[4] Conolly, B. W. (1975) Lecture Notes on Queueing Systems. Ellis Horwood, Chichester.Google Scholar