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On the transient waiting times for a GI/M/1 priority queue

Published online by Cambridge University Press:  14 July 2016

G. Dalen  and
B. Natvig
G. Dalen
Affiliation:
University of Oslo
B. Natvig*
Affiliation:
University of Oslo
*
∗∗Postal address: Matematisk Institutt, Universitetet i Oslo, Blindern, Oslo 3, Norway.
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Abstract

In this paper we consider the GI/M/1 queueing model with infinite waiting-room capacity. The customer arriving at t = 0 will find k — 1 customers waiting. The latter customers belong to a second priority class, whereas the ones arriving in [0,∞) belong to a first priority class and have the higher priority. Within each class we have a first-in-first-out queueing discipline. A customer, once at the service-point, remains there until his service is completed. Then the next customer for service is the one of highest priority among those queueing.

For this model we derive the transient waiting times for customers belonging to both priority classes. The results are of special interest in appointment systems where customers may not turn up.

Keywords

GI/M/1 PRIORITY QUEUETRANSIENT WAITING TIMESNON-PREEMPTIVE PRIORITY DISCIPLINEAPPOINTMENT SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 227 - 234
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

∗

Present address: Norsk Hydro, 3900 Porsgrunn, Norway.

References

Bhat, U. N. (1967) Some explicit results for the queue GI/M/1 with group service. Sankhya A 29, 199–206.Google Scholar
Dalen, G. (1976) An Analysis of a Generalized D/M/1 Queue (In Norwegian). Cand. real. Thesis, University of Oslo.Google Scholar
Dalen, G. and Natvig, B. (1978) On the transient waiting time for GI/M/1 with a ‘head of the line’ priority discipline (abstract). Adv. Appl. Prob. 10, 315–316.CrossRefGoogle Scholar
Natvig, B. (1975) A Contribution to the Theory of Birth-and-Death Queueing Models. Ph.D. Thesis, University of Sheffield.Google Scholar
Prabhu, N. U. and Bhat, U. N. (1963) Some first passage problems and their application to queues. Sankya A 25, 281–292.Google Scholar
Takács, L. (1962) A single server queue with recurrent input and exponentially distributed service times. Operat. Res. 10, 395–399.CrossRefGoogle Scholar