IJPAM: Volume 116, No. 2 (2017)

Title

DISTRIBUTION OF THE WAITING AND SERVICE TIME
IN AN M/M/$ m $ PREEMPTIVE-RESUME LCFS
QUEUE WITH IMPATIENT CUSTOMERS

Authors

Hideaki Takagi
University of Tsukuba,
Tsukuba Science City, Ibaraki 305-8573, JAPAN

Abstract

We study an M/M/$ m $ preemptive-resume last-come, first-served (PR-LCFS) queue with impatient customers without priority classes. We focus on the time interval from arrival to either service completion or abandonment, whichever occurs first, of an arbitrary customer in the steady state. The problem is formulated as a combination of two one-dimensional birth-and-death processes, each with two absorbing states. We provide explicit expressions in terms of Laplace-Stieltjes transform of the distribution function for the first passage time to service completion and abandonment, which is decomposed into the waiting and service time. As two special cases, an M/M/$ m $ preemptive-loss LCFS system with impatient customers and an M/M/$ m $ preemptive-resume LCFS queue with patient customers only are treated separately. Some numerical example is presented for computation of theoretical formulas.

History

Received: 2017-07-30
Revised: 2017-09-11
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 60K25, 90B22
Key Words and Phrases: multiserver queue, preemptive-resume, last-come first-served, impatient customers, waiting time distribution, birth-and-death process, first passage time, absorbing state

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Bibliography

1
L. Durr, A single-server priority queuing system with general holding times, Poisson input, and reverse-order-of-arrival queuing discipline. Operations Research, 17, No.2 (1969), 351-358, doi: https://doi.org/10.1287/opre.17.2.351.

How to Cite?

DOI: 10.12732/ijpam.v116i2.21 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 501 -


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