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Benes's formula for M/G/1–FIFO ‘explained' by preemptive-resume LIFO

Published online by Cambridge University Press:  14 July 2016

Robert B. Cooper  and
Shun-Chen Niu
Robert B. Cooper*
Affiliation:
Florida Atlantic University
Shun-Chen Niu*
Affiliation:
The University of Texas at Dallas
*
∗Postal address: College of Business and Public Administration, Computer and Information Systems Department, Florida Atlantic University, P.O. Box 3091, Boca Raton, FL 33431–0991, USA.
∗∗Postal address: School of Management and Administration. The University of Texas at Dallas, Box 830688, Richardson, TX 75083–0688, USA.
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Abstract

We provide a term-by-term interpretation of Beneš's well-known but mysterious inversion of the Pollaczek–Khintchine formula. The strategy is to recognize the equality of waiting time in M/G/1–FIFO with remaining work in M/G/1–LIFO–preemptive resume. In the process, we give a new and simple derivation of some known results for M/G/1–LIFO–preemptive resume.

Keywords

POLLACZEK–KHINTCHINE FORMULA
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 550 - 554
Copyright
Copyright © Applied Probability Trust 1986 

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References

Beneš, V. E. (1957) On queues with Poisson arrivals. Ann. Math. Statist. 28, 670–677.Google Scholar
Burman, D. Y. (1981) Insensitivity in queueing systems. Adv. Appl. Prob. 13, 846–859.CrossRefGoogle Scholar
Cooper, R. B. (1981) Introduction to Queueing Theory, 2nd edn. Elsevier North-Holland, New York.Google Scholar
Fakinos, D. (1981) The G/G/l queueing system with a particular queue discipline. J. R. Statist. Soc. B 43, 190–196.Google Scholar
Gross, D. and Harris, C. M. (1985) Fundamentals of Queueing Theory, 2nd edn. Wiley, New York.Google Scholar
Kelly, F. P. (1976) The departure process from a queueing system. Math. Proc. Camb. Phil. Soc. 80, 283–285.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
Kleinrock, L. (1975) Queueing Systems, Vol. 1. Wiley, New York.Google Scholar
Niu, S. C. (1983) Equilibrium analysis of insensitive generalized semi-Markov processes: a uniformization approach. Unpublished.Google Scholar
Ott, T. J. (1984) The sojourn-time distribution in the M/G/1 queue with processor sharing. J. Appl. Prob. 21, 360–378.Google Scholar
Prabhu, N. U. (1980) Stochastic Storage Processes: Queues, Insurance Risk, and Dams. Springer-Verlag, New York.CrossRefGoogle Scholar
Schassberger, R. (1978) Insensitivity of steady-state distribution of generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.CrossRefGoogle Scholar
Wolff, R. W. (1982) Poisson arrivals see time averages. Operat. Res. 30, 223–231.CrossRefGoogle Scholar
Yashkov, S. F. (1983) A derivation of response time distribution for an M/G/1 processor-sharing queue. Prob. Control. Inf. Theory 12, 133–148.Google Scholar