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Stationary increments in the accumulated work process in processor-sharing queues

Published online by Cambridge University Press:  14 July 2016

R. D. Foley  and
Georgia-Ann Klutke
R. D. Foley*
Affiliation:
Georgia Institute of Technology
Georgia-Ann Klutke*
Affiliation:
University of Massachusetts
*
∗Postal address: Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332–0205, USA.
∗∗Present address: Department of Mechanical Engineering. The University of Texas at Austin, Austin, TX 78712–1063, USA.
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Abstract

We present a new approach to the processor-sharing queue that allows us to study the accumulated work process of a job that requires an amount of processing time x. Our approach simplifies the proofs of some earlier results on expected conditional response times and extends them to the M/G/φ (·) class. The approach illuminates some of the paradoxical features of these systems.

Keywords

RANDOM TIME CHANGE
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 671 - 677
Copyright
Copyright © Applied Probability Trust 1989 

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References

Asare, B. K. and Foster, F. G. (1983) Conditional response times in the M/G/1 processor-sharing system. J. Appl. Prob. 20, 910–915.Google Scholar
Coffman, E. G., Muntz, R. R. and Trotter, H. (1970) Waiting time distributions for processor-sharing systems. J. Assoc. Compul. Mach. 17, 123–130.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Kleinrock, L. (1967) Time-shared systems: a theoretical treatment. J. Assoc. Comput. Mach. 14, 242–261.Google Scholar
Kleinrock, L. (1976) Queueing Systems, Vol. 2. Wiley, New York.Google Scholar
O'Donovan, T. M. (1974) Direct solutions of M/G/1 processor-sharing models. Operat. Res. 22, 1232–1235.Google Scholar
Ott, T. (1984) The sojourn-time distribution in the M/G/1 queue with processor sharing. J. Appl. Prob. 21, 360–378.Google Scholar
Ross, S. (1981) Stochastic Processes. Wiley, New York.Google Scholar
Sakata, M., Noguchi, S. and Oizumi, J. (1971) An analysis of the M/G/1 queue under roundrobin scheduling. Operat. Res. 19, 371–385.Google Scholar
Schassberger, R. (1984) A new approach to the M/G/1 processor-sharing queue. J. Appl. Prob. 21, 202–213.Google Scholar
Van Doorn, E. (1981) Stochastic Monotonicity and Queueing Applications of Birth-Death Processes. Springer-Verlag, Berlin.Google Scholar
Yashkov, S. F. (1983) A derivation of response time distributions for an M/G/1 processor sharing queue. Prob. Control Inf. Theory 12, 133–148.Google Scholar