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BOUNDING THE STATIONARY DISTRIBUTION OF THE M/G/1 QUEUE SIZE

Published online by Cambridge University Press:  19 September 2006

Sheldon M. Ross
Sheldon M. Ross
Affiliation:
Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, E-mail: smross@usc.edu
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Abstract

We start with a simple derivation of an identity connecting the conditional expected residual service time as seen by an arrival and the steady-state tail distribution function of the number of customers in the system, which was previously proven by Mandelbaum and Yechiali. We then show how to use it to obtain bounds on the the stationary distribution of the number of customers in the M/G/1 queue.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 571 - 574
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Mandelbaum, A. & Yechiali, U. (1979). Individual optimization in the M/GI/1 queue, Appendix A. Technical Report, Department of Statistics, Tel Aviv University.
Fakinos, D. (1982). The expected remaining service time in a single server queue. Operations Research 30(5): 1014–1017.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.