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NEGATIVE PROBABILITIES AT WORK IN THE M/D/1 QUEUE

Published online by Cambridge University Press:  15 December 2006

Henk Tijms  and
Koen Staats
Henk Tijms
Affiliation:
Department of Econometrics and Operations Research, Vrije University, 1081 HV Amsterdam, The Netherlands, and, Tinbergen Institute Amsterdam, 1018 WB Amsterdam, The Netherlands, E-mail: tijms@feweb.vu.nl
Koen Staats
Affiliation:
Department of Econometrics and Operations Research, Vrije University, 1081 HV Amsterdam, The Netherlands
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Abstract

This article derives amazingly accurate approximations to the state probabilities and waiting-time probabilities in the M/D/1 queue using a two-phase process with negative probabilities to approximate the deterministic service time. The approximations are in the form of explicit expressions involving geometric and exponential terms. The approximations extend to the finite-capacity M/D/1/N + 1 queue.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 1 , January 2007 , pp. 67 - 76
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

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