Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T01:37:30.949Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Brun, O. & Garcia, J. (2000). Analytical solution of finite capacity M/D/1 queues. Journal of Applied Probability 37: 1092–1098.Google Scholar
Franx, G.J. (2001). A simple solution for the M/D/c waiting-time distribution. Operations Research Letters 29: 221–229.Google Scholar
Franx, G.J. (2004). A full probabilistic approach to waiting-time distributions. Doctoral dissertation, Vrije University, Amsterdam.
Nojo, S. & Watanabe, H. (1987). A new stage method getting arbitrary coefficient of variation through two stages. Transactions of the IECIE 70: 33–36.Google Scholar
Tijms, H.C. (2003). A first course in stochastic models. Chichester: Wiley.
Van Hoorn, M.H. & Seelen, L.P. (1986). Approximations for the G/G/c queue. Journal of Applied Probability 23: 484–494.Google Scholar