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

Author:

Tijms Henk,Staats Koen

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.

Publisher

Cambridge University Press (CUP)

Subject

Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability

Reference6 articles.

1. Franx, G.J. (2004).A full probabilistic approach to waiting-time distributions.Doctoral dissertation,Vrije University,Amsterdam.

2. Tijms, H.C. (2003).A first course in stochastic models.Chichester:Wiley.

3. Franx, G.J. (2001).A simple solution for the M/D/cwaiting-time distribution.Operations Research Letters 29:221–229.

4. Nojo, S. & Watanabe, H. (1987).A new stage method getting arbitrary coefficient of variationthrough two stages.Transactions of the IECIE 70:33–36.

5. Van Hoorn, M.H. & Seelen, L.P. (1986).Approximations for the G/G/cqueue.Journal of Applied Probability 23:484–494.

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