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

  • Henk Tijms (a1) and Koen Staats (a2)

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.

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REFERENCES

Brun, O. & Garcia, J. (2000). Analytical solution of finite capacity M/D/1 queues. Journal of Applied Probability 37: 10921098.
Franx, G.J. (2001). A simple solution for the M/D/c waiting-time distribution. Operations Research Letters 29: 221229.
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: 3336.
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: 484494.

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