Negative probabilities at work in the M/D/1 queue

H.C. Tijms; K. Staats

doi:10.1017/S0269964807070040

Negative probabilities at work in the M/D/1 queue

H.C. Tijms
, K. Staats

Research output: Contribution to journal › Article › Academic › peer-review

10 Citations (Scopus)

1 Downloads (Pure)

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 + queue.

Original language	English
Pages (from-to)	67-76
Number of pages	10
Journal	Probability in the Engineering and Informational Sciences
Volume	21
Issue number	1
DOIs	https://doi.org/10.1017/S0269964807070040
Publication status	Published - 2007

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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 + queue.",

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AB - 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 + queue.

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Negative probabilities at work in the M/D/1 queue

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