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On the transient state probabilities for a queueing model where potential customers are discouraged by queue length

Published online by Cambridge University Press:  14 July 2016

Bent Natvig
Bent Natvig*
Affiliation:
University of Trondheim — NTH, Norway
*
*Now at the University of Sheffield.
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Abstract

Earlier work by Hadidi and Conolly and contemporary work by the author point to the great operational advantages of state-dependent queueing models. Let pin (t) be the state probabilities and p∗in the corresponding L.T.'s relative to the single server birth-and-death queueing process with parameters λn = λ/(n + 1), n ≥ 0, μn = μ, n ≥ 1. We have obtained an exact formulation of p∗i0, p∗in (n ≥ 1) being determined recursively. An exact expression for p10(t) is given in the case of low traffic intensities, and this has been approximated efficiently. Numerical evaluations show that the steady-state is reached very rapidly.

Keywords

BIRTH AND DEATH QUEUEING PROCESSSTATE DEPENDENT QUEUEING MODELDISCOURAGED CUSTOMERSQUEUE LENGTHOPERATIVE ADVANTAGESTRANSIENT BEHAVIOURNUMERICAL EVALUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 345 - 354
Copyright
Copyright © Applied Probability Trust 1974 

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References

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