On the transient state probabilities for a queueing model where potential customers are discouraged by queue length
- 1 June 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (02) , 345-354
- https://doi.org/10.1017/s0021900200036792
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 p 10(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
This publication has 4 references indexed in Scilit:
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- On the Improvement of the Operational Characteristics of Single-Server Queues by the Use of a Queue-Length-Dependent Service MechanismJournal of the Royal Statistical Society Series C: Applied Statistics, 1969
- The classification of birth and death processesTransactions of the American Mathematical Society, 1957
- The differential equations of birth-and-death processes, and the Stieltjes moment problemTransactions of the American Mathematical Society, 1957