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

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.