A Queueing Model Where Potential Customers are Discouraged by Queue Length

We consider the birth-death process {X(t): 0 ≤ t < ∞} with parameters $$ \begin{gathered} {\lambda _n} = \lambda /(n + 1)\quad \quad \quad \quad \quad n = 0,1, \ldots \ldots \hfill \\ {\mu _n} = 0\quad \quad \quad \quad \quad \quad \quad \quad n = 0 \hfill \\ = \mu \quad \quad \quad \quad \quad \quad \quad \quad \quad n = 1,2, \ldots \ldots , \hfill \\ \end{gathered} $$ (7.1.1) which serves as a single server queueing model where potential customers are discouraged by queue length (cf. Conolly (1975), Hadidi (1975) and Natvig (1974, 1975)).