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Transient analysis of a queue where potential customers are discouraged by queue length. (English) Zbl 1008.60098
The authors employ a continued-fraction approach to analyse the time-dependent behaviour of the birth-death process with rates $$\lambda_n = \lambda/(n+1)$$ and $$\mu_n = \mu$$, which serves as a model for a queueing system in which potential customers are discouraged by queue length. The results are compared with those of the system M/M/$$\infty$$, which has the same stationary distribution.

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
##### Keywords:
birth-death queue; transient behaviour; continued fraction
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