Summary: Single-server-single-queue-FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the result obtained are used to investigate the features of a special queueing model characterized by parameters (\(\lambda\) (N-n),\(\mu\) n).
This model retains the qualitative features of the C-model proposed by B. W. Conolly [Lecture notes on queueing systems. (1975; Zbl 0312.60047)] and J. Chan and B. W. Conolly [Comparative effectiveness of certain queueing systems with adaptive demand and service mechanisms. Comput. Oper. Res. 5, 187-196 (1978)]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments.
Finally, some computational results are given to compare the model discussed in this paper with the C-model.