An analysis of repeated call model with a finite number of sources

Repeated call model is one of the queueing models which appear in various communication systems. Repeated call model has been studied, but there has been little study on the finite source repeated call model. This paper deals with a single-server service system with a finite number of sources and with repeated calls. Assuming that the arrival process is quasi-random, the service time is drawn from an arbitrary distribution and the repetition interval is exponentially distributed. Traffic measures such as mean waiting time and mean number of waiting calls are derived by using the supplementary variable technique and the discrete transforms. A numerical example for the traffic characteristic is shown. The effect of repetition interval distribution is also studied by computer simulation. An application to disk memories in the Facsimile Intelligent and Communication System is given and the process waiting time is quantitatively analyzed. This evaluation is compared with the evaluation by the existing theory.