An on-off single server queueing model with finite waiting room and its application to computer communications

Abstract

A queueing model with finite waiting room, Poisson arrivals, constant service time, synchronous transmission and a single server interrupted through a first-order Markov process is studied. The buffer's access to a channel, transmitting data at a field rate is controlled by a switch which in turn is controlled through a first-order Markov process. The relationships among overflow probabilities, buffer size and expected queueing delay due to buffering are obtained. A recursive method for computation of steady-state probabilities of the buffer states is developed. The system of multiplexing data in analog speech signals on telephone lines is considered as an application of the model studied. The results of this study are portrayed on graphs and may be used as the guide lines for the buffer design in digital systems. The system of multiplexing data in analog speech signals using this model, is simulated on the EC-1030 computer to check the validity of the analytical results. Simulation results are also portrayed on the graphs for comparison. Although this study arose in the buffer design required for multiplexing the data in analog speech, the queueing model developed is quite general and may be useful for other industrial applications.