Abstract
A queueing model with finite waiting-room, burst (batch) Poisson arrivals, synchronous transmission and server interruptions through a first-order Markov process is studied. Using average burst-length and traffic intensity as parameters, the relationships among overflow probabilities, buffer size and expected burst-queueing delay due to buffering are obtained. A recursion method for computation of steady-state probabilities of the buffer states is developed. This allows an estimation of the buffer lengths required for overflow probabilities less than or equal to 10-6 with the use of lesser computer memory. A system of multiplexing of data with burst Poisson arrivals in analog speech signals is considered as an application of this model. The results of this study are portrayed on the graphs and may be used as guidelines in buffer-design problems in many digital voice-data systems. Although this problem arose in the study of data multiplexing in speech, the queueing model developed is quite general and may be useful for other industrial applications.
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