Buffer design in a closed form with hybrid input and random server interruptions

Abstract

A closed-form solution to the buffer design problem is presented by studying a queueing model with a hybrid input traffic arrival process (mixture of Poisson and burst Poisson processes), synchronous output and single server with random interruptions. The queueing model developed is of unified nature as it includes Poisson and burst Poisson arrival processes and the mixture of the two as well. It is shown that, at a modified offered load, the empty buffer probability in an infinite buffer equals that of a finite buffer with actual offered load as its input. The modified offered load is shown to be equal to the carried load of the finite buffer. Thus, it is shown that the expression for the buffer-content state probability of the finite buffer of any length can be directly deduced from that of the infinite buffer, and hence various performance parameters can be evaluated. An integrated digital voice-data system is taken as an example for the model developed. The relationships among buffer size, overflow probability and average message queueing delay due to buffering are portrayed on graphs with the average burst length, the traffic intensity and the input traffic mixture ratio taken as parameters. It is concluded that the burst nature of the input traffic is a very important factor in the buffer design problem.