Approximation model for multi-service transmission

Abstract

Disparate service times of different classes of traffic in multi-service transmission models cause numerical difficulties in exact analysis. Utilizing the difference in time scale, an approximation model is developed. The accumulation and depletion of low priority data packets are modelled as the service time and inter-arrival time processes of a PH/PH/1 queue. The PH/PH/1 model is related to the stochastic fluid flow model, and the eigenvalues of a key matrix determine the stationary distribution of the waiting time (and the idle time) of the PH/PH/1 queue and of the buffer content in the stochastic fluid flow model. Exploiting the common results of the two methods, numerical examples are presented for the moments of queue length of low priority data packets conditional on various levels of voice calls or active speakers present. A stochastic fluid flow interpretation is given of the coupling matrix employed in the matrix-algebraic method of PH/PH/1 queue and the connection with results obtained via a random walk model is observed.