Integration of Discrete-Time Correlated Markov Processes in a TDM System

Abstract

In this paper, we consider a discrete-time queueing model for a Time Division Multiplexing (TDM) system with integration of voice and data (a model introduced by Li and Mark [16]). The voice traffic is a superposition of N Markov chains, which alternate between two states: the talkspurt state and the silence state. The data traffic is Poisson and independent of the voice sources. We show that the average queue size is increasing in certain correlation coefficients of the voice sources, increasing convex in the proportion of time the voice sources are in talkspurts, increasing convex in the number of voice sources, and increasing convex in the data traffic intensity. However, it is decreasing convex in the number of channels. These structural results yield various bounds. To take video traffic into account as well, we adapt a model of Maglaris et al. [18]. In their model, video traffic is generated by a continuous-state autoregressive Markov process that matches the average rate and the autocovariance of the output of a video coder. We show that if we replace their autoregressive model by a two-state Markov chain model with the same rate and correlation coefficient, we obtain an upper bound for the queue size. This replacement enables us to treat the video traffic as a voice source and use the techniques developed for dealing with voice/data integration to obtain bounds and estimates.