The superposition of discrete-time Markov renewal processes with an application to statistical multiplexing of bursty traffic sources

The main contribution in this paper is the introduction of a methodology for approximately characterizing the superposition process of N greater than or equal to 2 arbitrary (and possibly heterogeneous) discrete-time Markov Renewal processes (MRP). In this model, the superposition process is characterized by an MRP with a state space that grows exponentially with N. We consider an on/off traffic source model, where the distribution of the on and off periods is arbitrary, as a special case of the general MRP. Subsequently, a queueing model for a FIFO finite-buffer multiplexer with arbitrary on/off input sources is analyzed. We provide numerical results for testing the algorithms introduced in the paper. We also study the effect of some of the statistical properties of on/off input sources on the multiplexer's performance.