A performance analysis of discrete-time tandem queues with Markovian sources

We present an exact performance analysis of tandem networks with an arbitrary number of multiplexers. Each multiplexer is fed by the output of its upstream neighbor as well as the traffic generated by a number of independent binary Markovian sources. We model the tandem network as a discrete-time queueing system. After determining the unknown boundary functions, the probability generating function (PGF) of the joint distribution of queue length and number of O n sources for each multiplexer is derived as a function of the transform of the busy period of its upstream neighbor. From this PGF, we determine closed form expressions for the mean and variance of queue length, as well as the mean packet delay. The solution has also been extended to tandem networks in which each multiplexer is fed by multiple types of traffic. Then, numerical results are presented and it has been shown that the multiplexing smooths the traffic. The mean queue lengths are very easy to calculate and the computation complexity does not increase with the number of sources in the network.