The influence of burstiness and correlation of traffic on an ATM multiplexer

This paper presents a traffic model for an ATM multiplexer providing video, voice, image, and data services. The traffic model classifies the input traffic into two types: real-time and non-real-time. The input process for real-time traffic is a Markov modulated Bernoulli process (MMBP), while that for non-real-time traffic is a Bernoulli process with batches. The z-transform of the cell interarrival time A_MMBP(z) is obtained. The average traffic load ρ_MMBP and the squared coefficient of variation of the time between success cell C²_MMBP are then obtained from the respective derivatives of A_MMBP(z). The autocorrelation coefficient of the cell interarrival time with lag 1 ψ, can be also obtained. This paper presents an iterative algorithm that can be used to calculate the MMBP probability distribution of the cell interarrival time. So far few results about discrete-time finite buffer queues with correlated inputs are known. This paper analyzes the performance of an ATM multiplexer considering the correlation and burst in cell arrivals. For the MMBP-stream, the waiting time distribution and the cell loss probability for MMBP+M^[X]/D/1/K finite buffer system are all exactly calculated with the use of a recursive algorithm. Calculations show the influence of burstiness and correlation on both the loss probability and waiting time. The accuracy of the analytical results has been largely validated by means of a simulation approach