Generating bursty random variables using matrix exponential distributions

In this paper we present our analysis of a dataset containing packet inter-arrival times and packet sizes for an Ethernet network. Packet inter-arrival times for this dataset are very bursty and have been shown to be selfsimilar. We generate a matrix exponential distribution that matches a subset of the attributes of the observed distribution. We then use the matrix exponential distribution to generate random variables which we use to conduct a simulation study of network performance. We show how the matrix exponential distribution is created and then used to generate random variables. We finally present the results of preliminary simulation studies that indicate that the matrix exponential distribution can successfully capture the very bursty behavior of the observed Ethernet packet inter-arrival times.