A Matrix Representation of CSMA/CD Networks

A continuous time Markov chain model of asynchronous, nonpersistent CSMA/CD networks is developed which allows their complete characterization by a matrix whose dimensions are independent of the number of users in the network. The model provides an efficient reeursive algorithm for computing the performance of finite population networks. It also allows many analytical results to be obtained when an infinite population and a constant load retransmission policy are considered. These analytic results include necessary and sufficient conditions for stability, the distribution of the number of busy users, an exact closed form expression for the expected delay, and the exact upper bound on the throughput-all obtained via the properties of the matrix mentioned above. The results on stability show that, for this CSMA/CD model, the definitions of stability in terms of expected drift, nonnull recurrence, and maximum possible throughput exceeding actual loading are all equivalent. The model can approximate as closely as desired any distribution for the packet length, transmission detection time, and collision truncation time. Taking advantage of this freedom, the performance of CSMA/CD networks is shown to be very sensitive to the distribution of the transmission detection time.