Abstract
We consider a CSMA/CD network with a gateway node. The asynchronous, nonpersistent CSMA/CD network is analyzed using a continuous-time Markov chain model. This model has a simple matrix-geometric solution for the limiting distribution of the number of busy users at the gateway. From this limiting distribution, we find closed-form expressions for the throughput, the distribution of the gateway queue length, the expected gateway delay, the expected gateway queue length, and the higher moments of the gateway queue length. The model also yields an upper bound on the throughput of the CSMA/CD network and an easily verified necessary and sufficient condition for network stability. The upper bound provides a measure of the amount of the channel capacity left after the gateway has taken its share. We also show how the model's flexibility can be used to analyze more complicated gateway arrival situations, such as group arrivals at the gateway.
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