A semi-Markovian model is developed for slotted p-persistent CSMA/CD with a finite population of buffered users. A subsequence of the queuing process at embedded Markov epochs is characterized as a multidimensional, nonnegative random walk which is spatially homogeneous and uniformly downward bounded. Sufficient conditions for ergodicity, recurrence and transience of the queuing process are obtained using multidimensional Lyapunov functions, and also by a supermartingale method of independent interest. For the CSMA/CD system with symmetric users, the stability conditions are evaluated in parameters based on an exact joint probability generating function of the random drift. Important properties of the queuing behavior and stability conditions are uncovered through a numerical analysis. In passing, we remark on queuing properties and stability conditions of slotted ALOHA for comparison with the CSMA/CD.
