This paper analyzes the performance of an ATM switching node considering cell arrival correlation. An ATM switching node is modeled as a discrete-time finite-buffer queue. Cell arrivals are assumed to follow a semi-Markovian process, where the number of cell arrivals in a lot depends on the states of the underlying (M-state) Markov chain in the current and previous slots. This paper presents analyses for various characteristics of the cell loss, as well as the distribution function of the cell output process from an ATM switching node. Obtained results include the cell loss probability, the consecutive loss probability, the distribution of loss period lengths, the joint distribution of successive cell interdeparture times, and the distribution of busy and idle periods. Through the numerical results, it is shown that both the correlation and the variation of cell arrivals significantly affect the cell loss and the output process characteristics.

This paper analyzes throughput and delay performance of two kinds of free access tree algorithms with mini-slots, and the other is that ternary feedback information is available. In these algorithms Q number of mini-slots are provided within a slot to offer feedback information on the state of the channel. The maximum throughputs of binary and ternary feedback algorithms are analytically obtained. It is also shown that the highest maximum throughput of 0.56714 is achieved when Q approaches infinity and mini-slot overhead goes to zero. The lower bound of the average transmission delays in these algorithms is analytically derived. The obtained lower bound is also a lower bound of the average delay of the whole class of free access algorithms.