Theory of non-overlapping packet arrivals

The theory of nonoverlapping packet arrivals is developed for variable-length and fixed-length packets. Closed-form expressions for the mean and variance of the number of arrivals in a given time interval are obtained using the initial- and final-value theorems of the Laplace transform. The implications of nonoverlapping packets can be seen using the mean queue occupancy formula. It is found that a fixed-length-packet protocol gives a small finite queue occupancy at high utilization, in contrast to a variable-length-packet protocol where the queue occupancy rises to infinity as the utilization approaches 100%.<>