Closed-form solutions for key performance measures of packet multiplexers with finite capacity queue

We revisit the packet multiplexer with a discrete-time single server queue of limited capacity, and we derive a set of exact closed-form solutions for the major performance measures, such as the distributions of queue length, waiting time and number of lost packets per arriving batch. Assuming equally utilised inputs, the results refer to batch arrivals of binomial and Poisson distributed size, whereas they generally hold for systems with two inputs. The analysis is based on both the commonly used Early Arrival and Late Arrival queueing models, and we show that these models are equivalent at any capacity in terms of both waiting time and loss probability if the Late Arrival queue can hold one additional packet compared to its Early Arrival counterpart.