Discrete time analysis of a slotted transmission system (Q1124225)

A synchronized (gated) queueing model is analyzed in order to predict performance of some slotted transmission systems. In the model N sources that alternate between active and passive periods are assumed. The time is slotted, and a packet (i.e., fixed length message) can start transmission only at the beginning of a frame. The number of packets generated in a frame forms a finite, irreducible and aperiodic Markov chain. Motivation and examples of such a chain are also presented in the paper. Finally, to finish the description, in every frame a maximum number of packets R can be transmitted. If a packet cannot be sent in a frame, then it is buffered. The main interest lies in the evaluation of the buffer size. This is done by a standard technique, namely, by establishing the probability generating function of the buffer size in a steady state condition. This generating function, due to the Markovian input, has a form of a matrix equation, which is solved numerically to produce some useful results. Finally, the theoretical results (obtained numerically) are verified by a simulation.