Formulas on Queues in Burst Processes - II

Formulas on Queues in Burst Processes--II By M. M. SONDHI, B. GOPINATH, and DEBASIS MITRA* (Manuscript received July 26, 1973) Queues arising in buffers due to either random interruptions of the channel or variable source rates are analyzed in the framework of a single digital system. Two motivating applications are: (i) multiplexing of data with speech on telephone channels and (ii) buffering of data generated by the coding of moving images in Picturephone® service. In the model a source feeds data to a buffer at a uniform rate. The buffer's access to a channel with fixed maximum rate of transmission is controlled by a switch; only when the switch is closed ("on") is the buffer able to discharge. The on-off sequence of the switch is indicated by a burst process which is a key element in this paper. In such a process, long periods during which the switch stays closed alternate with periods, called bursts, during which the on-off sequence is a first-order Markov process. The length of a burst is randomly distributed. This is a generalization of the memoryless burst process considered in an earlier paper.1 In that paper we gave formulas for the efficient computation of various functionals of the queues arising in the system. Now we extend these formulas to hold for the generalized class of burst processes. I. INTRODUCTION In a recent paper1 we considered the problem of buffering the output of a uniform source whose access to a given transmission channel is controlled by a burst process.