A discrete-time system of infinite-capacity buffers in tandem is studied. The input process to the first buffer consists of individual arrivals characterized by a geometric distribution of the time between arrivals; and the probability that the output channel of each buffer, except the last, is transmitting at any epoch depends only on the number of digits in the buffer at that epoch. The transmitting state of the last buffer may depend more generally on the history of that buffer. The analysis shows that in equilibrium, the input processes to the subsequent buffers in the system are geometric with the same parameter as the input process to the first buffer. Therefore, each buffer in the system can be analyzed separately. Furthermore, the equilibrium state probabilities for a given buffer at a given epoch are independent of those for any other buffer in the system at the same epoch.

A discrete buffered system with infinite buffer size, Poisson arrival process, and the output channel available only periodically according to a geometric density function is analyzed. Under the assumption that a stochastic equilibrium is reached, theZtransform of the density function of the buffer occupancy is obtained as the result of this study.

A mathematical model for a general buffered telecommunication system with the output channel available only periodically is constructed and analyzed in this paper. Under the assumptions that certain system parameters are continuous variables, it is shown that the probability density functions for the peaks and valleys of the buffer content are exactly the same as the density functions for the response time and the waiting time, respectively, for aGI/G/1queuing system, with the density functions for the arrival processGIand the service processGobtained from the statistical functions for the parameters of the original buffered system.