In a Jackson-type queuing network with feedback, the equilibrium state distribution of each queue is that of anM/M/ssystem. In support of a previous conjecture that nevertheless the input processes in such a network are not Poisson, the marginal interarrival-time distribution for an equilibriumM/M/1queuing system with feedback, counting both fed-back and exogenous customers as arrivals, is calculated. Since this distribution is a mixture of two exponentials, the total input to such a system is not Poisson.

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.