On truncation properties of finite-buffer queues and queueing networks (Q2711559)

The authors consider censoring of a discrete-time stochastic process with respect to some region \(R\), defined by cutting off from the trajectories all parts not lying in \(R\). If the process is ergodic, then the censored process has as stationary distribution the truncated version of the original one. This idea is developed further for Markov chains with discrete time and, under a certain balance condition, also with continuous time. The results are then applied to \(\text{M}^k/\text{G}^Y/1/k\) queues and queueing networks with finite buffers and jump-over blocking, for which the truncation property of the stationary distribution can be proved.