Bounding Stationary Expectations for Queues and Storage Processes Fed by Stationary Input SequencesPeter W. Glynn and Zeyu Zheng Queueing Models and Service Management, Volume 5, Number 2 (2022). In many queueing applications, it is of interest to allow dependence within the input sequence to the model, thereby permitting auto-correlation within the service times or inter-arrival times. This leads naturally to models that are fed by stationary sequences of random variables. When the model has a stationary distribution, conditions guaranteeing finiteness of a given stationary expectation may be needed. It may also be of value to obtain computable bounds on such stationary expectations. This paper develops a Lyapunov-type condition that provides such a computable bound. An implication of the bound is a criterion that guarantees tightness of the associated queueing model. In addition, the paper studies such queueing systems via the perspective of iterated random functions, showing how one can establish existence of stationary distributions via monotonicity or contraction arguments. The results are illustrated via an application to the delay sequence of the single server queue. |