On stochastic ordering and control charts for traﬃc intensity. Issue 4 (1st October 2016) - Morais, Manuel Cabral; Pacheco, António
ABSTRACT: Traﬃc intensity ( ρ ) is a crucial parameter of a queueing system because it is a measure of the average occupancy of a server. Expectedly, an increase in ρ must be detected quickly so that appropriate corrective actions are taken. In this article, we briefly review existing procedures used to monitor the traﬃc intensity of GI ∕ M ∕1, M ∕ G ∕1, and a few other queues. We focus on control charts to detect increases in ρ whose control statistics are integer-valued and/or can be (approximately) modeled by discrete time Markov chains. Finally, we investigate the stochastic monotonicity properties of the associated probability transition matrices and explore the implications of these properties to provide insights on the performance of such control charts.