The traffic intensity is a crucial parameter of a queueing system since it is a measure of the average occupancy of a server. Expectedly, an increase in the traffic intensity must be detected quickly so that appropriate corrective actions are taken.

In this talk, we:

• briefly review existing procedures used to monitor the traffic intensity of M/G/1, GI/M/1 and a few other queues;
• focus on control charts to detect increases in traffic intensity whose control statistics are integer-valued and/or can be (approximately) modelled by discrete time Markov chains;
• investigate the stochastic monotonicity properties of the associated probability transition matrices;
• explore the implications of these properties to provide insights on the performance of such control charts.

(Joint work with António Pacheco)