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

CEMAT - Center for Computational and Stochastic Mathematics