On the use of quasi-stationary distributions in monitoring a single server queue

In the operation of stochastic systems, and of queues in particular, it is important to recognize quickly the development in time of situations not compatible with their design criteria. Once such an anomalous condition is detected, it has to be decided, if the occurrence of that event can be attributed to chance or is due to a change in the parameters governing the system. This procedure of tracking the system is defined as monitoring. The design of a monitor and the selection of suitable threshold regions for monitoring a single server queue are the subjects of this thesis. The notion of profile curves, useful in formalizing monitoring schemes for queues, is also discussed. Finally, some numerical examples are presented to illustrate the performance of the monitor designed