Rare-event analysis and simulation of queues with time-varying rates

Excerpt

In this study, we are interested in rare-event probabilities in Markovian queues with time-varying arrival rates (nonhomogeneous Poisson arrivals) and time-varying service rates. Time-varying queues, as they are called, act as important models for service systems such as call centers, for communication systems such as wireless networks, for road intersection control in traffic management, for hospital admissions in health care logistics [8]. All these systems should operate properly under many situations, meaning that unwanted events, such as breakdown, failure, congestion, or overflow, happen rarely. In order to quantify and analyse the occurrence of a disaster, we investigate here a simple, specific case. Namely we consider an \(M_t/M_t/1\) queue which is stable on average, but that reaches a high level in a short time interval, representing the unwanted event. …