Large Deviations and Importance Sampling for Queuing Systems with Discontinuous Service Policies Leder, Kevin Z. creator 2008 x, 135 p. born digital Thesis (Ph.D.) -- Brown University (2008) Wang, Hui director Dupuis, Paul reader Hult, Henrik reader Brown University. Applied Mathematics sponsor theses The first two thirds of this thesis are concerned with the properties of a single server using the weighted-serve-the-longest queue policy (WSLQ). It addresses three separate, but closely related, issues of the policy. The first issue addressed is the identification of the rate function for the large deviations principle of the queue length process of a server utilizing the WSLQ policy. Another issue addressed is the explicit identification of the exponential decay rate for the probability of a buffer overflow event. Lastly an importance sampling change of measure is developed to efficiently estimate the probability of buffer overflow. The last third of the thesis deals with two queues in tandem under the additional condition that the service rate of the first server will slow down when the size of the second queue reaches a predetermined threshold. The large deviations properties and design of importance sampling changes of measure are discussed for the event of overflow in the second queue. Importance Sampling Sample Path Large Deviations Queueing Theory Queuing theory RPB 20091218 engEnglish10.7301/Z0W66J20In CopyrightCollection is open for research.dissertations