Multiphase fluctuation analysis in a queue with an enhanced maintenance.

摘要

In this dissertation, we study a class of exhaustive MX/G/1/infinity type queues with a single server performing secondary maintenance jobs during its vacationing period. During its vacation time, the server performs secondary jobs which are randomly generated in batches and counted. When the time of absence expires, the server is called off. However, it does not interrupt its service on any job and on any packet of jobs. Only when its work on the packet is finished and its maintenance time is longer than T (an arbitrary random time) does the server returns to the system and waits for customers if none is present.;Also in this dissertation we explore the queuing process, both upon departure epochs and at arbitrary times. We use fluctuation analysis to find the Laplace-Carson inverse, all leading to an explicit functional (a Kendall-like formula) for the queuing system with compound Poisson input and general service time. In all, we are able to arrive at analytically tranctable formulas for the queuing processes. We obtain the limiting probability distribution of the continuous time parameter queuing process and some important performance measures, such as the mean service cycle, mean number of jobs processed at the maintenance facility per unit time, the main number of switchovers, per unit time, and the mean buffer load, also per unit time.