| In this dissertation, we study a class of exhaustive MX/C/1/infinity type queues with a single server performing secondary maintenance jobs during his vacationing periods. Unlike most of queues with vacations, during which server's duties are not specified, in our models the server performs physical jobs. In addition, we introduce a policy which non-rigidly restricts the server to stay no longer than some fixed time T. However, if the server is in a middle of a packet of jobs, he must finish them first before his return. The latter takes place at the first opportune time after T. In some models we study, the server stays in the system waiting if the number of customers accumulated in the system so far is less than some N. In some other models, the server was allowed to return to the maintenance facility and work on secondary jobs, packet by packet, until by the completion of one of them, the queue has raised N or above. The initial time constaint T was not utilized during such second phase of server's maintenance. Furthermore, the time T in some of our models could also be random. We considered a few models, in which it was Erlang (gamma) distributed.;In another setting, we introduce another threshold L which the working server was not supposed to exceed (unless he has been completing a packet) prior to his calling off. In the combination of the two thresholds, T and L we implement a policy under which the server returns to the system thereby completing phase I after his vacancy time expired or the number of jobs he served is at least L, whichever of the two events comes first. Upon his return, if there was at least one waiting customer, the server will resume the main service. Otherwise, he will stay and wait for any first batch of the customers to come, but not temporarily return to the maintenance as it was the case in the other models.;In all mentioned systems, we explore the queueing process, both upon departure epochs and at any time point. We use different techniques and methodologies to solve this class of problems randing from fluctuation analysis, stochastic games, semi-regenerative techniques, and time sensitive analysis. In all, we are able to arrive at explicit formulas for the queueing processes. We also obtain 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. iv... |
