Fluctuation analysis in a queue with (L,N)-policy and secondary maintenance

This dissertation generalizes numerous classes of queues with vacationing servers. In our model, a server not only leaves the system, but he services packets of jobs at a secondary facility (SF) up until the total number of single jobs exceeds a specific threshold L with no suspension of any packet that needs to be finished. Upon his return to the system, the server observes if the queue has accumulated to N (N-policy). If it is not the case, the server returns to the SF and processes just one packet of jobs, after which he is available to return to the system and so on. He continues with "single" trips until the threshold N in the system is crossed. We use various techniques (including fluctuation analysis) to deliver explicit formulas for the queueing process with discrete time parameters. We also utilize some game-theoretic principles to efficiently construct our model. We also use time sensitive analysis to investigate the queueing process at arbitrary epochs of time. The results are obtained in explicit forms for several related models. Computational examples illustrate their analytical tractability. We arrive at various performance measures and discuss optimization problems.