Queues served in cyclic order with an arbitrary start-up distribution

This article considers a system of queues served in cyclic order by a single server. Each time the system becomes empty, it is restarted with a random initial population. The motivation for considering this problem came from the performance analysis study of a microprocessor-based system charged with executing several different types of tasks. The processor executes these tasks in cyclic order, but when all such tasks are completed, the processor becomes unavailable for a period of time while it does lower-priority (background) work. Thus, when the server returns to work on the higher-priority tasks a random population of these tasks have accumulated.