Feedback Queueing Models for Time-Shared Systems

Time-shared processing systems (e.g. communication or computer systems) are studied by considering priority disciplines operating in a stochastic queueing environment. Results are obtained for the average time spent in the system, conditioned on the length of required service (e.g. message lenght or number of computations). No chage is made for swap time, and the results hold only for Markov assumptions for the arrival and service processes.

Two distinct feedback models with a single quantum-controlled service are considered. The first is a round-robin (RR) system in which the service facility processes each customer for a maximum of q sec. If the customer's service is completed during this quantum, he leaves the system; otherwise he returns to the end of the queue to await another quantum of service. The second is a feedback (FB_N) system with N queues in which a new arrival joins the tail of the first queue. The server gives service to a customer from the nth queue only if all lower numbered queues are empty. When taken from the nth queue, a customer is given q sec of service. If this completes his processing requirement he leaves the system; otherwise he joins the tail of the (n + 1)-st queue (n = 1, 2, · · ·, N - 1). The limiting case of N → ∞ is also treated. Both models are therefore quantum-controlled, and involve feedback to the tail of some queue, thus providing rapid service for customers with short service-time requirements. The interesting limiting case in which q → 0 (a “processor-shared” model) is also examined. Comparison is made with the first-come-first-served system and also the shortest-job-first discipline. Finally the FB_∞ system is generalized to include (priority) inputs at each of the queues in the system.