Time-shared Systems: a theoretical treatment

Time-shared computer (or processing) facilities are treated as stochastic queueing systems under priority service disciplines, and the performance measure of these systems is taken to be the average time spent in the system. Models are analyzed in which time-shared computer usage is obtained by giving each request a fixed quantum Q of time on the processor, after which the request is placed at the end of a queue of other requests; the queue of requests is constantly cycled, giving each user Q seconds on the machine per cycle. The case for which Q → 0 (a processor-shared model) is then analyzed using methods from queueing theory. A general time-shared facility is then considered in which priority groups are introduced. Specifically, the pth priority group is given g_pQ seconds in the processor each time around. Letting Q → 0 gives results for the priority processor-shared system. These disciplines are compared with the first-come-first-served disciplines. The systems considered provide the two basic features desired in any time-shared system, namely, rapid service for short jobs and the virtual appearance of a (fractional capacity) processor available on a full-time basis. No charge is made for swap time, thus providing results for “ideal” systems. The results hold only for Poisson arrivals and geometric (or exponential) service time distributions.