The method of analysis employing decomposition of busy periods has, in various forms, been applied to the M/G/1 queueing system under a variety of scheduling rules This paper extends the technique of decomposition of busy periods in order to deal with the M/M/c queueing system. Particular attention is given to a special busy period referred to as a "delay cycle." The delay cycle commences with a delay period (of general distribution) in which jobs arrive but are not serviced, at the conclusion of the delay period, processing begins and continues until the system is empty. Closed form solutions are obtained for various entities such as distribution of busy period length and expected waiting time conditioned on the type of busy period in progress at the tmae of job arrival. These results are applied and extended to the analysis of six examples of multiprocessor systems.

A mult~resource queuemg system is a single congestion point associated with a number of resources which may be of different types Amwng jobs s~multaneously require some comblnaUon of these resources for the duration of the processing time of the jobs.The capacity bound for such a system, given the characteristics of the input stream, is defined as the smallest input rate which is guaranteed to saturate the system regardless of the scheduling rule which ~s employed.An algorithm for calculating this bound is presented.The algorithm also specifies the proportion of time that the system should spend m processing various lob combinations in order to achieve the capacity hound.The ~mphcat~ons of this result are discussed for a number of resource allocation problems arising m computer systems. KEY WORDS AND PHRASES: computer