Analysis and Applications of the Delay Cycle for the M/M/c Queueing System

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.