Bounds on parallel‐processing of queues with multiple‐phase jobs

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Abstract
Currently, both the hardware and software designs of many large computing systems aim at improved system performance through exploitation of parallelism in multiprocessor systems. In studying these systems, mathematical modelling and analysis constitute an important step towards providing design tools that can be used in building such systems. With this view the present paper describes a queueing model of a multiprocessor system operating in a job‐shop environment in which arriving jobs consist of a random number of segments (sub‐jobs). Two service disciplines are considered: one assumes that the sub‐jobs of a given job are capable of parallel operation on different processors while the other assumes that the same sub‐jobs must be operated in a strictly serial sequ'snce. The results (in particular, the mean number in the system and waiting time in queue) obtained for these two disciplines are shown to be bounds for more general job structures.

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