Formal method for scheduling, routing and communication protocol

The PRAM model has been shown to be an optimal design for emulating both loose and tightly coupled multiprocessors for unit time operations. When virtual processors are required, multiplexing work to available processors is employed. This introduces a form of latency incurred by operating system overhead. Further complications arise when bandwidth creates bottlenecking of work units. G.E. Blelloch (1989) showed how to add parallel prefix operations (scans) to an extended PRAM model which uses unit step, not time operations. This paper shows how the Psi(ψ) calculus can be used to group work units, i.e. pipelining the work units, so that multiplexing is not required. The authors instead pipeline work units to processors and show how the number of processors need not be equivalent to the number of data components. Partitioning array data structures and pipelining groups of partitions to processors can minimize latency and bottlenecking on distributed message passing multiprocessing architectures