We consider a problem involving the design of a system for concurrent processing of application software using multiple processors on a local area network. The task control-flow graph which graphically describes the software logic is allowed to be an arbitrary directed multigraph. We establish equations of flow conservation which arise in the execution of modules on the set of interconnected processors. Incorporating these equations, we develop a mixed integer programming model to find an optimal allocation of program modules, with possible replications, to the set of capacitated processors. The objective is to minimize the total interprocessor communication cost and module execution cost subject to the capacity constraints of processors and the broadcast channel. The decisions involved are: how many copies of each module should be maintained; how to allocate module copies across processors; and how to distribute invocations of each module across its copies on different processors. We report numerical results from solving the model.
