Design of steady-state behavior of concurrent repetitive processes: an algebraic approach

This paper addresses the problem of designing the steady-state behavior of a set of repetitive processes competing for access to common resources. Its objective is to develop algebraic formulae that express system behavior as a function of the characteristics of the component processes and synchronization protocols involved. Based on a matrix representation proposed, conditions are developed that guarantee that the system will achieve a steady state. A composition operator-a tool for synthesizing a chain of repetitive processes-is defined, and its application to the design of repetitive systems with required parameters is considered. It is also shown that the composition operator supplemented with an appropriate synchronization protocol makes it possible to prevent starvation occurrence. Finally, extension of the results to other selected topologies is discussed.