A Graph-Theoretic Model for the Scheduling Problem and its Application to simultaneous Resource Scheduling

ABSTRACT As computer and communications systems become more complex, system designers are broadening their concern from the scheduling of individual resources to scheduling tasks which require multiple resources simultaneously. However there are relatively few published results for simultaneous resource scheduling problems. Equally importantly, although there are algorithms for special instances of these problems in different application areas, there is no general model that provides a framework for applying results across application boundaries. In this paper we present a graph-theoretic model for formally specifying scheduling problems. We apply the model to several simultaneous resource scheduling problems, drawn from the increasingly important application area of scheduling input/ouput (I/O) tasks in a parallel computer system. The model is thus used to specify the I/O scheduling problem for parallel computers with tree architectures, parallel I/O in the presence of a class of mutual exclusion constraints, and scheduling parallel I/O for computers with multiple I/O bus architectures. We use the model for recognition of the similarity between scheduling problems, the transformation of one scheduling problem to a different scheduling problem, and the decomposition of a problem into subproblems. We thus obtain an optimal algorithm for parallel I/O in tree architectures, an optimal algorithm for scheduling parallel I/O in the presence of limited mutual exclusion constraints, and an improved heuristic for parallel I/O in multiple bus architectures.