Scheduling Algebra

The goal of this paper is to develop an algebraic theory of process scheduling. We specify a syntax for denoting processes composed of actions with given durations. Subsequently, we propose axioms for transforming any specification term of a scheduling problem into a term of all valid schedules. In particular, we axiomatize an operator that restricts attention to the efficient schedules. These schedules turn out to be representable as trees, because in an efficient schedule actions can only start at time zero or when a resource is released, i.e. upon termination of the action binding a required resource. All further delay would be useless. Nevertheless, we do not consider resource constraints explicitly at the time being. We show that a normal form exists for every closed term of the algebra and establish soundness of our axiom system with respect to a schedule semantics, as well as completeness for efficient processes.