Finding a Feasible Schedule on a Tree-Connected Processor System

A tree-connected processor system (TPS) is a system in which m processors are connected in the form of an in-tree or out-tree. Each job arriving at a TPS flows on a directed path, from a processor specified for the job to the root (or on a directed path from the root to a processor specified for the job), and is processed by processors lying on the directed path. This paper discusses the feasibility decision problem on a TPS. It is a problem to decide whether or not each job can be processed within its deadline from its arrival time, and to find a schedule if the processing is feasible which realizes the processing. As a result for general TPS's, it is shown that the problem can be solved in O(mn log n) time for jobs with unit processing times, where m is the number of processors and n is the number of jobs. Especially, an algorithm proposed for TPS with an in-tree structure is on-line and can be used even when the information concerning jobs is obtained only at their arrivals.