The Multiprocessor Scheduling of Precedence-Constrained Task Systems in the Presence of Interprocessor Communication Delays

Abstract

The problem of scheduling precedence-constrained task systems characterized by interprocessor communication delays is addressed. It is assumed that task duplication is permitted. The target machine is a homogenous multiprocessor with an unbounded number of processors. The general problem is known to be NP-hard; however, when communication delays are small relative to task execution times, the C.P.M. based approach of Colin and Chrétienne (1991) yields an optimal schedule in polynomial time. Extensions to this method of Colin and Chrétienne are presented here, which allow for polynomial-time optimal schedule generation for certain categories of task systems with arbitrary precedence relations, processing times, and communication delays.

Normative design of organizations. I. Mission planning

“…If, in addition, the processing of a task can be separated in time among different platforms, our problem is related to the vehicle routing problem and its extensions (for a review, see [25] and [45], for the latest results, see [15] and [21]). In the case when travel times among task locations are much smaller than the task processing times (and therefore can be ignored), our problem reduces to a multiprocessor scheduling problem with precedence constraints (for a review, see [11] and [16]; for recent studies see [5], [10] and [63]). For a review of general scheduling problems, see [16] and [52].…”

“…The opposite of this situation is when the delay occurs only when tasks are processed on different platforms (communication delays) with no delay for processing by the same platform. This has relevance in multiprocessor scheduling with inter-processor communication delays [5]. Another variation is the existence of time windows for processing each task (that is, the earliest start times, called release times, and the latest end-times, called deadlines, define opportunity windows for tasks).…”