The E-T-C Scheduling Model - A new framework for the specification of Real-Time Scheduling Problems

Scheduling in Real-time systems differs from scheduling in conventional models in two principal ways: (a) Parameter variability, (b) Existence of complex constraints between jobs. Our focus has been on variable execution times. Whereas traditional models assume fixed values for job execution time, we model execution times of jobs through convex sets. The second feature unique to real-time systems,is the presence of temporal relationships that constrain job execution. Consider for instance the requirement that job 1 should conclude 10 units before job 2. This can be modeled through a simple, linear relationship, between the start and execution times of jobs 1 and 2. In real-time scheduling, it is important to guarantee a priori, the scheduling feasibility of the system. Depending upon the nature of the application involved, there are different schedulability specifications viz. Static, Co-Static and Parametric. Each specification comes with its own set of flexibility issues. In this paper, we present a framework that enables the specification of real-time scheduling problems and discuss the relationship between flexibility and complexity in the proposed model. In this paper, we describe the features of our real-time scheduling framework called the E-T-C ( Execution-Time-Constraints ) Real-Time Scheduling model. The Scheduling model is composed of sub-models, viz. the Job model, the Constraint model and the Query model. The Job model describes the type of jobs that we are interested in scheduling. The Constraint model is concerned with the nature of relationships constraining the execution of the jobs. The query model specifies what it means for a set of jobs to be schedulable, subject to constraints imposed as per the Constraint model. An instance of a problem in the E-T-C model is specified by instantiating the variables in the sub-models. We focus on the following issues: (a) Designing a framework that enables specification of real-time scheduling problems, and (b) Studying instantiations of interest in this framework. The rest of this paper is organized as follows: Section 1 describes the Job model within the E-T-C scheduling framework. The Constraint model is discussed in the succeeding section viz. Section 2. Section 3 details the Query model and presents the types of queries that we consider in this thesis. A classification scheme for Scheduling problems in the E-T-C model is introduced in 4. Section 6 provides a complexity picture of various instantiations in the E-T-C model. We conclude in Section 7 by summarizing the discussion in this paper. 1 Job Model in E-T-C Assume an infinitely extending time axis, starting at time . This axis is divided into intervals of length ; these intervals are ordered and each interval is called a scheduling window e.g. represents the first scheduling window, represents the second scheduling window and in general, ! represents the #" $ scheduling window. scheduling window. We are given a set of ordered, non-preemptive, jobs