On the Average Complexity of the Processor Demand Analysis for Earliest Deadline Scheduling

Schedulability analysis of a set of sporadic tasks scheduled by EDF on a single processor system is a well known and solved problem: the Processor Demand Analysis is a necessary and sufficient test for EDF with pseudo-polynomial complexity. Over the years, many researchers have tried to find efficient methods for reducing the average-case running time of this test. The problem becomes relevant when doing sensitivity analysis of the worst-case execution times of the tasks: the number of constraints to check is directly linked to the complexity of the analysis. In this paper we describe the problem and present some known facts, with the aim of summarising the state of the art and stimulate research in this direction.