Worst Case Response Time Analysis of Sporadic Task Graphs with EDF Non-preemptive Scheduling on a Uniprocessor

Abstract

This paper considers the problem of non-preemptive hard realtime scheduling of sporadic task graphs on a uniprocessor with Earliest Deadline First (EDF) scheduling. A sporadic task graph associated to an application is characterized by a set of subtasks under precedence constraints with deadline constraints. We study feasibility conditions based on the computation of the worst case response times of any subtask of a task graph. We investigate the late deadline constraint.

Real-Time Scheduling of DAG Tasks in Self-Powered Sensors with Scavenged Energy

“…In 2005, Zhao et al [12] provided an approach to schedule a set of sporadic graph tasks with fixed priority, for different scheduling contexts. This research had been lately improved in [13] to assume Fixed Job Priority (FJP) scheduling of graph tasks under Earliest Deadline First (EDF) algorithm. By using priority-based resource scheduling and resource partitioning, Jayachandran and Abdelzaher [14] focused on uniprocessor scheduling in distributed systems where jobs are depicted by Directed Acyclic Graphs (DAGs) by employing a Delay Composition theorem.…”

A Uniprocessor Scheduling Policy for Non-Preemptive Task Sets with Precedence and Temporal Constraints

“…2 This work has been extended to systems with precedence, deadline, and latency constraints. [4][5][6][7]18 Nonetheless, non-preemptive EDF strategies under these conditions are known to be suboptimal. 12 We introduce a modified EDF policy called Column-Restricted EDF (CR-EDF) that, although also suboptimal, leverages the structure of the well-formed network to produce schedules that achieve execution times within a few percent of the best possible makespan.…”

“…Recall our assumption that d {(2,3),(2,4)} was nontrivial; for Equation 18 to hold, d {(2,3),(2,4)} would have to be a trivial deadline. In this situation, we could prune d {(2,2),(2,4)} from the set of deadline constraints, d {(2,2),(2,4)} would no longer be a complex deadline constraint, and there would not be any complex tasks in the network.…”

“…t max | t=sτ 2,3 = d {(2,3),(2,4)}(15) t min | t=sτ 2,3 = LB AP SP (τ 2,3 , τ 2,4 ) (16)t slack | t=sτ 2,3 = d {(2,3),(2,4)} − LB AP SP (τ 2,3 , τ 2,4 )(17)Recall that, For the Russian Dolls method to be valid, we must ensure that the slack associated with a task group does not decrease with time. If this is true, thent slack | t=sτ 2,2 ≤ t slack | t=sτ 2,3 d {(2,2),(2,4)} − LB AP SP (τ 2,2 , τ 2,4 ) ≤ d {(2,3),(2,4)} − LB AP SP (τ 2,3 , τ 2,4 ) d {(2,2),(2,4)} − d {(2,3),(2,4)} ≤ LB AP SP (τ 2,2 , τ 2,4 ) − LB AP SP (τ 2,3 , τ 2,4 ) d {(2,2),(2,4)} − d {(2,3),(2,4)} ≤ c 2,2 + θ 2,2 d {(2,2),(2,4)} ≤ c 2,2 + θ 2,2 + d {(2,3),(2,4)}(18)When Equation18 does not hold, then the Russian Dolls Test is invalid because we cannot ensure that nesting a candidate task within G(τ 2,2 ) will yield sufficient slack for the candidate's task group to finish executing within the specified deadlines. For example, consider the situation where an outer deadline, such as d {(2,2),(2,4)} constrains a task group with complex deadlines, yielding more slack than is allowed for the inner deadline, such as d {(2,3),(2,4)} .…”