aperiodic task scheduling
DESCRIPTION
APERIODIC TASK SCHEDULING. Notation:. Earliest Due Date (EDD) - Jackson’s Rule. Set of tasks:. Problem:. Algorithm:. Earliest Due Date (EDD) - Jackson’s Rule. Earliest Due Date (EDD) – Example 1. Earliest Due Date (EDD) – Example 2. Earliest Due Date (EDD) – Guaranteed Feasibility. - PowerPoint PPT PresentationTRANSCRIPT
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APERIODIC TASK SCHEDULING
Notation:
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Earliest Due Date (EDD) - Jackson’s Rule
Set of tasks:
Problem:
Algorithm:
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Earliest Due Date (EDD) - Jackson’s Rule
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Earliest Due Date (EDD) – Example 1
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Earliest Due Date (EDD) – Example 2
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Earliest Due Date (EDD) – Guaranteed Feasibility
Order tasks by increasing deadlines. Then:
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Earliest Deadline First (EDF) – Horn’s Algorithm
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Earliest Deadline First (EDF) – Horn’s Algorithm
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Earliest Deadline First (EDF) – Example
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Earliest Deadline First (EDF) – Guarantee of Schedualability
Dynamic Scheduling:
Assume Schedulable
Need to Guarantee that
Assuming all tasks are ordered by increasing deadlines:
Worst case finishing time:
For Guaranteed Schedulability:
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EDF - Non-Preemptive Scheduling
The problem is NP hard
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Non-Acyclic Search Tree Scheduling
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Bratley’s Algorithm
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Jack Stankovic’s Spring Algorithm
This does not yield an optimal schedule, but the general problem is NP hard. This does lend itself to artificial intelligence and learning.
The objective is to find a feasible schedule when tasks are have different types of constraints, such as
– precedence relations,
– resource constraints,
– arbitrary arrivals,
– non-preemptive properties, and
– importance levels.
A heuristic function H is used to drive the scheduling toward a plausible path.
At each level of the search, function H is applied to each of the remaining tasks. The task with the smallest value determined by the heuristic function H is selected to extend the current schedule. If a schedule is not looking strongly feasible, a minimal amount of backtracking is used.
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Jack Stankovic’s Spring Algorithm
Precedence constraints can be handled by adding a term E =1 if the task is eligible and E = infinity if it is not.
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Jack Stankovic’s Spring Algorithm
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Scheduling with Precedence Constraints
Latest Deadline First - Optimizes max Lateness
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Latest Deadline First
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EDF with Precedence Constraints
The problem of scheduling a set of n tasks with precedent constraints and dynamic activations can be solved if the tasks are preemptable.
The basic ideas is transform a set of dependent tasks into a set of independent tasks by adequate modification of timing parameters. Then, tasks are scheduled by the Earliest Deadline First (EDF) algorithm, iff is schedulable. Basically, all release times and deadlines are modified so that each task cannot start before its predecessors and cannot preempt their successors.
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EDF with Precedence Constraints
Modifying the release time:
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EDF with Precedence Constraints
Modifying the Deadlines:
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Summary
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