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Time Demand Analysis

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**Schedulability of Fixed-Priority Tasks**

We have identified several simple schedulability tests for fixed priority scheduling: A system of n independent preemptable periodic tasks with Di = pi can be feasibly scheduled on one processor using RM if and only if U ≤ n⋅(21/n – 1) A system of simply periodic independent preemptable tasks with Di ≥ pi is schedulable on one processor using the RM algorithm if and only if U ≤ 1 [similar results for DM] But: there are algorithms and regions of operation where we don’t have a schedulability test and must resort to exhaustive simulation Is there a more general schedulability test? Yes, but not as simple as those we’ve seen so far… Real Time System

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**Schedulability Test for Fixed-Priority Tasks**

Fixed priority algorithms are predictable and do not suffer from scheduling anomalies The worst case execution time of the system occurs with the worst case execution time of the jobs Unlike dynamic priority algorithms, which can exhibit anomalous behaviour Use this as the basis for a general schedulability test: Find the critical instant when the system is most loaded, and has its worst response time Use time demand analysis to determine if the system is schedulable at that instant Prove that, if a fixed-priority system is schedulable at the critical instant, it is always schedulable Real Time System

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**Finding the Critical Instant**

Real Time System

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**Finding the Critical Instant**

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**Using the Critical Instant**

Having determined the critical instants, show that for each job Ji,c released at a critical instant, that job and all higher priority tasks complete executing before their relative deadlines If so, the entire system be schedulable… That is: don’t simulate the entire system, simply show that it has correct characteristics following a critical instant This process is called time demand analysis Real Time System

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Time-Demand Analysis Real Time System

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Time Demand Analysis Real Time System

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Time Demand Analysis Real Time System

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**Time Demand Analysis…calculate**

Example: Test if is satisfied for Time-Demand Function Ok! Ok! Not satisfied! Real-Time Systems

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**Time Demand Analysis For each , determine the time-demand function**

according to 2. Check whether the inequality is satisfied for values of that are equal to The time complexity of the time-demand analysis for each task is Real-Time Systems

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Another example

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Another Example: Step 1 Real-Time Systems

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Example: Step 2 Real-Time Systems

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Example: Step 3 Real-Time Systems

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Example: Step 4 Real-Time Systems

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**Time demand Analysis: Summary**

Real Time System

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Courseware Scheduling of Distributed Real-Time Systems Jan Madsen Informatics and Mathematical Modelling Technical University of Denmark Richard Petersens.

Courseware Scheduling of Distributed Real-Time Systems Jan Madsen Informatics and Mathematical Modelling Technical University of Denmark Richard Petersens.

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