lec09_fixpriority2

# lec09_fixpriority2 - Priority-Driven Scheduling of Periodic...

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1 Priority-Driven Scheduling of Periodic Tasks (2) - Chapter 6 - Schedulable utilization bound • Simpler method for the schedulabiity check

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2 Utilization A periodic task’s utilization U i of an active resource is the ratio between its execution time and period: U i = C i /p i Given a set of periodic tasks on an active resource, e.g. the CPU, the CPU’s utilization is equal to the sum of periodic tasks’ utilization: = i i i p C U • Can we find a bound called “schedulable utilization bound” under which a task set is guaranteed to be schedulable? e schedulabl is set task , if bound i i i U p C U = Processor utilization factor • For a given algorithm A, we are interested in finding its schedulability bound (e.g., the schedulability bound of EDF is 1)
3 Processor utilization factor Entire Set of (e 1 ,…e n , p 1 , … p n ) Entire set of (e 1 ,…e n ) with fixed (p 1 , … p n) Fully utilized Find the minimum utilization factor among all fully utilized dots (barelly schedulable task set) Which pattern of e and p values? Now, we can consider only (e and p) combinations that make the system barely schedulable. How to find a (e and p) combination that has the minimal utilization factor? Always start with examples ± intuition ± generic theorem 0 0 369 7 U = 2/3 + 2/7 0 0 7 U = (2- )/3 + (2+2 )/7  3 / 7 / ) 3 / 7 ( /7 7/3 : increase /3 : decrease = <

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4 Which pattern of p values? For e values: “No-overflow theorem” What about p values? 0 0 369 7 U = 1/3 + 4/7 0 0 7 U = 1/(3*2) + (4+1)/7 Decrease: 1/3 – 1/(2*3)=1/(2*3) Increase: 1/7 Since 7 > 2*3, U decreases Transform (Ratio 3) to 2 22 12 2 11 121 2 12 1 2 1 1 2 21 2 1 10 ;3 , . . 2 4 1 0 4 , 2 2421 0 2 * 4 24 2 42 () ( ) ( ) ( ) 0 1 0 2 * 4 1 0 0 , 2 2 pp ee p w h e r e e g eee pi f ee e ee p p if p p p Since p  += =  ++= = ++ +− + + > =− > > 2 1 3, 3 2. ,1.5 1 and 2 p wehave Thus p => >> > =  ; p 2 > 2p 1 p 1 is doubled, so we obtain ratio 2 among the periods 0 10 48
5 Transform (Ratio k > 2) to 2 2 1 2 1 1 1 2 1 2 1 1 2 2 1 1 2 1 2 1 1 2 1 1 2 2 2 1 1 2 1 2 1 2 1 2 1 2 ) 1 ( since , 0 ) 2 ( ) 1 ( ) 2 ( ) 2 ( ) 1 ( sform after tran ; ) 2 ( 2 ) 2 ( ) 1 ( original ; 2 ) 1 ( and 1 ) 1 ( 1 Thus, . 1 have we , p p k p e k p k e k p e k e p k e p e p e p e k e e

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lec09_fixpriority2 - Priority-Driven Scheduling of Periodic...

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