Paper Presentation. Amo Guangmo Tong. University of Taxes at Dallas February 11, 2014

Transcription

1 Paper Presentation Amo Guangmo Tong University of Taxes at Dallas February 11, 2014 Amo Guangmo Tong (UTD) February 11, / 26

2 Overview 1 Techniques for Multiprocessor Global Schedulability Analysis 2 New Response Time Bounds for Fixed Priority Multiprocessor Scheduling Amo Guangmo Tong (UTD) February 11, / 26

3 Techniques for Multiprocessor Global Schedulability Analysis Techniques for Multiprocessor Global Schedulability Analysis Sanjoy Baruah Amo Guangmo Tong (UTD) February 11, / 26

4 System Model Hard real-time system T n sporadic tasks T n = (e n, D n, p n ) m identical processors,m > 1 minimum inter-arrival time or period, p i > 0 execution time e i < p i relative deadline D i p i (constrained) utilization u i = e i /p i Amo Guangmo Tong (UTD) February 11, / 26

5 Schedule Algorithms Partitioned FJP(fixed job priority) algorithms Assign tasks to processors. Schedule tasks on each uniprocessor. Example: Global FJP algorithms In this schedule algorithm, tasks can execute and resume on any processors. Schedulable and Schedulability test Amo Guangmo Tong (UTD) February 11, / 26

6 Contributions Global FJP and partitioned FJP are incomparable. Provide a schedulability test for global EDF. Amo Guangmo Tong (UTD) February 11, / 26

7 Global and partitioned FJP scheduling are incomparable. Step 1 Sometimes global FJP scheduling is better than partitioned FJP scheduling. Example: τ 1 = (2, 3), τ 2 = (3, 4), τ 3 = (5, 12); u 1 = 2/3, u 2 = 3/4, u 3 = 5/12. Because u 1 + u 2 > 1,u 2 + u 3 > 1,u 1 + u 3 > 1, partitioned FJP dose not work. The following figure shows global FJP works Amo Guangmo Tong (UTD) February 11, / 26

8 Global and partitioned FJP scheduling are incomparable. Step 2 Sometimes partitioned FJP scheduling is better than global FJP scheduling. Example: τ 1 = (2, 3), τ 2 = (3, 4), τ 3 = (3, 12), τ 4 = (4, 12); u 1 = 2/3, u 2 = 3/4, u 3 = 3/12, u 4 = 4/12. Because u 1 + u 4 = 1,u 2 + u 3 = 1, partitioned FJP works. However no global FJP works. (If we assume τ 3,1 has higher priority than τ 4,1, then τ 4,1 misses its deadline.) Miss deadline Amo Guangmo Tong (UTD) February 11, / 26

9 A schedulability test for global EDF Let focus on τ i,j. r i,j = t a, d i,j = t d, D i = t d t a, t o is the latest time instant before t a at which at least one processor is idle. L: the union of intervals in [t a, t d ) during which all m processors are executing jobs other than τ i,j. Some proc. Is idle Amo Guangmo Tong (UTD) February 11, / 26

10 A schedulability test for global EDF If τ i,j misses its deadline, then L > D i e i. So there exists an L L where L = D i e i. And the total execution of all tasks done in [t o, t a ) L is m(a i + D i e i ). Some proc. Is idle Amo Guangmo Tong (UTD) February 11, / 26

11 A schedulability test for global EDF Let I (τ k, τ i, A i ) denote the upper bound of the workload of τ k that could be done in [t o, t a ) L where L is any subset of [t a, t d ) with length D i e i. I (τ k, τ i, A i ) = I (e k, D k, A i, e i, D i ) If, for any value of A i, n k=1 I (τ k, τ i, A i ) < m(a i + D i e i ), then any job τ i,j of τ i cannot miss its deadline. Some proc. Is idle Amo Guangmo Tong (UTD) February 11, / 26

12 Test If for any value A, n k=1 I (τ k, τ 1, A) < m(a + D 1 e 1 ), jobs in τ 1 will meet deadline. n k=1 I (τ k, τ 2, A) < m(a + D 2 e 2 ), jobs in τ 2 will meet deadline.... n k=1 I (τ k, τ n, A) < m(a + D n e n ), jobs in τ n will meet deadline. Thus, if for all i from 1 to n, and any value A i, n k=1 I (τ k, τ i, A i ) < m(a i + D i e i ), then no job in τ will miss deadline. Amo Guangmo Tong (UTD) February 11, / 26

13 I (τ k, τ i ) I (τ k, τ i, A i ) denote the upper bound of the workload of τ k that could be done in [t o, t a ) L where L is any subset of [t a, t d ) with length D i e i. I (τ k, τ i, A i ) = I (e k, D k, A i, e i, D i ) No carry in job Carry in job Some proc. Is idle Amo Guangmo Tong (UTD) February 11, / 26

14 Pseudo-polynomial Previous : O(P(n)) Now:O(P(m, e i, d i )) Other weakness of improvement. Amo Guangmo Tong (UTD) February 11, / 26

15 New Response Time Bounds for Fixed Priority Multiprocessor Scheduling New Response Time Bounds for Fixed Priority Multiprocessor Scheduling Nan Guan, Martin Stigge, Wang Yi and Ge Yu Amo Guangmo Tong (UTD) February 11, / 26

16 System Model sporadic real-time system T n sporadic tasks T n = (e n, d n, p n ) m identical processors,m > 1 minimum inter-arrival time or period, p i > 0 execution time e i < p i relative deadline D i D i p i (constrained-deadline) D i and P i have no relationship(arbitrary-deadline) utilization u i = e i /p i f i,j denotes the finish time of τ i,j, define response time of τ i,j as f i,j r i,j Amo Guangmo Tong (UTD) February 11, / 26

17 Content Response time bound for constrained-deadline system Response time bound for arbitrary-deadline system Amo Guangmo Tong (UTD) February 11, / 26

18 Constrained-deadline system To analyze deadline miss Some proc. Is idle To analyze response time bound Some proc. Is idle Amo Guangmo Tong (UTD) February 11, / 26

19 Constrained-deadline system When we analyze τ i,j : Let Ω i (x) be the maximum value of the sum of all higher-priority tasks interference among all possible cases. x Carry-in job Amo Guangmo Tong (UTD) February 11, / 26

20 Constrained-deadline system Then we solve the equation: x = Ω i(x) m x + e i Remember: Ω i (x) be the maximum value of the sum of all higher-priority tasks interference against τ i,j. Amo Guangmo Tong (UTD) February 11, / 26

21 Constrained-deadline system Then x is an upper bound of response time of τ i,j x Response time Amo Guangmo Tong (UTD) February 11, / 26

22 Arbitrary-deadline system For constrained-deadline system, we analyze : Some proc. Is idle For arbitrary-deadline system, we analyze : x Amo Guangmo Tong (UTD) February 11, / 26

23 Arbitrary-deadline system Similarly, we solve the equation: x = Ω i(x,h) m x + h e i Remember : Ω i (x, h) be the maximum value of the sum of all higher-priority tasks interference against τ i,j. Amo Guangmo Tong (UTD) February 11, / 26

24 Constrained-deadline system Then an upper bound of response time of τ i,j is x (h 1) p i x Response time of h jobs Amo Guangmo Tong (UTD) February 11, / 26

25 Weakness or improvement Amo Guangmo Tong (UTD) February 11, / 26

26 The End Amo Guangmo Tong (UTD) February 11, / 26