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| -rw-r--r-- | Documentation/scheduler/sched-deadline.txt | 45 |
1 files changed, 42 insertions, 3 deletions
diff --git a/Documentation/scheduler/sched-deadline.txt b/Documentation/scheduler/sched-deadline.txt index c794ebfc08a5..bd4123b761e5 100644 --- a/Documentation/scheduler/sched-deadline.txt +++ b/Documentation/scheduler/sched-deadline.txt @@ -137,6 +137,9 @@ CONTENTS A real-time task can be periodic with period P if r_{j+1} = r_j + P, or sporadic with minimum inter-arrival time P is r_{j+1} >= r_j + P. Finally, d_j = r_j + D, where D is the task's relative deadline. + Summing up, a real-time task can be described as + Task = (WCET, D, P) + The utilization of a real-time task is defined as the ratio between its WCET and its period (or minimum inter-arrival time), and represents the fraction of CPU time needed to execute the task. @@ -170,9 +173,35 @@ CONTENTS of the tasks running on such a CPU is smaller or equal than 1. If D_i != P_i for some task, then it is possible to define the density of a task as WCET_i/min{D_i,P_i}, and EDF is able to respect all the deadlines - of all the tasks running on a CPU if the sum sum(WCET_i/min{D_i,P_i}) of the - densities of the tasks running on such a CPU is smaller or equal than 1 - (notice that this condition is only sufficient, and not necessary). + of all the tasks running on a CPU if the sum of the densities of the tasks + running on such a CPU is smaller or equal than 1: + sum(WCET_i / min{D_i, P_i}) <= 1 + It is important to notice that this condition is only sufficient, and not + necessary: there are task sets that are schedulable, but do not respect the + condition. For example, consider the task set {Task_1,Task_2} composed by + Task_1=(50ms,50ms,100ms) and Task_2=(10ms,100ms,100ms). + EDF is clearly able to schedule the two tasks without missing any deadline + (Task_1 is scheduled as soon as it is released, and finishes just in time + to respect its deadline; Task_2 is scheduled immediately after Task_1, hence + its response time cannot be larger than 50ms + 10ms = 60ms) even if + 50 / min{50,100} + 10 / min{100, 100} = 50 / 50 + 10 / 100 = 1.1 + Of course it is possible to test the exact schedulability of tasks with + D_i != P_i (checking a condition that is both sufficient and necessary), + but this cannot be done by comparing the total utilization or density with + a constant. Instead, the so called "processor demand" approach can be used, + computing the total amount of CPU time h(t) needed by all the tasks to + respect all of their deadlines in a time interval of size t, and comparing + such a time with the interval size t. If h(t) is smaller than t (that is, + the amount of time needed by the tasks in a time interval of size t is + smaller than the size of the interval) for all the possible values of t, then + EDF is able to schedule the tasks respecting all of their deadlines. Since + performing this check for all possible values of t is impossible, it has been + proven[4,5,6] that it is sufficient to perform the test for values of t + between 0 and a maximum value L. The cited papers contain all of the + mathematical details and explain how to compute h(t) and L. + In any case, this kind of analysis is too complex as well as too + time-consuming to be performed on-line. Hence, as explained in Section + 4 Linux uses an admission test based on the tasks' utilizations. On multiprocessor systems with global EDF scheduling (non partitioned systems), a sufficient test for schedulability can not be based on the @@ -206,6 +235,16 @@ CONTENTS Symposium, 1998. http://retis.sssup.it/~giorgio/paps/1998/rtss98-cbs.pdf 3 - L. Abeni. Server Mechanisms for Multimedia Applications. ReTiS Lab Technical Report. http://disi.unitn.it/~abeni/tr-98-01.pdf + 4 - J. Y. Leung and M.L. Merril. A Note on Preemptive Scheduling of + Periodic, Real-Time Tasks. Information Processing Letters, vol. 11, + no. 3, pp. 115-118, 1980. + 5 - S. K. Baruah, A. K. Mok and L. E. Rosier. Preemptively Scheduling + Hard-Real-Time Sporadic Tasks on One Processor. Proceedings of the + 11th IEEE Real-time Systems Symposium, 1990. + 6 - S. K. Baruah, L. E. Rosier and R. R. Howell. Algorithms and Complexity + Concerning the Preemptive Scheduling of Periodic Real-Time tasks on + One Processor. Real-Time Systems Journal, vol. 4, no. 2, pp 301-324, + 1990. 4. Bandwidth management ======================= |