![Schedulability Test
Lopez [3] proves that the worst-case achievable
utilization for EDF scheduling and FF allocation (EDF-FF)
takes the value
If all the tasks have an utilization factor C/T under a value
α, where m is the number of processors
where
1
( , )
1
EDF FF
wc
m
U m
1/
](https://image.slidesharecdn.com/multiprocessorreal-timescheduling-240223111953-e502a6d7/85/Multiprocessor-Real-Time-Scheduling-pptx-21-320.jpg)
Multiprocessor Real-Time Scheduling.pptx
- 1. Multiprocessor Real-Time Scheduling Supervised by Prof. Dr. Dhuha Basheer By Asmaa Mowafaq ALQassab & Nagham Salim ALLaila
- 2. Multiprocessor Models Identical (Homogeneous): All the processors have the same characteristics, i.e., the execution time of a job is independent on the processor it is executed. Uniform: Each processor has its own speed, i.e., the execution time of a job on a processor is proportional to the speed of the processor. A faster processor always executes a job faster than slow processors do. Unrelated (Heterogeneous): Each job has its own execution time on a specified processor A job might be executed faster on a processor, but other jobs might be slower on that processor.
- 3. Scheduling Models Global Scheduling: A job may execute on any processor. The system maintains a global ready queue. Execute the M highest-priority jobs in the ready queue, where M is the number of processors. It requires high on-line overhead. Partitioned Scheduling: Each task is assigned on a dedicated processor. Schedulability is done individually on each processor. It requires no additional on-line overhead. Semi-partitioned Scheduling: Adopt task partitioning first and reserve time slots (bandwidths) for tasks that allow migration. It requires some on-line overhead.
- 4. Scheduling Models 6 2 3 4 7 5 CPU 1 CPU 2 CPU 3 Waiting Queue CPU 1 CPU 2 CPU 3 1 4 9 8 6 2 3 5 7 Global Scheduling CPU 1 CPU 2 CPU 3 1 4 6 2 5 Partitioned Scheduling Semi-partitioned Scheduling 3 3 7 7
- 5. Global Scheduling All ready tasks are kept in a global queue A job can be migrated to any processor. Priority-based global scheduling: Among the jobs in the global queue, the M highest priority jobs are chosen to be executed on M processors. Task migration here is assumed with no overhead. Global-EDF: When a job finishes or arrives to the global queue, the M jobs in the queue with the shortest absolute deadlines are chosen to be executed on M processors. Global-RM: When a job finishes or arrives to the global queue, the M jobs in the queue with the highest priorities are chosen to be executed on M processors.
- 6. Global Scheduling Advantages: Effective utilization of processing resources (if it works) Unused processor time can easily be reclaimed at run- time (mixture of hard and soft RT tasks to optimize resource utilization) Disadvantages: Adding processors and reducing computation times and other parameters can actually decrease optimal performance in some scenarios! Poor resource utilization for hard timing constraints Few results from single-processor scheduling can be used
- 7. Schedule Anomaly Anomaly 1 A decrease in processor demand from higher-priority tasks can increase the interference on a lower-priority task because of the change in the time when the tasks execute Anomaly 2 A decrease in processor demand of a task negatively affects the task itself because the change in the task arrival times make it suffer more interference
- 8. Anomaly 1
- 9. Anomaly 2
- 10. Dhall effect Dhall effect : For Global-EDF or Global-RM, the least upper bound for schedulability analysis is at most 1. On 2 processors: T3 is not schedulable Task T D C U T1 10 10 5 0.5 T2 10 10 5 0.5 T3 12 12 8 0.67
- 11. Schedulability Test A set of periodic tasks t1, t2, . . . , tN with implicit deadlines is schedulable on M processors by using preemptive Global EDF scheduling if where tk is the task with the largest utilization Ck/Tk
- 12. Weakness of Global Scheduling Migration overhead Schedule Anomaly
- 13. Partitioned Scheduling Two steps: Determine a mapping of tasks to processors Perform run-time single-processor scheduling •Partitioned with EDF Assign tasks to the processors such that no processor’s capacity is exceeded (utilization bounded by 1.0) Schedule each processor using EDF
- 14. Bin-packing Problem The problem is NP- complete !!
- 15. Bin-packing to Multiprocessor Scheduling The problem concerns packing objects of varying sizes in boxes (”bins”) with the objective of minimizing number of used boxes. Solutions (Heuristics): First Fit Application to multiprocessor systems: Bins are represented by processors and objects by tasks. The decision whether a processor is ”full” or not is derived from a utilization-based schedulability test.
- 16. Partitioned Scheduling Advantages: Most techniques for single-processor scheduling are also applicable here Partitioning of tasks can be automated Solving a bin-packing algorithm Disadvantages: Cannot exploit/share all unused processor time May have very low utilization, bounded by 50%
- 17. Partitioned Scheduling Problem Given a set of tasks with arbitrary deadlines, the objective is to decide a feasible task assignment onto M processors such that all the tasks meet their timing constraints, where Ci is the execution time of task ti on any processor m.
- 18. Partitioned Algorithm First-Fit: choose the one with the smallest index Best-Fit: choose the one with the maximal utilization Worst-Fit: choose the one with the minimal utilization
- 19. Partitioned Example 0.2 -> 0.6 -> 0.4 -> 0.7 -> 0.1 -> 0.3 0.2 0.4 0.6 0.1 0.3 0.7 0.2 0.4 0.6 0.1 0.3 0.7 0.2 0.7 0.1 0.3 0.4 First Fit Best Fit Worst Fit 0.6
- 20. EDF with First Fit
- 21. Schedulability Test Lopez [3] proves that the worst-case achievable utilization for EDF scheduling and FF allocation (EDF-FF) takes the value If all the tasks have an utilization factor C/T under a value α, where m is the number of processors where 1 ( , ) 1 EDF FF wc m U m 1/
- 22. Demand Bound Function Define demand bound function as We need approximation to enforce polynomial- time schedulability test
- 25. Weakness of Partitioned Scheduling Restricting a task on a processor reduces the schedulability Restricting a task on a processor makes the problem NP- hard Example: Suppose that there are M processors and M + 1 tasks with the same period T and the (worst-case) execution times of all these M + 1 tasks are T/2 + e with e > 0 With partitioned scheduling, it is not schedulable
- 26. Semi-partitioned Scheduling Tasks are first partitioned into processor. To reduce the utilization, we again pick the processor with the minimum task utilization If a task cannot fit into the picked processor, we will have to split it into multiple (two or even more) parts. If ti is split and assigned to a processor m and the utilization on processor m after assigning ti is at most U(scheduler,N), then ti is so far schedulable.
- 27. Semi-partitioned EDF Tmin is the minimum period among all the tasks. By a user-designed parameter k, we divide time into slots with length S = Tmin/k . We can use the first-fit approach by splitting a task into 2 subtasks, in which one is executed on processor m and the other is executed on processor m + 1. Execution of a split task is only possible in the reserved time window in the time slot. Applying first-fit algorithm, by taking SEP as the upper bound of utilization on a processor. If a task does not fit, split this task into two subtasks and allocate a new processor, one is assigned on the processor under consideration, and the other is assigned on the newly allocated processor.
- 29. Semi-partitioned EDF For each time slot, we will reserve two parts. If a task ti is split, the task can be served only within these two pre-defined time slots with length xi and yi . A processor can host two split tasks, ti and tj. ti is served at the beginning of the time slot, and tj is served at the end. The schedule is EDF, but if a split task instance is in the ready queue, it is executed in the reserved time region.
- 30. Semi-partitioned EDF We can assign all the tasks ti with Ui > SEP on a dedicated processor. So, we only consider tasks with Ui no larger SEP. When executing, the reservation to serve ti is to set xi to S X (f + lo_split(ti )) and yi to S X (f + high_split(ti )). SEP is set as a constant.
- 31. Two Split Tasks on a Processor For split tasks to be schedulable, the following sufficient conditions have to be satisfied lo_split(ti ) + f + high_split(ti ) + f <= 1 for any split task ti . lo_split(tj ) + f + high_split(ti ) + f <= 1 when ti and tj are assigned on the same processor. Therefore, the “magic value” SEP However, we still have to guarantee the schedulability of the non-split tasks. It can be shown that the sufficient condition is
- 33. Magic Values: f
- 35. Reference Multiprocessor Real-Time Scheduling Dr. Jian-Jia Chen: Multiprocessor Scheduling. Karlsruhe Institute of Technology (KIT): 2011-2012 Global Scheduling Sanjoy K. Baruah: Techniques for Multiprocessor Global Schedulability Analysis. RTSS 2007: 119-128 Partitioned Scheduling Sanjoy K. Baruah, Nathan Fisher: The Partitioned Multiprocessor Scheduling of Sporadic Task Systems. RTSS 2005: 321-329 Semi-partitioned Scheduling Björn Andersson, Konstantinos Bletsas: Sporadic Multiprocessor Scheduling with Few Preemptions. ECRTS 2008: 243-252
- 37. Critical Instants? The analysis for uniprocessor scheduling is based on the gold critical instant theorem. Synchronous release of events does not lead to the critical instant for global multiprocessor scheduling
Editor's Notes
- #7: Supported by most multiprocessor operating systems Windows NT, Solaris, Linux, ...
- #9: Task 3 misses its deadline when task 1 increases its period. This can happen for the following schedulable task set (with priorities assigned according to RM): (T1 = 3; C1 = 2); (T2 = 4; C2 = 2); (T3 =12; C3 = 8). When \tau_1 increases its period to 4, tau_3 becomes unschedulable. This is because tau_3 is saturated and its interference increases from 4 to 6.
- #10: Consider the following schedulable task set (with priorities assigned according to RM): (T1 = 4; C1 = 2); (T2 = 5; C2 = 3); (T3 = 10; C3 = 7). If we increase T3, the resulting task set becomes unschedulable. When T3 increases its period to 11, the second instance of T3 misses its deadline. This is because the interference increases from 3 to 5 and 3 is already saturated.
- #11: One heavy task tk : Dk = Tk = Ck M light tasks ti s: Ci = e and Di = Ti = Ck -e, in which e is a positive number, very close to 0.
- #23: DBF(\tau_i, t) <= DBF*(\tau_i,t) < 2* DBF(\tau_i,t)
- #30: X+y/S= C/T
- #31: X+y/S= C/T lo_split(ti )+high_split(ti )=C/T <SEP