Cpr E 458558 RealTime Systems Some Scheduling Results

Cpr. E 458/558: Real-Time Systems Some Scheduling Results Cpr. E 458/558: Real-Time Systems (G. Manimaran) 1

Understanding Fundamentals • Understanding the boundary between polynomial and NP-complete problems can provide insights into developing useful heuristics. • Understanding the algorithms that achieve some of the polynomial results can again provide basis for developing heuristics. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 2

Understanding Fundamentals (cont. ) • Understanding the fundamental limitations of on-line algorithms will help designers avoid scheduling anomalies and misconceptions. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 3

Performance Metrics • Minimizing Schedule Length. • Minimizing Sum of Completion Times. • Maximizing Weighted Sum of Values (Useful in RT systems). • Minimizing the Maximum Lateness (useful in RT systems). Cpr. E 458/558: Real-Time Systems (G. Manimaran) 4

Uniprocessor - some results • One processor, Non-preemptive, Minimizing the Max. Lateness (Polynomial). • One processor, Non-preemptive, release time constraint, Minimizing the Max. Lateness (NPhard). • One processor, Preemptive, release time constraint, Minimizing the Max. Lateness (Polynomial). Cpr. E 458/558: Real-Time Systems (G. Manimaran) 5

Uniprocessor - more results • Result: When there are mutual exclusion constraints, it is impossible to find a totally online optimal scheduler. • Result: The problem of deciding whether it is possible to schedule a set of periodic tasks that use semaphores only to enforce mutual exclusion in NP-hard. • Overload Result: There does not exist an online scheduling algorithm with a competitive factor greater than 0. 25. (this is for general case: arbitrary number of processors). Cpr. E 458/558: Real-Time Systems (G. Manimaran) 6

Multiprocessor – Some Results • Result: The multiprocessor scheduling on P processors with task preemption allowed and with minimization of the number of late tasks is NP-hard. • Result: For two or more processors, no deadline scheduling algorithm can be optimal without complete a prior knowledge of deadlines, computation times, and task ready times. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 7

Multiprocessor – more results • EDF is not optimal in the multiprocessor case. • No on-line scheduling algorithm can guarantee a cumulative value greater than one half for the dual processor case. (A special case of overload result) Cpr. E 458/558: Real-Time Systems (G. Manimaran) 8

Multiprocessor; Single Deadline; Non-premptive NP-completeness is mainly due to non-uniform task execution time and resource constraints. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 9

Multiprocessor – Online scheduling model Cpr. E 458/558: Real-Time Systems (G. Manimaran) 10

Multiprocessing Anomalies • Assume that a set of tasks is optimally schedulable on a multiprocessor with some priority order, a fixed number of processors, fixed computation times, and precedence constraints. • Result: For the stated problem, changing the priority list, increasing the number of processors, reducing the computation times, or weakening the precedence constraints can increase the schedule length. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 11

Multiprocessing Anomalies (cont. ) • These anomalies may cause some of the already guaranteed tasks to miss their deadlines. • It can be shown that run-time anomalies cannot occur in a multiprocessor schedule when the tasks are independent. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 12

Run-time Anomaly Run-time anomaly may occur when the actual computation time of a task differs from its worst case computation time in a nonpreemptive multiprocessor schedule with resource constraints. A processor is said to be work conserving if it is never idle when there is a task to execute. Any work conserving scheme may lead to run-time anomaly. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 13

Run-time Anomaly – Example: Ti=(ai , ci , di ) T 1=(0, 22); T 2=(0, 12, 25); T 3=(10, 8, 26); T 4=(8, 10, 30). T 3 and T 4 have resource conflicts; Actual computation time of T 1 is 10. Cpr. E 458/558: Real-Time Systems (G. Manimaran) 14