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

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. CprE 458/558: Real-Time Systems (G. Manimaran)

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

CprE 458/558: Real-Time Systems (G. Manimaran) 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). CprE 458/558: Real-Time Systems (G. Manimaran)

Uniprocessor - some results One processor, Non-preemptive, Minimizing the Max. Lateness (Polynomial). One processor, Non-preemptive, release time constraint, Minimizing the Max. Lateness (NP-hard). One processor, Preemptive, release time constraint, Minimizing the Max. Lateness (Polynomial). CprE 458/558: Real-Time Systems (G. Manimaran)

Uniprocessor - more results Result: When there are mutual exclusion constraints, it is impossible to find a totally on-line 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 on-line scheduling algorithm with a competitive factor greater than 0.25. (this is for general case: arbitrary number of processors). CprE 458/558: Real-Time Systems (G. Manimaran)

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. CprE 458/558: Real-Time Systems (G. Manimaran)

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) CprE 458/558: Real-Time Systems (G. Manimaran)

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

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

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. CprE 458/558: Real-Time Systems (G. Manimaran)

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. CprE 458/558: Real-Time Systems (G. Manimaran)

CprE 458/558: Real-Time Systems (G. Manimaran) 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 non-preemptive 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. CprE 458/558: Real-Time Systems (G. Manimaran)

Run-time Anomaly – Example Example: Ti=(ai ,ci ,di ) T1=(0,20,22); T2=(0,12,25); T3=(10,8,26);T4=(8,10,30). T3 and T4 have resource conflicts; Actual computation time of T1 is 10. CprE 458/558: Real-Time Systems (G. Manimaran)