Quantifying the Sub-optimality of Non-preemptive Real-time Scheduling Abhilash Thekkilakattil, Radu Dobrin and Sasikumar Punnekkat

Research Agenda Quantify the goodness of non-preemptive scheduling ●Preemption behavior vs. processor speed ●Derive processor speed-up bound to enable non-preemptive feasibility Minimize preemption overheads using processor speed-up ●Preemption analysis for limited preemption schedulers ●Derive minimum processor speed that minimizes scheduler specific overheads

Preemptive vs. Non-preemptive Scheduling Preemptive EDF is uniprocessor optimal Strict domination of preemptive scheduling paradigm Fairly well investigated No algorithm is uniprocessor optimal under non-idling paradigm No online non-preemptive scheduler with inserted idle times exists Less investigated compared to preemptive scheduling Feasibility: Does a schedule exists that guarantees no deadline misses for a given real-time task set? Preemptive SchedulingNon-preemptive Scheduling

Set of uniprocessor feasible task sets Set of non-idling non-preemptive feasible task sets Set of limited preemptive feasible task sets Non-preemptive EDF Preemptive EDF Limited preemptive EDF Question: How good is non-preemptive scheduling when compared to uniprocessor optimal (preemptive) scheduling algorithms? Preemptive vs. Non-preemptive Scheduling

State of the Art The efficiency of a scheduler is commonly measured by resource augmentation –how much extra resources (CPU) are required to reach optimality? Task modelPreemptive (EDF vs. FPS) Non-preemptive (EDF vs. FPS) Implicit deadline Constrained deadline Arbitrary deadline Davis et al EDF feasibilityFPS feasibility Preemptive EDF feasibility Non-preemptive EDF feasibility

System Model ● Constrained deadline sporadic task sets (deadline ≤ period) ● Worst Case Execution Time scales linearly with processor speed ● Limited-preemptive scheduler -Floating non-preemptive region (f-NPR) scheduler max. length of f-NPR = L i Task j (high priority) Task i (low priority)

Limited-Preemption Feasibility Analysis Task i Task j Task k LiLi Feasibility condition: DkDk DjDj S.Baruah, The limited-preemption uniprocessor scheduling of sporadic task systems, ECRTS’05 L i + DBF(D k ) ≤ D k DBF(D k ) L i + DBF(D j ) ≤ D j DBF(D j ) DiDi

Limited-Preemption Feasibility Analysis Task i Task j Task k LiLi Feasibility condition: DkDk DjDj S.Baruah, The limited-preemption uniprocessor scheduling of sporadic task systems, ECRTS’05 DBF(D j ) L i + DBF(D k ) ≤ D k DiDi

Task i Task j Task k LiLi Feasibility condition: DkDk DjDj DBF(D j ) speed-up DiDi Limited-Preemption Feasibility Analysis

Processor Speed-up Bound Proof in the paper ? Speed (S) The maximum S

1 4C max /D min 4L/D min Preemption Behavior vs. Processor Speed All feasible task sets are guaranteed a non-preemptive execution for L units All feasible task sets are guaranteed a fully non-preemptive schedule Slower Processor Speed Faster Set of uniprocessor feasible task sets Set of non-idling non- preemptive feasible task sets on a uniprocessor Set of limited-preemption feasible task sets Feasibility Bucket

Research Agenda Quantify the goodness of non-preemptive scheduling ●Preemption behavior vs. processor speed ●Derive processor speed-up bound to enable non-preemptive feasibility Minimize preemption overheads using processor speed-up ●Preemption analysis for limited preemption schedulers ●Derive minimum processor speed that minimizes scheduler specific overheads

Research Agenda Quantify the goodness of non-preemptive scheduling ●Preemption behavior vs. processor speed ●Derive processor speed-up bound to enable non-preemptive feasibility Minimize preemption overheads using processor speed-up ●Preemption analysis for limited preemption schedulers ●Derive minimum processor speed that minimizes scheduler specific overheads

Scheduler Specific Overheads Non-preemptive Scheduling Low runtime overhead: zero preemption costs Mutual exclusion by construction  Increased blocking: low utilization Preemptive Scheduling Zero blocking: high utilization  High runtime overhead: preemption costs  Need for costly synchronization protocols high priority low priority preemption cost high priority low priority blocking Limited-Preemption Scheduling Best of preemptive and non-preemptive: preempt only when necessary high priority low priority Bounded non-preemptive region preemption cost

Scheduler Specific Overheads high priority low priority Bounded max. length of f-NPR Limited-preemption scheduler Vary the bound on the max length of f-NPR  No control on the bound on number of preemptions Control the bound on the number of preemptions  Limited control on the preemption points Full control on the preemption points: possibility to minimize preemption overheads Bounded max. length of f-NPR high priority low priority Our method:

Minimizing Preemption Related Overheads Task attributes Largest non-preemptive regions Sensitivity analysis Minimum processor speed that guarantees feasibility Max. no. of preemptions Preferred preemption points Derivation of non- preemptive regions Step 1 Step 2

Step 1: Deriving f-NPRs Preferred preemption points ( ) Req. 1: Bound the number of preemptions Req. 2: Enable preemptions at optimal points Default max. length of f-NPR Max. length of the desirable f-NPR We use processor speed-up Task level requirements: Task i

Step 2: Sensitivity Analysis min = 1 optimal speed max = 1 4C max /D min 4L/D min Slower Processor Speed Faster Default max. length of f-NPR Max. length of the desirable f-NPR

Tightening the Augmentation Bound Speed (S) Less pessimistic unified result:

Conclusions ●Quantification of the sub-optimality of non-preemptive scheduling -Non-preemptive scheduling is not uniprocessor optimal under the work conserving paradigm -Optimal online non-preemptive scheduler with inserted idle times cannot exist -Our contribution allows to use processor speed-up to enable non-preemptive feasibility for arbitrary task sets ●Analysis of preemption behavior vs. processor speed: the feasibility bucket ●Method to minimize preemption overheads -Derivation of non-preemption requirements -Sensitivity analysis to calculate the optimal speed-up ●Future work: extension to multiprocessor scheduling

Thank you ! Questions ?