Schedulability Analysis of Synchronous Digraph Real-Time Tasks - PowerPoint PPT Presentation

Schedulability Analysis of Synchronous Digraph Real-Time Tasks Morteza Mohaqeqi, Jakaria Abdullah, Nan Guan, Wang Yi Uppsala University ECRTS 2016

Introduction Real-Time Task Models: Digraph (DRT) recurring branching (RB) non-cyclic GMF generalized MF (GMF) multiframe (MF) sporadic Liu & Layland Synchronous Digraph Real-Time Tasks - 1/18 - Mohaqeqi, Abdullah, Guan and Yi

Introduction Real-Time Task Models: Proposed by M. Stigge et al. (2011) Real-time tasks with Digraph (DRT) different job types recurring branching (RB) 30 non-cyclic v 5 v 6 GMF generalized MF (GMF) 8 9 multiframe (MF) sporadic v 7 10 Liu & Layland Synchronous Digraph Real-Time Tasks - 1/18 - Mohaqeqi, Abdullah, Guan and Yi

The Digraph Real-Time (DRT) Task Model minimum � 1 , 10 � � WCET , deadline � inter-release v 2 15 Job Types 20 • WCET 40 • Relative deadline � 4 , 15 � v 1 v 4 � 1 , 20 � Conditional flow 10 25 (Branch) v 3 � 2 , 5 � Synchronous Digraph Real-Time Tasks - 2/18 - Mohaqeqi, Abdullah, Guan and Yi

The Digraph Real-Time (DRT) Task Model minimum � 1 , 10 � � WCET , deadline � inter-release v 2 15 Job Types 20 • WCET 40 • Relative deadline � 4 , 15 � v 1 v 4 � 1 , 20 � Conditional flow 10 25 (Branch) v 3 � 2 , 5 � v 1 v 2 v 4 v 3 t 0 5 10 15 20 25 30 35 40 45 50 55 60 Synchronous Digraph Real-Time Tasks - 2/18 - Mohaqeqi, Abdullah, Guan and Yi

The Digraph Real-Time (DRT) Task Model minimum � 1 , 10 � � WCET , deadline � inter-release v 2 15 Job Types 20 • WCET 40 • Relative deadline � 4 , 15 � v 1 v 4 � 1 , 20 � Conditional flow 10 25 (Branch) v 3 � 2 , 5 � v 1 v 2 v 4 v 3 t 0 5 10 15 20 25 30 35 40 45 50 55 60 v 1 v 2 v 1 t 0 5 10 15 20 25 30 35 40 45 50 55 60 Synchronous Digraph Real-Time Tasks - 2/18 - Mohaqeqi, Abdullah, Guan and Yi

Outline A Review on DRT 1 Synchronous DRT 2 Schedulability Analysis 3 Conclusion 4 Synchronous Digraph Real-Time Tasks - 3/18 - Mohaqeqi, Abdullah, Guan and Yi

Synchronous DRT Synchronized Release Synchronous Digraph Real-Time Tasks - 4/18 - Mohaqeqi, Abdullah, Guan and Yi

Semantics Task T 1 : Task T 2 : 1 20 v 2 v 5 v 6 2 1 15 s 1 25 s 1 40 8 9 v 1 v 3 4 1 v 7 10 10 25 1 v 4 2 Synchronous Digraph Real-Time Tasks - 5/18 - Mohaqeqi, Abdullah, Guan and Yi

Semantics Task T 1 : Task T 2 : 1 20 v 2 v 5 v 6 2 1 15 s 1 25 s 1 40 8 9 v 1 v 3 4 1 v 7 10 10 25 1 v 4 2 v 1 v 2 v 3 T 1 t 0 5 10 15 20 25 30 35 40 v 5 v 6 blocked T 2 t 0 5 10 15 20 25 30 35 40 Synchronous Digraph Real-Time Tasks - 5/18 - Mohaqeqi, Abdullah, Guan and Yi

Overview Assumptions Uniprocessor Preemptive scheduling Fixed priority Synchronous Digraph Real-Time Tasks - 6/18 - Mohaqeqi, Abdullah, Guan and Yi

Overview Assumptions Uniprocessor Preemptive scheduling Fixed priority Contributions � Schedulability analysis � Heuristics for better efficiency Synchronous Digraph Real-Time Tasks - 6/18 - Mohaqeqi, Abdullah, Guan and Yi

Outline A Review on DRT 1 Synchronous DRT 2 Schedulability Analysis 3 Conclusion 4 Synchronous Digraph Real-Time Tasks - 7/18 - Mohaqeqi, Abdullah, Guan and Yi

DRT Schedulability � 1 � � 2 � 15 v 1 v 2 8 9 v 3 10 � 1 � v 1 v 2 v 3 v 3 t 0 5 10 15 20 25 30 35

DRT Schedulability � 1 � � 2 � 15 rf ( t ) v 1 v 2 Request Function 8 9 v 3 10 � 1 � t v 1 v 2 v 3 v 3 t 0 5 10 15 20 25 30 35 Synchronous Digraph Real-Time Tasks - 8/18 - Mohaqeqi, Abdullah, Guan and Yi

DRT Schedulability Condition Notation: A set of tasks τ = { T 1 , T 2 , . . . , T n } π i : A path in T i ’s graph Synchronous Digraph Real-Time Tasks - 9/18 - Mohaqeqi, Abdullah, Guan and Yi

DRT Schedulability Condition Notation: A set of tasks τ = { T 1 , T 2 , . . . , T n } π i : A path in T i ’s graph Theorem (Stigge 2013) A job with WCET “ e ” and relative deadline “ d ” is schedulable under a set of higher priority tasks τ if and only if for all ( π 1 , . . . , π n ) ∈ Π( τ ) : � ∃ t ≤ d : e + rf π i ( t ) ≤ t (1) T i ∈ τ Synchronous Digraph Real-Time Tasks - 9/18 - Mohaqeqi, Abdullah, Guan and Yi

DRT Schedulability Condition Notation: A set of tasks τ = { T 1 , T 2 , . . . , T n } π i : A path in T i ’s graph Theorem (Stigge 2013) A job with WCET “ e ” and relative deadline “ d ” is schedulable under a set of higher priority tasks τ if and only if for all ( π 1 , . . . , π n ) ∈ Π( τ ) : � ∃ t ≤ d : e + rf π i ( t ) ≤ t (1) T i ∈ τ rf π i ( t ) could be derived independently. Synchronous Digraph Real-Time Tasks - 9/18 - Mohaqeqi, Abdullah, Guan and Yi

SDRT Schedulability � 1 � � 2 � 15 rf ( t ) v 1 v 2 s 1 8 9 s 1 v 3 10 � 1 � t v 1 v 2 v 3 v 3 t 0 5 10 15 20 25 30 35 Synchronous Digraph Real-Time Tasks - 10/18 - Mohaqeqi, Abdullah, Guan and Yi

Alignment Task T 1 : Task T 2 : 1 20 v 2 v 5 v 6 2 1 15 s 1 25 s 1 40 8 9 v 1 v 3 4 1 v 7 10 10 25 1 v 4 2 v 1 v 2 v 3 T 1 0 5 10 15 20 25 30 35 40 v 5 v 6 T 2 0 5 10 15 20 25 30 35 40

Alignment Unsynchronized rf 1 s 1 rf 2 s 1 v 1 v 2 v 3 0 5 10 15 20 25 30 35 40 v 5 v 6 0 5 10 15 20 25 30 35 40

Alignment Unsynchronized Synchronized (Aligned) rf 1 rf 1 s 1 s 1 rf 2 rf 2 s 1 s 1 v 1 v 2 v 3 v 1 v 2 v 3 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 v 5 v 6 v 5 v 6 blocked 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

SDRT Schedulability Condition τ = { T 1 , T 2 , . . . , T n } π i : A path in T i ’s graph Theorem A job with WCET “ e ” and relative deadline “ d ” is schedulable under a set of tasks τ if and only if for all π = ( π 1 , . . . , π n ) ∈ Π( τ ) , ∀ R ∈ RF π : � ∃ t ≤ d : e + rf i ( t ) ≤ t rf i ∈ Synch ( R ) T i ∈ τ hp Synchronous Digraph Real-Time Tasks - 13/18 - Mohaqeqi, Abdullah, Guan and Yi

SDRT Schedulability Condition τ = { T 1 , T 2 , . . . , T n } π i : A path in T i ’s graph Theorem A job with WCET “ e ” and relative deadline “ d ” is schedulable under a set of tasks τ if and only if for all π = ( π 1 , . . . , π n ) ∈ Π( τ ) , ∀ R ∈ RF π : � ∃ t ≤ d : e + rf i ( t ) ≤ t rf i ∈ Synch ( R ) T i ∈ τ hp Efficient Exploration � Removing dominated request function � Search using an “abstraction and refinement” approach Synchronous Digraph Real-Time Tasks - 13/18 - Mohaqeqi, Abdullah, Guan and Yi

Experiments: Analysis Efficiency 15 Run-Time (seconds) 10 5 0 0 10 20 30 40 Number of Total Actions (Utilization = 0.5)

Experiments: Analysis Efficiency 15 Run-Time (seconds) 10 5 0 0 10 20 30 40 Number of Total Actions (Utilization = 0.5) 15 Run-Time (seconds) 10 5 0 0 10 20 30 40 Number of Total Actions (Utilization = 0.7)

s 1 s 1 v 1 v 2 v 4 v 5 s 2 s 2 v 3 v 6 Step 1 v 1 v 2 v 4 v 5 Over-approx. v 3 v 6 Under-approx. v 1 v 2 v 4 v 5 v 3 v 6 Synchronous Digraph Real-Time Tasks - 15/18 - Mohaqeqi, Abdullah, Guan and Yi

over-approx. s 1 s 1 v 1 v 2 v 4 v 5 τ under-approx. s 2 s 2 v 3 v 6 refinement n 0 1 2 3 ... level Step 1 Step 2 s 1 s 1 v 1 v 2 v 4 v 5 v 1 v 2 v 4 v 5 Over-approx. v 3 v 6 v 3 v 6 s 1 s 1 Under-approx. v 1 v 2 v 4 v 5 v 1 v 2 v 4 v 5 v 3 v 6 v 3 v 6 Synchronous Digraph Real-Time Tasks - 15/18 - Mohaqeqi, Abdullah, Guan and Yi

Experiments 15 Without abstraction and refinement Run-Time (seconds) With abstraction and refinement 10 5 0 0 10 20 30 40 Number of Total Actions (Utilization = 0.5) 15 Without abstraction and refinement Run-Time (seconds) With abstraction and refinement 10 5 0 0 10 20 30 40 Number of Total Actions (Utilization = 0.7)

Outline A Review on DRT 1 Synchronous DRT 2 Schedulability Analysis 3 Conclusion 4 Synchronous Digraph Real-Time Tasks - 17/18 - Mohaqeqi, Abdullah, Guan and Yi

Conclusion and Future Work SDRT as an extension of DRT Expressiveness . . . perodic DRT SDRT Timed Automata sporadi Synchronous Digraph Real-Time Tasks - 18/18 - Mohaqeqi, Abdullah, Guan and Yi

Conclusion and Future Work SDRT as an extension of DRT Expressiveness . . . perodic DRT SDRT Timed Automata sporadi Multicore Scheduling • Task-level paritioning • Job-level paritioning Synchronous Digraph Real-Time Tasks - 18/18 - Mohaqeqi, Abdullah, Guan and Yi

Schedulability Analysis of Synchronous Digraph Real-Time Tasks Morteza Mohaqeqi, Jakaria Abdullah, Nan Guan, Wang Yi Uppsala University ECRTS 2016 Thanks!

Appendix Request Function Dominance Abstraction and Refinement Experiment Setting Experiments: Path Combinations (RF Dominance) Experiments: Acceptance Ratio Why Synchronized Release? Multirate Tasks Critical Instant SDRT vs. DAG

Experiment Settings Table: Task set parameters Task Type Small Medium Large [ 3 , 5 ] [ 5 , 9 ] [ 7 , 13 ] Vertices Branching degree [ 1 , 3 ] [ 1 , 4 ] [ 1 , 5 ] p [ 50 , 100 ] [ 100 , 200 ] [ 200 , 400 ] e [ 1 , 2 ] [ 1 , 4 ] [ 1 , 8 ] [ 25 , 100 ] [ 50 , 200 ] [ 100 , 400 ] d