Workload Models for System-Level Timing Analysis: Expressiveness vs. Analysis Efficiency

Transcription

1 Workload Models for System-Level Timing Analysis: Expressiveness vs. Analysis Efficiency Nan Guan, Martin Stigge and Wang Yi Uppsala University, Sweden Uppsala University, China

2 Complex Real-Time Systems Input Stream I/O DSP I/O BUS Input Stream ECU FPGA I/O 2

3 Complex Real-Time Systems Input Stream I/O DSP I/O Output Stream BUS Input Stream ECU FPGA I/O Output Stream 3

4 Timing Analysis What s the maximal delay at each component? What s the maximal end-to-end delay? Input Stream I/O DSP BUS I/O Output Stream Input Stream ECU FPGA I/O Output Stream 4

5 Timing Analysis Input Stream I/O DSP I/O Output Stream BUS Input Stream ECU FPGA I/O Output Stream Task-Level Timing Analysis Find out the resource requirement for each task WCET estimation 5 System-Level Timing Analysis According to the WCET, budgeting the CPU resource for each task Schedulability Analysis (Response Time Analysis)

6 Workload models Operational Models: release patterns/executions Periodic/sporadic models [Liu & Layland, 1973] Tree/Graph-based models [Baruah, Stigge et al RTSS 2013] Timed automata [Alur, 1990 Fersman et al 2002, UPPAAL & TIMES] x = 5 x:=0 p q x:= 0 x= 13 (p,0) (q,5) (p,18) (p,23) Denotational Models: resource requirement over time Demand (Request) Bound Functions (DBF) [Baruah et al, 1990s] Real-Time Calculus (with origin from Network calculus) [Thiele/Samarjit 2000 Guan et al RTSS 2013] # jobs Input Stream I/O DSP BUS I/O Output Stream time ECU FPGA I/O Input Stream Output Stream 6

7 Expressiveness vs. Analysis Efficiency Task automata

8 Abstraction Expressiveness vs. Analysis Efficiency vs. Analysis Precision Task automata Exact Approximate

9 OUTLINE An Overview on RT workload models from the simplest to the most complex from Liu & Layland classic periodic model to timed automata Recent Results the graph-based model [RTAS 2011, RTSS 2013, Stigge & Yi] Combinatorial Abstraction for Schedulability Analysis

10 Modeling a system for analysis System = a set of Tasks Task 1 Task 2 Task n Tasks releasing jobs, J = (e, d) -- basic unit of workload Release time r Worst-case execution time e Deadline d Job release patterns: periodicity, branching structures, loop Feasibility/Schedulability: Can we check s.t. all jobs meet their deadlines?

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12 1973

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14 Task automata

15 (upto RTSS 2011)

16 [Baruah et al 2003, RTSS 2010]

17 Restrictions of DAG/RRT model

18 Restrictions of DAG/RRT model

19 Restrictions of DAG/RRT model

20 [Stigge et al RTAS 2011]

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25 How to check the feasibility?

26 [Baruah et al]

27 Example: L&L tasks (ei, pi) ei pi t t

28 Example: Sporadic tasks: (ei, di, pi) ei pi di

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30 There exists a Bound for systems where the Worst-case utilization c (long-term rate) is less than 1

31 dbf(t) is bounded by Cmax + t*c Cmax= sum of WCETs for all jobs c = the worst-case utilization (note: C<1)

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33 Calculating demand pairs for graph models

34 [Stigge et al, RTAS 2011]

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41 [Stigge et al, RTAS 2011]

42 How about synchronization among tasks? How about general constraints on job releases?

43 Task Automata [Fersman/Yi et al, TACAS 2002/TIMES tool] a b

44 States/Configurations of automata A state is a triple: (m, u, q) Location (node) clock assignment (valuation) job queue Feasibility/schedulability is a reachability problem for timed automata Code the problem and use UPPAAL 44

45 Timed automata

46 How about static priority scheduling?

47 Static-priority Schedulability [Stigge/Wang, ECRTS 2012] Task automata

48 Summary Models Feasibility -- EDF-schedulability Analysis Complexity Static-priority Schedulability Timed Automata Strongly NP-hard General graphs (Di-graph) Pseudo-P Strongly NP-hard Trees/DAGs (RRT) Pseudo-P Strongly NP-hard Cyclic graphs (GMF) Pseudo-P Strongly NP-hard Sporadic, D<T Pseudo-P Pseudo-P Sporadic, D=T (Layland & Liu) Linear Pseudo-P [Stigge/Wang, ECRTS 2012]

49 Static priority schedulability is Strongly NP-hard for all except L&L (and sporadic) model What to do?

50 OUTLINE An Overview on RT workload models from the simplest to the most complex from Liu & Layland classic periodic model to timed automata Recent Results the graph-based model [RTAS 2011, RTSS 2013, Stigge & Yi] Combinatorial Abstraction Refinement for Schedulability Analysis

51 Problem setting

52 Problem setting

53 Problem setting

54 Problem setting

55 Every Request Function corresponds to an execution path in the graph

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57 Every Request Function corresponds to an execution path in the graph

58 Every Request Function corresponds to an execution path in the graph

59 Overapproximation: mrf (maximum of rf s) mrf Every Request Function corresponds to an execution path in the graph

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66 Timed automata

67 Summary Models Feasibility -- EDF-schedulability Analysis Complexity Static-priority Schedulability Timed Automata Strongly NP-hard (or impossible) Original ETH Strongly NP-hard Strongly NP-hard General graphs (Di-graph) Pseudo-P Strongly NP-hard Trees/DAGs (RRT) Pseudo-P Strongly NP-hard Cyclic graphs (GMF) Pseudo-P Strongly NP-hard Finitary RTC Pseudo-P Pseudo-P Sporadic, D<T Pseudo-P Pseudo-P Sporadic, D=T (Layland & Liu) Linear Pseudo-P

68 Conclusion Analysis is often easier for models with no urgency/synchrony e.g. job releases with minimal separation distance, no upper bound no synchronization between tasks Analysis related static priority is more difficult than feasibility (EDFschedulability) It is strongly conp-hard for all models more expressive than GMF Efficient techniques exist: Combinatorial Abstraction [RTSS 2013, Stigge/Yi] Finitary RTC [RTSS 2013, Guan/Yi] Current/future work: making a tool integrating all these!