Performance Model Checking Scenario-Aware Dataflow Bart Theelen, Marc Geilen, Jeroen Voeten

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Transcript of Performance Model Checking Scenario-Aware Dataflow Bart Theelen, Marc Geilen, Jeroen Voeten

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Performance Model Checking Scenario-Aware Dataflow Bart Theelen, Marc Geilen, Jeroen Voeten Slide 2 2 Overview Dataflow Formalisms Timed Probabilistic Systems Performance Model Checking Experimental Results Conclusions & Outlook Slide 3 Dataflow Formalisms Example digital signal processing areas 3 Streaming Multi-MediaLoop-Control in Mechatronics Dataflow formalisms describe task graphs where potential parallelism is made explicit MP3 Decoder Slide 4 Dataflow Formalisms: Expressivity vs Analyzability 4 Stuijk, et al. Scenario-Aware Dataflow: Modeling, Analysis and Implementation of Dynamic Applications. SAMOS11 Synchronous Dataflow (Weighted Marked Graphs) Kahn Process Networks Scenario-Aware Dataflow Slide 5 Scenario-Aware Dataflow(SADF) Scenario = operation modes with similar resource usage Detectors control processes by sending scenario-valued tokens Detectors contain automata to capture scenario occurrences Real-life: data-dependent control behaviour (normal state machine) Modelling worst/best-case only: non-deterministic state machine Modelling worst/best-case & average-case: Markov chain 5 kernel data channel detector RateIP0P0 PxPx a001 b00x c991x d101 e 0x x = {30, 40, 50,60, 70, 80, 99} MPEG-4 Decoder control channel rate tokens Slide 6 Processes run in parallel according to extended actor semantics 1.Determine scenario depending on 1.Kernels & Detectors: scenario-valued control tokens 2.Detectors: next state of Markov chain 2.Wait until sufficient tokens available 3.Perform the actual task (sample from discrete time distribution) 4.Produce and consume tokens Scenario-Aware Dataflow(SADF) 6 RateIP0P0 PxPx a001 b00x c991x d101 e 0x x = {30, 40, 50,60, 70, 80, 99} MPEG-4 Decoder Slide 7 Timed Probabilistic Systems(TPS) Compositional semantic model with guarded (interactive) action transitions probabilistic transitions deterministic time transitions Alternates action/time transitions with probabilistic fan-out Pattern for generic discrete execution time distributions time advances exactly t i time units with probability p i for i=1,,n 7 a p t t1t1 p1p1 pnpn 1 1 tntn Slide 8 Illustrative Example 8 Rate11 22 a20 b10 ProcessScenario Execution Time Probability A11 198/11 511/11 572/11 B 11 55/19 1712/19 472/19 22 131/15 3113/15 631/15 D 11 34/14 131/14 299/14 22 73/4 191/4 TPS for Kernel ATPS for Detector D Slide 9 Semantic Properties Model checking based on (relevant) state-space Exploit semantic properties to limit state-space explosion SADF satisfies various semantic properties Time additivity, action persistency, action urgency, action determinacy Only non-determinism between actions as a result of concurrency Policy for resolving non-determinism does not effect net behaviour 9 policy for resolving non- determinism may however effect performance result Slide 10 Performance Model Checking Direct computation of quantitative results based on model checking techniques Broad variety of performance metrics Mostly complex reward-based properties Mostly time-related properties 10 MetricType Probabilities Relevant Scope Max Buffer OccupancyWorst CaseNoAll States Min/Max Response DelayBest/Worst CaseNoTransient Min/Max Inter-Firing DelayBest/Worst CaseNoAll States Response Deadline Miss ProbabilityProbabilistic ReachabilityYesTransient Expected Response DelayExpected ReachabilityYesTransient ThroughputEvent RateYesSteady State Periodic Deadline Miss Probability Sample Average / Expected Reachability YesSteady State Average Inter-Firing LatencySample AverageYesSteady State Variance in Inter-Firing LatencySample VarianceYesSteady State Average Buffer OccupancyTime-Weighted AverageYesSteady State Variance in Buffer OccupancyTime-Weighted VarianceYesSteady State Policy for resolving non- determinism only affects Max Buffer Occupancy Slide 11 Model Checking Strategy - Theory 11 TPS per SADF Process Discrete Markov Chain Move Transition Labels into States |S| Deterministic TPS of Complete SADF Model Resolve Non-Determinism | S | TPS of Complete SADF Model Parallel Composition |S||S| p2p2 S2S2 a p1p1 S1S1 S3S3 S 1, - S2, aS2, a S 3, a p1p1 p2p2 Information on occurrence of actions and time available through reward functions on states only | S | >| S | Reduced Discrete Markov Reward Model Remove Irrelevant States |S c |6h Slide 16 Statistical Model Checking as Alternative Statistical model checking supported by modelling SADF in POOSL POOSL is much more expressive than SADF but also has TPS semantics Compositional estimation of confidence intervals for long-run averages 16 Case StudyThroughputTime [s] MPEG-4 AVC131.027 0.001 Channel Equalizer0.16244310 -3 0.012 MPEG-4 SP (PD = 1) 0.74526810 -3 0.8 MPEG-4 SP (PD = 2) 1.0538810 -3 40.7 MPEG-4 SP (PD = 3) 1.0637810 -3 906.9 MP3 (PD = 1) 2.3344910 -7 26.8 MP3 (PD = 2) 2.6809610 -7 624.6 MP3 (PD = 3) 2.6809610 -7 20356 MP3 (PD = 9) > 6h 95% Confidence IntervalTime [s] [131.027, 131.027]0.14 [0.16244310 -3, 0. 16244310 -3 ]0.75 [0.74497610 -3, 0.74793110 -3 ]7.4 [1.0389910 -3, 1.0895310 -3 ]6.86 [1.0403510 -3, 1.0634410 -3 ]6.85 [2.3334010 -7, 2.3338310 -7 ]32.8 [2.6809610 -7, 2.6809610 -7 ]31.5 [2.6809610 -7, 2.6809610 -7 ]32.1 [2.6809610 -7, 2.6809610 -7 ]30.6 Slide 17 Conclusions & Outlook Performance model checking approach for SADF Compositional TPS semantics with discrete time distributions Exploit semantic properties Removal of metric-dependent irrelevant states On-the-fly construction of relevant state-space Broad variety of pre-defined performance metrics All expressible as temporal reward formula Statistical model-checking for long-run averages as alternative Increase flexibility to allow computing user-defined metrics Lift Markov chain reduction to bisimulation reduction on TPS Support temporal rewards as property specification language Could contemporary quantitative model checkers supporting Probabilistic Timed Automata be a suitable alternative? 17