Model Checking Technology Scheduling Optim al & Real Tim e using CORA CORA CORA
April 2002 – June 2005 IST-2001-35304 Informationsteknologi � Academ ic partners: � I ndustrial Partners − Nijmegen − Axxom − Aalborg − Bosch − Dortmund − Cybernetix − Grenoble − Terma − Marseille − Twente − Weizmann UCb UC
SIDMAR Overview Crane A Machine 1 Machine 2 Machine 3 @10 @20 2 @10 2 2 Lane 1 Machine 4 Machine 5 15 @10 I NPUT OBJECTIVES sequence Lane 2 of steel loads 16 Informationsteknologi (“pigs”) Buffer Crane B � powerful, unifying GOAL: Maximize Storage Place GOAL: Maximize utilization OUTPUT utilization mathematical modelling @40 sequence of higher of plant Continuos of plant quality steel Casting Machine � efficient computerized problem-solving tools LTR Project VHS (Verification of Hybrid systems) SIDMAR Modelling � distributed real-time A Single Load systems Crane A � time-dependent behaviour Machine 2 Machine 3 Machine 1 and dynamic resource Lane 1 Machine 4 Machine 5 allocation Lane 2 Buffer Crane B Storage Place � TI MED AUTOMATA Continuos Casting Machine UPPAAL Model UCb UC
Mem ory Managem ent CPS: Informal description Smart Card Personalization Radar Video Processing Subsystem Cybenetix, France Frequency Diversity CPS obtains and makes Advanced Noise Advanced Noise Piles of blank cards Personalisation available for other Reduction Techniques Reduction Techniques 9.170 GHz systems information about 9.438 GHz environment of a car. This Costal Surveillance information may be used The CPS considered in for: this case study e 0,5 Case Studies e 1,5 e 0,4 Parking assistance e 1,4 One sensor group only e 0,3 e 2,5 echo e 1,3 Informationsteknologi e 2,4 Pre-crash detection e 0,2 Combiner e 1,2 e 2,3 (currently 2 sensors) (VP3) e 2,2 e 3,5 Blind spot supervision e 3,4 e 3,3 Only the front sensors e 3,2 Lane change assistance combiner and corresponding Airport Surveillance Test Sweep Integration � Cybernetix: Stop & go controllers and possibly reject Etc Application: pre-crash − Smart Card Maximize throughput detection, parking Maximize throughput Based on Short Range CLASSI C CLASSI C CLASSI C assistance, stop & go Personalization Radar (SRR) technology UC UC b � Terma: Ed Brinksma Car Periphery Supervision System: Case Study 3 2 Input A Input B Product flow of a Product − Memory Interface 8 (100MHz) 8 (100 MHz) Überschrift Buffer 1 Überschrift 256 (100 MHz) 1 Kbytes � Bosch: Buffer 2 256 (100 MHz) Dispersion 1 Kbytes Storage − Car Periphery Buffer 3 A' 8 (100MHz) 256 (100 MHz) 512 bytes Sensing Adder 1 Buffer 4 Dose Spinner S' 16 (100 MHz) 256 (100 MHz) S = A + S' - A' 2 Kbytes CORA CORA � AXXOM: CORA 128 (200 MHz) Buffer 5 16 (100 MHz) 8 (100MHz) 256 (100 MHz) SDRAM 512 bytes − Lacquer Production Buffer 6 B' 8 (100MHz) 256 (100 MHz) B 512 bytes Mixing Vessel Filling Stations Adder 2 Buffer 7 T' 256 (100 MHz) T = B + T' - B' 16 (100 MHz) 2 Kbytes � Benchmarks Buffer 8 T 256 (100 MHz) 16 (100 MHz) 2 Kbytes Laboratory Buffer 9 S 256 (100 MHz) 2 Kbytes UC UCb Output S Output T UC UC Arbiter b 05.06.2005 Axxom Software AG Seite: 3
UCb UC Informationsteknologi
Overview � Timed Automata & Scheduling Informationsteknologi � Priced Timed Automata and Optimal Scheduling . a t a m o t u A � Optimal Infinite Scheduling d e m i T d , e n c e i s r P s u g m n s i s U a R g . n w I i . e l J u i d v , n e e R h e c s n S r o a l L i a t a . m G u i l a � Optimal Controller Synthesis t . p K v O E , n e n c a n m a m r h r e o B f r e . G P S C I R T E M G I S M C A � Optimal Scheduling and Off-Line Test Generation UCb UC
OBJECTI VE: OBJECTI VE: Get your CAR out Get your CAR out Your CAR EXI T Rush Hour UCb UC Informationsteknologi
Rush Hour UCb UC Informationsteknologi
Rush Hour UCb UC Informationsteknologi
Real Tim e Scheduling UNSAFE • Only 1 “Pass” • Only 1 “Pass” Crossing • Cheat is possible Times • Cheat is possible Informationsteknologi (drive close to car with “Pass”) 5 (drive close to car with “Pass”) 10 Pass 20 25 SAFE CAN THEY MAKE I T TO SAFE The Car & Bridge Problem WI THI N 70 MI NUTES ??? UC UCb
Real Tim e Scheduling UNSAFE Solve Solve 5 Scheduling Problem Informationsteknologi Scheduling Problem using UPPAAL using UPPAAL 10 SAFE 20 25 UC UCb
Steel Production Plant Crane A � A. Fehnker, T. Hune, K. G. Machine 2 Machine 3 Machine 1 Larsen, P. Pettersson Informationsteknologi � Case study of Esprit-LTR Lane 1 project 26270 VHS Machine 4 Machine 5 � Physical plant of SIDMAR located in Gent, Belgium. Lane 2 � Part between blast furnace and hot rolling mill . Buffer Crane B Objective: m odel the plant, obtain Storage Place schedule and control program for plant. Continuos Casting Machine UC UCb
Steel Production Plant Crane A Input: sequence of steel Machine 2 Machine 3 Machine 1 @10 Informationsteknologi loads (“pigs”). @20 2 @10 2 2 Lane 1 Machine 4 Machine 5 15 @10 Lane 2 Load follows Recipe to 16 obtain certain quality, Buffer Crane B e.g: start; T1 @10; T2 @20; ∑ =127 Storage Place T3 @10; T2 @10; @40 end within 120. Continuos Output: sequence of Casting Machine higher quality steel. UC UCb
UPPAAL Crane B UPPAAL UPPAAL Crane B A single load A single load (part of) (part of) UCb UC Informationsteknologi
Controller Synthesis for LEGO Model crane a m1 m2 m3 � LEGO RCX Informationsteknologi Mindstorms. � Local m4 m5 controllers with control crane b programs. � IR protocol for buffer remote invocation of storage programs. central � Central controller casting controller. 1971 lines of RCX code (n=5), Synthesis 24860 - “ - (n=60). UC UCb
Tim ed Autom ata [ Alur & Dill’89] Resource Synchronization Informationsteknologi Guard Reset Sem antics: Invariant ( Idle , x= 0 ) � ( Idle , x= 2.5) d(2.5) � ( InUse , x= 0 ) use? � ( InUse , x= 5) d(5) � ( Idle , x= 5) done! � ( Idle , x= 8) d(3) � ( InUse , x= 0 ) use? UCb UC
Com position Task Resource Synchronization Informationsteknologi Shared variable Sem antics: ( Idle , Init , B= 0, x= 0) � ( Idle , Init , B= 0 , x= 3.1415 ) d(3) � ( InUse , Using , B= 6, x= 0 ) use � ( InUse , Using , B= 6, x= 6 ) d(6) � ( Idle , Done , B= 6 , x= 6 ) done UCb UC
Jobshop Scheduling R E S O U R C E S Informationsteknologi Sport Economy Local Comic Stip News Kim 2 . 5 min 4 . 1 min 3 . 3 min 1 . 10 min J O B s Maria 1. 10 min 2 . 20 min 3 . 1 min 4 . 1 min Nicola 4 . 1 min 1 . 13 min 3 . 11 min 2 . 11 min Problem: compute the minimal MAKESPAN UC UCb
Jobshop Scheduling in UPPAAL Informationsteknologi Sport Economy Local News Comic Stip Kim 2 . 5 min 4 . 1 min 3 . 3 min 1 . 10 min Maria 1. 10 min 2 . 20 min 3 . 1 min 4 . 1 min Nicola 4 . 1 min 1 . 13 min 3 . 11 min 2 . 11 min UCb UC
B-&-B algorithm running for 60 sec. [TACAS’2001] Lawrence Job Shop Problems Lawrence Job Shop Problems Experim ents UCb UC j= 10 j= 15 j= 20 j= 10 j= 15 Informationsteknologi m= 5 m= 10
Task Graph Scheduling Optim al Static Task Scheduling � Task P = { P 1 ,.., P m } � Machines M = { M 1 ,..,M n } P 2 P 1 Informationsteknologi � Duration Δ : ( P × M) → N ∞ 2 ,3 1 6 ,1 0 � < : p.o. on P (pred.) � A task can be executed 6 ,6 1 0 ,1 6 P 6 P 3 P 4 2 ,3 only if all predecessors have completed � Each machine can process at most one task at a time � Task cannot be preempted. P 7 P 5 2 ,2 8 ,2 M = { M 1 ,M 2 } UCb UC
Task Graph Scheduling Optim al Static Task Scheduling � Task P = { P 1 ,.., P m } � Machines M = { M 1 ,..,M n } P 2 P 1 Informationsteknologi � Duration Δ : ( P × M) → N ∞ 2 ,3 1 6 ,1 0 � < : p.o. on P (pred.) � A task can be executed 6 ,6 1 0 ,1 6 P 6 P 3 P 4 2 ,3 only if all predecessors have completed � Each machine can process at most one task at a time � Task cannot be preempted. P 7 P 5 2 ,2 8 ,2 M = { M 1 ,M 2 } UCb UC
Task Graph Scheduling Optim al Static Task Scheduling � Task P = { P 1 ,.., P m } � Machines M = { M 1 ,..,M n } P 2 P 1 Informationsteknologi � Duration Δ : ( P × M) → N ∞ 2 ,3 1 6 ,1 0 � < : p.o. on P (pred.) 6 ,6 1 0 ,1 6 P 6 P 3 P 4 2 ,3 P 7 P 5 2 ,2 8 ,2 M = { M 1 ,M 2 } UC UCb
Abdeddaïm, Kerbaa, Maler Experim ental Results UCb UC Informationsteknologi
Optim al Task Graph Scheduling Pow er-Optim ality � Energy-rates : P 2 P 1 Informationsteknologi C : M → N x N 2 ,3 1 6 ,1 0 cost’= = 1 6 ,6 1 0 ,1 6 P 6 P 3 P 4 2 ,3 cost’= = 4 P 7 P 5 2 ,2 8 ,2 1 W 2 W UC UCb 4 W 3 W
Optim al Scheduling Priced Tim ed Autom ata
Priced Tim ed Autom ata Behrmann, Fehnker, et all (HSCC’01) Timed Automata + COST variable Alur, Torre, Pappas (HSCC’01) l 2 l 1 l 3 x · 2 Informationsteknologi 3 · y 0 · y · 4 c’ = 4 c’ = 2 ☺ c + = 4 x: = 0 cost rate c + = 1 cost update y · 4 x: = 0 UC UCb
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