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Tools and Application of Timed Automata UPPAAL & Optimal Scheduling. Kim G. Larsen kgl@cs.auc.dk. C UPPAAL Thomas Hune Jakob I Rasmussen Ansgar Fehnker Judi Romijn Frits Vaandrager Ed Brinksma Patricia Bouyer CASE STUDIES Thomas Hune Gerd Behrmann Arne Skou Anders Brødløs.

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tools and application of timed automata uppaal optimal scheduling

Tools and Application of Timed AutomataUPPAAL & Optimal Scheduling

Kim G. Larsen

kgl@cs.auc.dk

contributors
CUPPAAL

Thomas Hune

Jakob I Rasmussen

Ansgar Fehnker

Judi Romijn

Frits Vaandrager

Ed Brinksma

Patricia Bouyer

CASE STUDIES

Thomas Hune

Gerd Behrmann

Arne Skou

Anders Brødløs

Contributors

UPPAAL

Gerd Behrmann

Wang Yi

Paul Pettersson

Johan Bengtsson

Fredrik Larsson

Alexandre David

Leonid Mokrushin

Brian Nielsen

c uppaal kronos
CUPPAAL & KRONOS

www.uppaal.com

c uppaal
CUPPAAL

Priced

CUPPAAL

www.uppaal.com

scheduling problem
Scheduling Problem
  • Scheduling/Planning Domain =
    • A number of objects
      • instances of different object types
      • individual states  global state
    • A number of actions on objects
      • required precondition on objects (= state condition)
      • resulting effect (= state transformation)
      • duration / cost (= time / energy / money / ..)
    • Problem:
      • compute an (optimal) plan/schedule that “solves” the problem.
rush hour
RushHour

Your CAR

OBJECTIVE:

Get your

CAR out

EXIT

jobshop scheduling
Jobshop Scheduling

[TACAS’2001]

  • NP-hard
    • Simulated annealing
    • Shiffted bottleneck
    • Branch-and-Bound
    • Gentic Algorithms

Problem: compute the minimalMAKESPAN

experiments
Experiments

B-&-B algorithm running

for 60 sec.

j=10

m=5

j=15

j=20

j=10

m=10

j=15

Lawrence Job Shop Problems

task graph scheduling optimal static task scheduling
Task Graph SchedulingOptimal Static Task Scheduling
  • Task P={P1,.., Pm}
  • Machines M={M1,..,Mn}
  • DurationD : (P£M) !N1
  • < : p.o. on P (pred.)
  • A task can be executed only if all predecessors have completed
  • Each machine can process at most one task at a time
  • Task cannot be preempted.

P2

P1

2,3

16,10

P6

6,6

P3

10,16

P4

2,3

P7

P5

2,2

8,2

M = {M1,M2}

task graph scheduling optimal static task scheduling1
Task Graph SchedulingOptimal Static Task Scheduling
  • Task P={P1,.., Pm}
  • Machines M={M1,..,Mn}
  • DurationD : (P£M) !N1
  • < : p.o. on P (pred.)

P2

P1

2,3

16,10

P6

6,6

P3

10,16

P4

2,3

P7

P5

2,2

8,2

M = {M1,M2}

experimental results
Experimental Results

Abdeddaïm, Kerbaa, Maler

task graph scheduling power optimal static task scheduling
Task Graph SchedulingPower-Optimal Static Task Scheduling
  • Task P={P1,.., Pm}
  • Machines M={M1,..,Mn}
  • DurationD : (P£M) !N1
  • < : p.o. on P (pred.)
  • Energy: C : M !N

P2

P1

2,3

16,10

0

P6

6,6

P3

10,16

P4

2,3

4

P7

P5

2,2

8,2

C(M1)=4; C(M2)=3

priced timed automata optimal scheduling
Priced Timed AutomataOptimalScheduling

Timed Automata + Costs on transitions and locations.

Cost of performing transition: Transition cost.

Cost of performing delay d: ( d x Location cost).

  • Trace:

(2.5)

(a,x=y=0)

(b,x=y=0)

(b,x=y=2.5)

(a,x=0,y=2.5)

4

2.5x 2

0

  • Cost of Execution Trace: Sum of costs: 4 + 5 + 0 = 9

Behrmann, Fehnker, et all (HSCC’01)

Alur, Torre, Pappas (HSCC’01)

cost’=1

cost’=2

cost’=0

x<3

x<3

cost+=4

y>2, x<2

c

a

x:=0

b

Problem :

Find the minimum cost of reaching location c

example aircraft landing
Example: Aircraft Landing

cost

E earliest landing time

T target time

L latest time

ecost rate for being early

l cost rate for being late

dfixed cost for being late

d+l*(t-T)

e*(T-t)

t

E

T

L

Planes have to keep separation distance to avoid turbulences caused by preceding planes

Runway

example aircraft landing1
Example: Aircraft Landing

x <= 5

x >= 4

x=5

4 earliest landing time

5 target time

9 latest time

3cost rate for being early

1 cost rate for being late

2fixed cost for being late

land!

cost+=2

x <= 5

x <= 9

cost’=3

cost’=1

x=5

land!

Planes have to keep separation distance to avoid turbulences caused by preceding planes

Runway

zones
Zones

y

Operations

Z

x

priced zone
Priced Zone

CAV’01

y

Z

2

-1

4

x

symbolic b b algorithm1
Symbolic B&B Algorithm

CAV’01

Linear Programming

Problems

aircraft landing
Aircraft Landing

CAV’01

Source of examples:

Baesley et al’2000

aircraft landing using mcf netsimplex
Aircraft LandingUsing MCF/Netsimplex

J.I. Rasmussen et al

similar for

Priced Task Graph

case studies controllers
Case-Studies: Controllers
  • Gearbox Controller [TACAS’98]
  • Bang & Olufsen Power Controller [RTPS’99,FTRTFT’2k]
  • SIDMAR Steel Production Plant [RTCSA’99, DSVV’2k]
  • Real-Time RCX Control-Programs [ECRTS’2k]
  • Experimental Batch Plant (2000)
  • RCX Production Cell (2000)
  • Terma, Memory Management for Radar (2002)
  • Analog Devices, Dynamic Voltage Scaling Strategies(2003)
case studies protocols
Case Studies: Protocols
  • Philips Audio Protocol [HS’95, CAV’95, RTSS’95, CAV’96]
  • Collision-Avoidance Protocol [SPIN’95]
  • Bounded Retransmission Protocol [TACAS’97]
  • Bang & Olufsen Audio/Video Protocol [RTSS’97]
  • TDMA Protocol [PRFTS’97]
  • Lip-Synchronization Protocol [FMICS’97]
  • Multimedia Streams [DSVIS’98]
  • ATM ABR Protocol [CAV’99]
  • ABB Fieldbus Protocol [ECRTS’2k]
  • IEEE 1394 Firewire Root Contention (2000)
  • Leader Election Algorithm in Ad-Hoc Network[posed by Leslie Lamport 2003]
conclusion
Conclusion

www.uppaal.com

steel production plant
Steel Production Plant

Crane A

  • A. Fehnker
  • Hune, Larsen, Pettersson
  • Case study of Esprit-LTRproject 26270 VHS
  • Physical plant of SIDMARlocated in Gent, Belgium.
  • Part between blast furnace and hot rolling mill.

Objective:model the plant, obtain schedule and control program for plant.

Machine 2

Machine 3

Machine 1

Lane 1

Machine 4

Machine 5

Lane 2

Buffer

Crane B

Storage Place

Continuos

Casting Machine

steel production plant1
Steel Production Plant

Crane A

Input: sequence of steel loads (“pigs”).

Machine 2

Machine 3

Machine 1

Lane 1

Machine 4

Machine 5

Lane 2

Load follows Recipe to

become certain quality, e.g:

start; T1@10; T2@20;

T3@10; T2@10;

end within 120.

Buffer

Crane B

Storage Place

Continuos

Casting Machine

Output: sequence of higher quality steel.

steel production plant2
Steel Production Plant

Crane A

Input: sequence of steel loads (“pigs”).

Machine 2

Machine 3

Machine 1

@10

@20

2

@10

2

2

Lane 1

Machine 4

Machine 5

5

@10

Lane 2

Load follows Recipe to

become certain quality, e.g:

start; T1@10; T2@20;

T3@10; T2@10;

end within 120.

6

Buffer

Crane B

Storage Place

=107

@40

Continuos

Casting Machine

Output: sequence of higher quality steel.

steel production plant3
Steel Production Plant

Crane A

Input: sequence of steel loads (“pigs”).

Machine 2

Machine 3

Machine 1

@10

@20

2

@10

2

2

Lane 1

Machine 4

Machine 5

15

@10

Lane 2

Load follows Recipe to

obtain certain quality, e.g:

start; T1@10; T2@20;

T3@10; T2@10;

end within 120.

16

Buffer

Crane B

Storage Place

=127

@40

Continuos

Casting Machine

Output: sequence of higher quality steel.

slide32

A single load

(part of)

Crane B

experiment
Experiment
  • BFS = breadth-first search, DFS = depth-first search, BSH = bit-state hashing,
  • “-” = requires >2h (on 450MHz Pentium III), >256 MB, or suitable hash-table size was not found.
  • System size: 2n+5 automata and 3n+3 clocks, if n=35: 75 automata and 108 clocks.
  • Schedule generated for n=60 on Sun Ultra with 2x300MHz with 1024MB in 2257s .
lego plant model
LEGO Plant Model

LEGO RCX Mindstorms.

Local controllers with control programs.

IR protocol for remote invocation of programs.

Central controller.

crane a

m1

m2

m3

m4

m5

crane b

buffer

storage

central

controller

casting

Synthesis

lego plant model1
LEGO Plant Model

Belt/Machine Unit.