Tools and Application of Timed Automata UPPAAL & Optimal Scheduling

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Tools and Application of Timed AutomataUPPAAL
Optimal Scheduling

• Kim G. Larsen
• kgl_at_cs.auc.dk

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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

• UPPAAL
• Gerd Behrmann
• Wang Yi
• Paul Pettersson
• Johan Bengtsson
• Fredrik Larsson
• Alexandre David
• Leonid Mokrushin
• Brian Nielsen

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CUPPAAL KRONOS
www.uppaal.com
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CUPPAAL
Priced
CUPPAAL
www.uppaal.com
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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.

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Rush Hour
Your CAR
OBJECTIVE Get your CAR out
EXIT
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Rush Hour
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Rush Hour
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Jobshop Scheduling
TACAS2001
NP-hard Simulated annealing Shiffted
bottleneck Branch-and-Bound Gentic Algorithms
Problem compute the minimal MAKESPAN
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Jobshop in UPPAAL
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Experiments
B--B algorithm running for 60 sec.
j10
m5
j15
j20
j10
m10
j15
Lawrence Job Shop Problems
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Task Graph SchedulingOptimal Static Task
Scheduling

• Task PP1,.., Pm
• Machines MM1,..,Mn
• Duration D (PM) ! N1
• lt 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
P3
P4
6,6
10,16
2,3
P7
P5
2,2
8,2
M M1,M2
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Task Graph SchedulingOptimal Static Task
Scheduling

• Task PP1,.., Pm
• Machines MM1,..,Mn
• Duration D (PM) ! N1
• lt p.o. on P (pred.)

P2
P1
2,3
16,10
P6
P3
P4
6,6
10,16
2,3
P7
P5
2,2
8,2
M M1,M2
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Experimental Results
Abdeddaïm, Kerbaa, Maler
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Task Graph SchedulingPower-Optimal Static Task
Scheduling

• Task PP1,.., Pm
• Machines MM1,..,Mn
• Duration D (PM) ! N1
• lt p.o. on P (pred.)
• Energy C M ! N

P2
P1
2,3
16,10
0
P6
P3
P4
6,6
10,16
2,3
4
P7
P5
2,2
8,2
C(M1)4 C(M2)3
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Priced Timed Automata Optimal Scheduling
Behrmann, Fehnker, et all (HSCC01)
Alur, Torre, Pappas (HSCC01)
cost1
cost2
cost0
xlt3
xlt3
cost4
ygt2, xlt2
c
a
x0
b
Problem Find the minimum cost of reaching
location c

• Timed Automata Costs on transitions and
  locations.
• Cost of performing transition Transition cost.
• Cost of performing delay d ( d x Location
  cost).

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Example Aircraft Landing
Planes have to keep separation distance to avoid
turbulences caused by preceding planes
Runway
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Example Aircraft Landing
x lt 5
x gt 4
x5
4 earliest landing time 5 target time 9 latest
time 3 cost rate for being early 1 cost rate
for being late 2 fixed cost for being late
land!
cost2
x lt 5
x lt 9
cost3
cost1
x5
land!
Planes have to keep separation distance to avoid
turbulences caused by preceding planes
Runway
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Zones
y
Operations
Z
x
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Priced Zone
CAV01
y
Z
2
-1
4
x
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Symbolic BB Algorithm
CAV01
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Symbolic BB Algorithm
CAV01
Linear Programming Problems
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Aircraft Landing
CAV01
Source of examples Baesley et al2000
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Aircraft LandingUsing MCF/Netsimplex
J.I. Rasmussen et al similar for Priced
Task Graph
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Case-Studies Controllers

• Gearbox Controller TACAS98
• Bang Olufsen Power Controller
  RTPS99,FTRTFT2k
• SIDMAR Steel Production Plant RTCSA99, DSVV2k
• Real-Time RCX Control-Programs ECRTS2k
• Experimental Batch Plant (2000)
• RCX Production Cell (2000)
• Terma, Memory Management for Radar (2002)
• Analog Devices, Dynamic Voltage Scaling
  Strategies (2003)

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Case Studies Protocols

• Philips Audio Protocol HS95, CAV95, RTSS95,
  CAV96
• Collision-Avoidance Protocol SPIN95
• Bounded Retransmission Protocol TACAS97
• Bang Olufsen Audio/Video Protocol RTSS97
• TDMA Protocol PRFTS97
• Lip-Synchronization Protocol FMICS97
• Multimedia Streams DSVIS98
• ATM ABR Protocol CAV99
• ABB Fieldbus Protocol ECRTS2k
• IEEE 1394 Firewire Root Contention (2000)
• Leader Election Algorithm in Ad-Hoc Network
  posed by Leslie Lamport 2003

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Conclusion
www.uppaal.com
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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
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Steel Production Plant
Crane A
Machine 2
Machine 3
Input sequence of steel loads (pigs).
Machine 1
Lane 1
Machine 4
Machine 5
Lane 2
Load follows Recipe to become certain quality,
e.g start T1_at_10 T2_at_20 T3_at_10 T2_at_10 end
within 120.
Buffer
Crane B
Storage Place
Continuos Casting Machine
Output sequence of higher quality steel.
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Steel Production Plant
Crane A
Machine 2
Machine 3
Input sequence of steel loads (pigs).
Machine 1
_at_10
_at_20
_at_10
2
2
2
Lane 1
Machine 4
Machine 5
5
_at_10
Lane 2
Load follows Recipe to become certain quality,
e.g start T1_at_10 T2_at_20 T3_at_10 T2_at_10 end
within 120.
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Buffer
Crane B
Storage Place
?107
_at_40
Continuos Casting Machine
Output sequence of higher quality steel.
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Steel Production Plant
Crane A
Machine 2
Machine 3
Input sequence of steel loads (pigs).
Machine 1
_at_10
_at_20
_at_10
2
2
2
Lane 1
Machine 4
Machine 5
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_at_10
Lane 2
Load follows Recipe to obtain certain quality,
e.g start T1_at_10 T2_at_20 T3_at_10 T2_at_10 end
within 120.
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Buffer
Crane B
Storage Place
?127
_at_40
Continuos Casting Machine
Output sequence of higher quality steel.
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A single load (part of)
Crane B
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Experiment

• BFS breadth-first search, DFS depth-first
  search, BSH bit-state hashing,
• - requires gt2h (on 450MHz Pentium III), gt256
  MB, or suitable hash-table size was not found.
• System size 2n5 automata and 3n3 clocks, if
  n35 75 automata and 108 clocks.
• Schedule generated for n60 on Sun Ultra with
  2x300MHz with 1024MB in 2257s .

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LEGO Plant Model
crane a
m1
m2
m3

• LEGO RCX Mindstorms.
• Local controllers with control programs.
• IR protocol for remote invocation of programs.
• Central controller.

m4
m5
crane b
buffer
storage
central controller
casting
Synthesis
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LEGO Plant Model
Belt/Machine Unit.