Coordination of Components in a Distributed Discrete-Event System - - PowerPoint PPT Presentation

✬ ✫ ✩ ✪

Coordination of Components in a Distributed Discrete-Event System

Ahmed Khoumsi Universit´ e de Sherbrooke, Canada. ISPDC, Lille, France, 4-6 July 2005

Outline

✬ ✫ ✩ ✪

Outline

• Introduction
• Problem, Coordination
• Model used: Automata with Actions (AwA)
• Input of the problem: DES distributed in several sites
• Approach of coordination
• Result of coordination: a component in each site
• Reducing communication
• Nonnegligible reaction delays and communication delays
• Application in supervisory control
• Conclusion: contributions and future work

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 1

Introduction

✬ ✫ ✩ ✪

Introduction

Let a distributed DES R that :

• executes events in several sites distant with each other,
• is observed by local components.

Each local component :

• observes only the events in its site
• may have to execute actions depending on the global state of R.

Consequence : a component may be unable to distinguish global states

• f R just from its local observations.

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 2

Problem, Coordination

✬ ✫ ✩ ✪

Problem, Coordination

Problem arises when a component:

• cannot distinguish two states of R
• does not execute the same actions in the two (indistinguishable)

states Coordination for solving the problem: the components coordinate themselves by exchanging (coordination) messages R2 R1

Site 1 Site 2 Distributed DES Events

• b

s e r v e s

• b

s e r v e s

Events communication

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 3

Model used : Automata with Actions (AwA)

✬ ✫ ✩ ✪

Model used : Automata with Actions (AwA)

A AwA is quite similar to a Finite State Automaton (FSA), with the difference that a set of actions can be associated to each state. Actions associated to a state q are executed each time q is reached.

1 2 3 4 5

ν µ α β γ δ a γ δ b c γ δ e b d δ c

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 4

Input of the problem: DES distributed in 2 sites

✬ ✫ ✩ ✪

Input of the problem: DES distributed in 2 sites

Distributed DES modeled by AwA R = (S, Σ1 ∪ Σ2, T, Γ1 ∪ Γ2, F, s0) S: set of states Σ1 ∪ Σ2 is the set of events executed by R, in sites 1 and 2, resp. Σi contains events observed by Ri, the component in site i. T is a transition relation: T ⊆ S × (Σ1 ∪ Σ2) × S. Γi contains actions executed by Ri. F: S − → 2Γ1∪Γ2 F(q) indicates the actions to be executed each time the state q is reached.

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 5

Approach of coordination: example

✬ ✫ ✩ ✪

Approach of coordination: example

a1 γ1 δ1 γ1 δ1 b1 c1 d2 c2 b1 c1 α1 β1 γ1 δ1 µ2ν2 δ1

1 2 3 4 5

[1; a1; 2], [3; c1; 2] in Site 1 and followed only by events and actions in the same site. No communication needs to follow these transitions. [3; d2; 4] in Site 2 and followed only by events in the same site and by no

• action. No communication needs to follow this transition.

[2; b1; 3], [5; b1; 3], [5; c1; 3] in Site 1 and followed by event d2 in Site 2. A communication from R1 to R2 must follow these transitions. [4; c2; 5] in Site 2 and followed by events and actions in Site 1. A communication from R2 to R1 must follow this transition.

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 6

Result of coordination: component in each site

✬ ✫ ✩ ✪

Result of coordination: component in each site

a1 γ1 δ1 α1 β1 γ1 δ1 r (5)

2 1

b1 γ1 δ1 c1 s (3)

2 1

s (3)

2 1

b1 c1 δ1 a1 c1 d2 δ1 b1 c2 c1 α1 β1 γ1 δ1 µ2ν2 b1 γ1 δ1 γ1 δ1 R1 µ2ν2 r (3)

1 2

d2 c2 s (5)

1 2

r (3)

1 2

r (3)

1 2

R2

2 1 2−3 5−3 3−4 5 5 2 3 4 1

R

4 4−5 5 1−2 3−2

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 7

Reducing communication

✬ ✫ ✩ ✪

Reducing communication

Lemma: A communication defined by (sj

i (k), r i j (k)) is useless (and thus, can be

removed) when r i

j (k) occurs only in transitions:

• whose destination state is associated to no action, and
• whose origin state has no other outgoing transition.

a1 r (5)

2 1

b1 γ1 δ1 c1 s (3)

2 1

s (3)

2 1

b1 c1 δ1 α1 β1 γ1 δ1 γ1 δ1 R1 µ2ν2 r (3)

1 2

d2 c2 s (5)

1 2

r (3)

1 2

r (3)

1 2

R2

becomes

γ1 δ1 b1 γ1 δ1 c1 δ1 c1 b1 r (5)

2 1

a1 α1 β1 γ1 δ1 R1 c2 d2 s (5)

1 2

d2 µ2ν2 R2

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 8

Nonnegligible reaction and communication delays

✬ ✫ ✩ ✪

Nonnegligible reaction and communication delays

Let: R be a reaction delay of a component to send a message C be a communication delay of a message D be an upper bound of R + C Lemma: The proposed coordination method is applicable if the distributed system stays during at least D in every state requiring communication.

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 9

Application in supervisory control

✬ ✫ ✩ ✪

Application in supervisory control

The coordination method has been applied in Supervisory Control Theory (SCT), where: Components are called supervisors. Actions consist of enabling/disabling events.

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 10

Conclusion

✬ ✫ ✩ ✪

Conclusion

Contributions : Proposition of a coordination method which is better than existing

• nes.

Future work :

• Implementation and application to concrete nontrivial systems,
• Generalization for real-time DES.

“Coordination of Components in a Distributed Discrete-Event System”, ISPDC, 4-6 July 2005. 11