View
213
Download
0
Embed Size (px)
Citation preview
Real-Time Synchronised Petri Nets
Giovanna Di Marzo SerugendoDino Mandrioli, Didier Buchs, Nicolas Guelfi
University of Geneva, Switzerland
PN’02 / 24th June 2002 Giovanna Di Marzo Serugendo
2
Motivations
Synchronised Petri Nets• CO-OPN
Real-Time• Time interval attached to transitions
Inhibitor Arcs• Maximum number of tokens in place
Real-Time Synchronised Petri Nets
3
Synchronised Petri nets
Concurrent Object-Oriented Petri Nets• Object-Orientation• External and Internal Transitions• Synchronisation Requests
• simple
• simultaneity, sequence, alternative operators
• transactional semantics (all or nothing)
• Abstract Data Types
This paper: • Object-based• Time stamped mono colored token
4
Real-Time
Time Interval• Attached to each transition • Merlin-Farber model• Instantaneous firing• Time of Firing:
• Bound by time interval in R+
• Relative to time when transition becomes enabled
tt, ,0 ', tt
5
move [5..15] put [2..10]
O1 O2
p1 p2
1
00
0
10
1
processing [1..9]
Real-Time Synchronised Petri Nets
Methods
Transition
Time IntervalSynchronisation
Objects
6
move [5..15] put [2..10]
O1 O2
p1 p2
1
00
0
10
1
processing [1..9]
Real-Time Synchronised Petri Nets
5X
]10..5[t
7
Real-Time Synchronised Petri Nets
move [5..15] put [2..10]
O1 O2
p1 p2
1
00
0
10
1
processing [1..9]
5
]14..6[t
X
8
move [5..15] put [2..10]
O1 O2
p1 p2
1
00
0
10
1
processing [1..9]
]10..6[t
Real-Time Synchronised Petri Nets
7
9
Semantics
How to deal with:• Merlin-Farber and Synchronisations
• Firing respecting Time interval
• Tokens production time
Synchronisation• Intersection of time intervals for simultaneity
• Correct time of production of tokens for sequence
• Non-determinism in the case of alternative
Inhibitor Arcs• Ensure inhibitor arc condition even with chains of synchronisations
10
Semantics
Structured Operational Semantics Rules (SOS)
4 Steps• Weak Transition System• Strong Transition System• Expanded Transition System (Synchronisation)• Observable Strong Time Semantics
• paths starting from initial marking
11
Transition System
Events• Methods and Transitions• Synchronisation /Simultaneous / Sequence / Alternative
Markings• Time Stamped Tokens
Time of Firing
}2{{},{}{}, put
2
12
Weak Transition System
Single Firings• synchronisation is not taken into account• time of firing occurs in time interval• inhibitor arc condition is verified• post-condition produces tokens stamped at time of firing
Elapsed Time Interval • does not impose transition firing at maximal bound of
interval
13
SOS Rules
move [5..15] put [2..10]
O1 O2
p1 p2
1
000
101
processing [1..9]
X
{}},0,0{{}},0,0,0{ put with move5
14
Strong Transition System
Elapsed Time Interval• Transition has to fire• Remove transitions that prevent other transitions to fire when
time elapses
Two transitions reaching maximal bound of firing at the same time:• both are allowed • one may still disable the other
15
Expanded Transition System
Synchronisation• move and put must fire at the same time• result takes into account both firings• Observable Transition: only move
Simultaneity• Both transitions occur at the same time• Observable Transition: e1 // e2
16
Expanded Transition System
Sequence• Transition e1 fires before e2 (t1 < t2)• Observable transition: e1 .. e2• Tokens stamped at t1 and t2• Tokens stamped at t2: not available before t2
Alternative• Transition e1 or transition e2 fires at t• Observable transition: e1 + e2• Tokens stamped at t• Result: due to e1 or e2
18
Strong Time Semantics
Retain observable transitions reachable from initial marking
Time increases
Semantics = paths of transitions starting from initial marking
19
Strong Time Semantics
{0,0,0},{}
move,5
{0,0},{5}
put,2
{0,0,0},{2}
{0,0},{}
processing,6 move,6
put,6
{0},{6}
{0,0},{6} ...
...
{0,0,0},{}
processing,3
...
{0,0},{5.5}move + put,5.5
...
......
time
20
Train
Railroad Crossing System Specification
• Trains• Level Crossing
Safety and Utility Properties• determination of time needed to operate the bar