Real-Time Synchronised Petri Nets Giovanna Di Marzo Serugendo Dino Mandrioli, Didier Buchs, Nicolas Guelfi University of Geneva, Switzerland PN’02 / 24th June 2002Giovanna Di Marzo Serugendo

2 Motivations w Synchronised Petri Nets CO-OPN w Real-Time Time interval attached to transitions w Inhibitor Arcs Maximum number of tokens in place * Real-Time Synchronised Petri Nets

3 Synchronised Petri nets w 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 w This paper: Object-based Time stamped mono colored token

4 Real-Time w 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

5 move [5..15] put [2..10] O1O2 p1p processing [1..9] Real-Time Synchronised Petri Nets Methods Transition Time Interval Synchronisation Objects

6 move [5..15] put [2..10] O1O2 p1p processing [1..9] Real-Time Synchronised Petri Nets 5X

7 move [5..15] put [2..10] O1O2 p1p processing [1..9] 5 X

8 move [5..15] put [2..10] O1O2 p1p processing [1..9] Real-Time Synchronised Petri Nets 7

9 Semantics w How to deal with: Merlin-Farber and Synchronisations Firing respecting Time interval Tokens production time w Synchronisation Intersection of time intervals for simultaneity Correct time of production of tokens for sequence Non-determinism in the case of alternative w Inhibitor Arcs Ensure inhibitor arc condition even with chains of synchronisations

10 Semantics w Structured Operational Semantics Rules (SOS) w 4 Steps Weak Transition System Strong Transition System Expanded Transition System (Synchronisation) Observable Strong Time Semantics paths starting from initial marking

11 Transition System w Events Methods and Transitions Synchronisation /Simultaneous / Sequence / Alternative w Markings Time Stamped Tokens w Time of Firing 2

12 Weak Transition System w 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 w Elapsed Time Interval does not impose transition firing at maximal bound of interval

13 SOS Rules move [5..15] put [2..10] O1O2 p1p processing [1..9] X 5

14 Strong Transition System w Elapsed Time Interval Transition has to fire Remove transitions that prevent other transitions to fire when time elapses w Two transitions reaching maximal bound of firing at the same time: both are allowed one may still disable the other

15 Expanded Transition System w Synchronisation move and put must fire at the same time result takes into account both firings Observable Transition: only move w Simultaneity Both transitions occur at the same time Observable Transition: e1 // e2

16 Expanded Transition System w 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 w Alternative Transition e1 or transition e2 fires at t Observable transition: e1 + e2 Tokens stamped at t Result: due to e1 or e2

17 Synchronisation 5 5 5

18 Strong Time Semantics w Retain observable transitions reachable from initial marking w 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, time

20 Train w Railroad Crossing System w Specification Trains Level Crossing w Safety and Utility Properties determination of time needed to operate the bar

21 Conclusion w Syntax and Semantics of Real-time Synchronised Petri Nets w Towards: Object-Oriented Real-Time Petri Nets w True Operational Semantics already realised first step towards reachability analysis w Future Work Axiomatisation: formal verification of properties