RealTime Synchronised Petri Nets Giovanna Di Marzo Serugendo

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

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 2

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 3

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 4

Real-Time Synchronised Petri Nets Synchronisation Time Interval move [5. . 15] Methods put [2. . 10] 1 0 1 processing [1. . 9] 1 0 0 0 p 1 O 1 Transition p 2 Objects O 2 5

Real-Time Synchronised Petri Nets move [5. . 15] put [2. . 10] 1 0 X 0 0 1 5 p 1 O 1 1 processing [1. . 9] 0 p 2 O 2 6

Real-Time Synchronised Petri Nets move [5. . 15] put [2. . 10] 1 1 X 5 0 0 0 p 1 O 1 1 processing [1. . 9] 0 p 2 O 2 7

Real-Time Synchronised Petri Nets move [5. . 15] put [2. . 10] 1 0 0 0 1 7 p 1 O 1 1 processing [1. . 9] 0 p 2 O 2 8

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 9

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 10

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

Weak Transition System w Single Firings • • w 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 12

SOS Rules put [2. . 10] move [5. . 15] 1 0 X 0 0 0 1 processing [1. . 9] 1 p 2 O 1 5 13

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 14

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: e 1 // e 2 15

Expanded Transition System w Sequence • • w Transition e 1 fires before e 2 (t 1 < t 2) Observable transition: e 1. . e 2 Tokens stamped at t 1 and t 2 Tokens stamped at t 2: not available before t 2 Alternative • • Transition e 1 or transition e 2 fires at t Observable transition: e 1 + e 2 Tokens stamped at t Result: due to e 1 or e 2 16

Synchronisation 5 5 5 17

Strong Time Semantics Retain observable transitions reachable from initial marking w Time increases w * Semantics = paths of transitions starting from initial marking 18

Strong Time Semantics put, 6 {0, 0}, {} {0, 0}, {5} move, 5 {0, 0, 0}, {} processing, 6 move, 6 {0, 0}, {6} {0}, {6} . . . move + put, 5. 5 {0, 0}, {5. 5}. . . put, 2. . . {0, 0, 0}, {2} {0, 0, 0}, {}. . . processing, 3 time 19

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

Conclusion Syntax and Semantics of Real-time Synchronised Petri Nets w Towards: w • 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 21