Reach-ability Graph Assignment Help

Basic Introduction To PETRI NETS - Reach-ability Graph

Reach-ability Graph

A reach-ability graph for an initially marked Petri net M0, is a directed graph (V, E), here V = R [M0] is a set of vertices, and E, the set of directed arcs, is specified by as:

(M1 , M2 ) ∈ E , if

  • M1 , M 2 ∈ R [M0 ] and
  • Either there exists a transition t ∈ T2130_Reach-ability Graph.pngsuch that or there exists a set, T1 ⊆ T , such as T1 is a set of concurrent transitions by firing all of that M1 reaches M2

In the reach-ability graph, the nodes are labeled by markings they show and the directed arcs are labeled by transitions or the set of concurrent transitions that firing takes the source node to the destination node.

Illustration .7

From the Petri net shown below in Figure (a)

  • In a tabular form, show the reachable markings of the Petri net.
  • Draw the reach-ability graph.

                                               42_Reach-ability Graph 1.png

Solution

Reach-able marking of Petri net of above figure (a) are represent in Table no.2 below.

                                                         Table no.2: Reachable Marking of Petri Net Shown in above figure (a)

 

p1

p2

p3

p4

p5

p6

p7

M0

1

1

1

0

0

0

0

M1

0

0

1

1

0

0

0

M2

1

0

1

0

1

0

0

M3

0

0

0

0

0

1

0

M4

0

1

1

0

0

0

1

In above table, M0, M1, M2, M3, M4 represent the different reachable markings. These markings can be shown in the form of a reach-ability graph.

                                                          1293_Reach-ability Graph 2.png

                             Figure: A Reach-ability Graph of a Marked Petri Net Model of a System as Shown in above figure (a)

Demerits and Merits of Classical Petri Nets

Expertsmind’s world class education services

We at www.expertsmind.com offer email based assignment help – homework help and projects assistance from k-12 academic level to college and university level and management and engineering studies. Our experts are helping students in their studies and they offer instant tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.

- Quality assignment help assistance 24x7 hrs
- Best qualified tutor’s network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work