tailieunhanh - Multiagent-Systems 2010 Part 4

Tham khảo tài liệu 'multiagent-systems 2010 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling and Analysis Methods for Multi-agent Systems 83 Algorithm 2 Petri net model of the multi-agent system The Petri net sub-models of each of the individual agents in the system should be joined based on their indirect interactions. In general this indirect interaction will be in such a way that an agent i action will change an environment state of agent j. This communication act can be regarded as a regular action in the construction of the complete model. There will be arcs added from the places modeling the environmental states of agent j to the transition modeling the communication in agent i. Analysis of the Petri net model The Petri net model of the multi-agent system can be analyzed to assess system properties like deadlock. Inspection of the reachability graph of the Petri net model can indicate if the model is live and bounded. On the other hand liveness and boundedness properties can also be assessed using invariant analysis 13 . Basically the liveness and boundedness of the net can be assessed by using the P-invariants and T-invariants obtained from the incidence matrix which give information regarding token conservation and transition firing sequences that leave the marking of the net unchanged. Let w i j be the weight of the arc that goes from transition ti to place Pj and t w j i be the weight of the arc from place Pj to transition ti. The incidence matrix A of a Petri net has I TI number of rows and ỉ PI number of columns. It is defined as A aij where aij - . Furthermore a P-invariant is a vector that satisfies Ax 0 and a T-invariant is a vector that satisfies AT y 0. A Petri Net model is covered by P-invariants if and only if for each place s in the net there exists a positive P-invariant x such that x s 0 . Furthermore a Petri net is structurally bounded if it is covered by P-invariants and the initial marking M0 is finite. In addition a Petri net model is covered by T-invariants if and only if for each transition t in the net there .