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Flexible Manufacturing System

Description - Model Specification - Analysis

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Description

A flexible manufacturing system with three machines published in [ CT93 ]. The original model is a GSPN with self-modifying arcs. The model is scalable by the initial amount of tokens N on places P1,P2,P3 and P12. The models below are restricted to an initial amount of tokens of maximal 10. Each of the transitions tP1s, tP2s and tP3s have been modeled by 10 different transitions , each representing a unique token assignment of the places P1s, P2s and P3s. This is required since Snoopy and Marcie do not support marking-dependent arcs weights.

For reasons of efficiency it is worth to reduce the GSPN to an SPN as proposed in [ MBC+95 ].

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Model specification

Snoopy - APNN* - Rewards

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Snoopy model for GSPN version with N=5

APNN* model for the GSPN version (fsm_gspn_N_le_10.apnn)

APNN* model for the SPN version (fsm_spn_N_le15.apnn)

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Reward structures for the GSPN (fsm_gspn.rw)

Reward structures for the SPN (fsm_spn.rw)

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Analysis

Reachability graph of the SPN model

N	states	state transitions
2	810	3,699
4	35,910	237,120
6	537,768	4,205,670
8	4,459,455	38,533,968
10	25,397,658	234,523,289
12	111,414,940	1,078,917,632
14	403,259,040	4,047,471,180

CSL formulas

Productivity of the system.

Transient probability to have N tokens on place P1.