Elementary siphons are useful in the development of a deadlock prevention policy for a discrete event system modeled with Petri nets. This paper proposes an algorithm to iteratively extract a set of elementary siphons...Elementary siphons are useful in the development of a deadlock prevention policy for a discrete event system modeled with Petri nets. This paper proposes an algorithm to iteratively extract a set of elementary siphons in a class of Petri nets, called system of simple sequential processes with resources （S3pR）. At each iteration, by a mixed-integer programming （MIP） method, the proposed algorithm finds a maximal unmarked siphon, classifies the places in it, extracts an elementary siphon from the classified places, and adds a new constraint in order to extract the next elementary siphon. This algorithm iteratively executes until no new unmarked siphons can be found. It finally obtains a unique set of elementary siphons and avoids a complete siphon enumeration. A theoretical analysis and examples are given to demonstrate its efficiency and practical potentials.展开更多
基金supported by the Natural Science Foundation of China under Grant No.60773001,61074035, 61064003,and 50978129the Fundamental Research Funds for the Central Universities under Grant No. JY 10000904001+2 种基金the National Research Foundation for the Doctoral Program of Higher Education,the Ministry of Education,P.R.China,under Grant No.20090203110009the"863"High-tech Research and Development Program of China under Grant No.2008AA04Z 109the Alexander von Humboldt Foundation
文摘Elementary siphons are useful in the development of a deadlock prevention policy for a discrete event system modeled with Petri nets. This paper proposes an algorithm to iteratively extract a set of elementary siphons in a class of Petri nets, called system of simple sequential processes with resources （S3pR）. At each iteration, by a mixed-integer programming （MIP） method, the proposed algorithm finds a maximal unmarked siphon, classifies the places in it, extracts an elementary siphon from the classified places, and adds a new constraint in order to extract the next elementary siphon. This algorithm iteratively executes until no new unmarked siphons can be found. It finally obtains a unique set of elementary siphons and avoids a complete siphon enumeration. A theoretical analysis and examples are given to demonstrate its efficiency and practical potentials.
