普通Petri网最大可达数的两段式死锁控制策略

摘要

This paper develops a two-stage deadlock control policy (DCP) with maximally reachable number (MRN) for the deadlock problems in ordinary Petri nets (OPNs).First,this DCP solves elementary siphons (ESs) and dependent siphons (DSs) in the original uncontrolled net (No,Mo) and then adds a control place (CP) and a control transition (CT) for each ES.Accordingly,an extended net system (N',M') is obtained.Second,the controllability test for DSs in No is executed by means of constructing an integer programming problem (IPP) of P-invadants of N'.If all DSs meet the controllability,then a live controlled system (N*,M*) is achieved directly,implying that the extended net system (N',M') is live.Conversely,the corresponding CPs and CTs are added for those DSs that cannot meet the controllability.Therefore,the live controlled system (N*,M*) can be obtained as well.Theoretical analysis and examples show the correctness and efficiency of the proposed DCE Compared with the relevant deadlock prevention policies with number of maximally permissive behavior (NMPB) in the existing literature for OPNs,the reachable number of the live controlled system (N*,M*) obtained by the proposed DCP is the same as that of the original uncontrolled net (No,Mo),i.e.,maximally reachable number (MRN) is greater than NMPB.%针对普通Petri网的死锁问题,本文提出了可实现最大可达数的两段式死锁控制策略(deadlock control policy,DCP).第1步,该策略求解原网(No,Mo)的基本信标(elementary siphons,ES)和从属信标(dependent siphons,DS),对每个基本信标添加控制库所(control place,CP)和控制变迁(control transition,CT),获得拓展网系统(N',M').第2步,构建拓展网系统的p-不变式整数规划问题,测试原网中从属信标的可控性.若所有从属信标满足可控条件,则直接得到活性受控网系统(N*,M*);反之,对不满足可控条件的从属信标也添加控制库所和变迁,从而也得到了(N*,M*).通过理论分析和算例验证,表明了该死锁控制策略的正确性和有效性.相比目前文献中的可实现最大许可行为数目(number of maximally permissive behavior,NMPB)的普通Petri网死锁预防策略,该DCP获取的活性受控网系统(N*,M*)可达数目与原网(No,Mo)是相同的,且最大可达数(maximally reachable number,MRN)高于最大许可行为数目NMPB.