Direct minimal empty siphon computation using MIP

An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

“…Therefore, it is necessary to consider the technical solutions to deadlock problems when designing an FMS. [7][8][9][10][11][12][13] In the past two decades, the research of resolving deadlocks has become the hot issues and many scholars and researchers have achieved a lot of remarkable results in theory and practical applications. 6,[14][15][16][17][18][19][20][21][22][23][24][25][26] Because of their own characteristics to easily and concisely describe the concurrent execution of processes and the reasonable distribution of shared resources in an FMS, 12,27 Petri nets have been widely used to model, analyze, and simulate the static and dynamic behaviors of an FMS, especially in deadlock problems.…”

“…However, many scholars focus on structural analysis, such as siphons 7,9,20,25,29 and resource transition circuits, 10,35 and have developed a large number of DPPs. Among these representative DPPs, E-policy 29 adopts the complete siphon enumeration method (CSEM) to solve all siphons causing deadlocks in an S 3 PR (systems of simple sequential processes with resources) and then adds a CP to each emptied siphon to prevent itself from being emptied.…”

“…But BP and CC are not ideal for the livenessenforcing supervisors synthesized from the controlled ESs and DSs. In the meantime, by MIP 3,8 or the revised MIP 7 (Li and Li 2012c), the partial siphon enumeration method (PSEM) is also used to solve those siphons that definitely cause deadlocks so that the computational loads for the related DPPs such as C-policy, 7 H-policy, 20,31 PR-policy, 4 P-policy, 25 and LLpolicy, 28 PR in the existing literature are used to illustrate the correctness and efficiency of the proposed DCA. Unlike these DPPs with NMPB in the existing literature, the proposed DCA can generally obtain a live controlled system (N 0 , M 0 ) and its reachable state number is the same as that of the original uncontrolled net (N 0 , M 0 ), that is, MRN is greater than NMPB.…”

“…(denoted as HHJ + ), 3,44 (denoted as HJX + ), 22,23 (denoted as LZ), 38 (denoted as UZ), 25 (denoted as PCF), 7 (denoted as C1), 40 (denoted as C2) and Li et al 41 (denoted as LAW + ) is also carried out via some tables, where Ã, J, R, DS, and DFS denote maximally reachable state, MPB, the ratio of the number of reachable states of the live controlled system (N Ã , M Ã ) to MRN, deadlock states, and deadlock-free states of the corresponding Petri net system, respectively.…”

Comments on “enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems”

“…Consequently, deadlocks occur due to processes holding resources mutually waiting for others to release their resources. Deadlock prevention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] adds monitors to problematic siphons to prevent them from becoming insufficiently marked.…”