Constructing the closed-form solution of control-related states real-time information for insufficient k-th order systems with one non-sharing resource to realize dynamic modeling large TNCS systems of petri nets

Abstract

ABSTRACTSince the contribution from the closed-form solution (CFS) of the number of control-related states (CRSs) of the variant k-th order system can enumerate the number of each type of CRS in real time, we can apply this real-time information to enhance the capability for dynamic modeling of such systems. For example, allocating a non-sharing waiting dummy resource (known as a deadlock thread-holder [DTH]) in each forbidden substate at that location will increase the maximum number of reachable states that can be derived using a CFS in real time. We can thus avoid the occurrence of deadlock without implementing an additional controller. To extend this capability to model a k-th order system with one non-sharing circle subnet allocated at the top position of the left-hand process (denoted as a top non-sharing circle subnet [TNCS] k-th order system) by Petri net (PN), which is the fundamental manufacturing model for different products sharing common parts, this paper extends the existing research on CFS for PNs to an insufficient k-th order system, which is the essential element for a TNCS system with one non-sharing resource. The proposed deadlock avoidance algorithm can be employed to realize the allocation of dynamic non-sharing processes.