Complex-valued token Petri nets

This paper presents a new extension to ordinary Petri nets (PNs) that uses complex-valued tokens. By allowing two kinds of tokens, "real" and "imaginary," each place marking contains both quantity and type information. Complex-valued token PNs were designed to integrate seamlessly with other popular Petri net extensions such as timed nets, stochastic nets, and colored nets. This simple and intuitive application of complex numbers and complex arithmetic to PNs provides a unique modeling tool. Some examples show the capabilities of this proposed class of PNs. Note to Practitioners-Discrete-event systems are often man-made systems such as transportation systems, computer communication networks, distributed software, and manufacturing systems. They typically involve the flow of information and physical goods through a network. The flow itself evolves in continuous time but the initiation or completion of the event happens at a discrete point in time. Analyzing the system's performance is key to their successful operation. This paper presents a new approach to performance analysis with application to supply-chain management.