Visualizing Petri Nets in 3D

Petri nets were invented by Carl Petri in the 1960s and represent a type of mathematical model useful for modeling concurrency and resource sharing in dynamic systems such as computers and other engineered or natural phenomena. A familiar example of resource sharing involves your refrigerator at home. It is a shared resource in that when one person "uses it" others must wait until that person is finished. Another familiar example that involves both concurrency and resource sharing is a gas station. Since each pump can only service a single car at a time, the pump is a shared resource, but there are several pumps that can be used concurrently. A more complex example that illustrates these concepts is a system that involves many parallel threads of activity, each identifying separate but concurrent activity. A system like this could be the Internet itself, which involves many data packets coursing through intermediate nodes and routers until they reach their final destination. Concurrency in this model would be where more than one Internet nodes are active at the same time, processing different packets. Resource sharing occurs where a node may be occupied processing one packet and cannot take any other packets sent from other nodes until it is finished.

Petri nets are typically represented through the use of 2D diagrams. Our work extends this type of visualization into the third dimension using VRML (Virtual Reality Modeling Language). VRML is the standard 3D modeling language for the World Wide Web; it is used to build interactive scene graphs that represent 3D worlds that can be navigated in real-time using Netscape or Internet Explorer. For a master's thesis, I (Dance) created a 3D Petri net model of the classical Dining Philosophers problem in which five philosophers are thinking and eating around a circular table with five chopsticks, one placed between each philosopher [1]. The concurrency of this system is the concurrent actions of the five philosophers thinking and eating. The resource sharing involves the chopsticks, since there are only five chopsticks and any single philosopher requires two chopsticks to eat. Given this scenario, at most two non-adjacent philosophers may eat simultaneously, since this will involve the use of four of the five chopsticks (one unused chopstick will be left on the table).

Extension into the third dimension is not required to achieve artistic effects but it opens up the possibility of mapping a number of different styles onto systems such as the Dining Philosophers. If the model is created in a 3D environment, then there are more opportunities to explore aesthetics that motivate students. Figure 1 shows a snapshot from a VRML session where the dining philosophers are modeled, performing their alternating "eating" and "thinking" phases. A voice was mapped onto these phases so that the identifier of the philosopher can be heard during the simulation, adding another source of communication to the aesthetic visualization. Employing the third dimension with aesthetics in the design of a Petri net enhances the visualization of the system, thus increasing the user's understanding and enjoyment of it.