A deadlock control method using elementary siphons of Petri nets

An important Petri net-based method to prevent deadlocks arising in flexible manufacturing systems (FMS) is to add control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Its disadvantage lies in that the method often adds too many additional places to the net. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes the concept of elementary siphons that are a special class of SMS and proves that by adding a control place for each elementary siphon to make sure that it is always marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy.