Many models are present in the literature that have been used for investigating deadlock avoidance, prevention, and detection algorithms. In this paper, a model is presented that concentrates on possible conditions that my exist in a system of n processes and k resource types with varying units of resources. The model is based on a graph in which each node represents a state of the entire system. It can be shown that this set of nodes can be partitioned into three sets such that all nodes in the first set represent the condition that the corresponding system is guaranteed to be free of deadlock; the second set represents the condition that the system is deadlocked; the second set represents the condition that the system is deadlocked; the third set represents the condition that the system may or may not be in a state of deadlock depending on how each given node has been reached from the initial node of the graph. The model has been exercised with various system configurations to obtain probabilistic estimates of deadlock existing in each node of the third set, and these results are given, as well as a description of the model.
Osterweil, Janis P. and Nutt, Gary J., "Modeling Process-Resource Activity ; CU-CS-084-75" (1975). Computer Science Technical Reports. 82.