# Distributed Management Systems for Infocommunication Networks: A Model Based on TM Forum Framework
## 3 Methods
### Elimination of Dead States and Interlocks
Figure 7: Execution model for two parallel BPs in interlock state. The first approach is to use a well-timed forced locking of processes [10]. To this effect, define the minimal number of processes to be locked and also the minimal number of states to preserve this interlock. Then transform the reachable marking graph by removing all the edges that connect dangerous and forbidden states. This procedure yields a graph containing the safe states only. In this example, the state \(S_{11}\) is the root of two dangerous segments, \(S_{21}-S_{31}\) and \(S_{12}-S_{13}\) (Figure 8). The well-timed forced locking of undesired processes can be implemented by introducing an input position \(c_{b}\) for the transitions \(t_{2}\) and \(t_{8}\) in the Petri net (Figure 9). In this case, following the activation of the transition \(t_{2}\) (\(t_{8}\)) and further evolvement of the process \(bp_{1}\) (\(bp_{2}\), respectively), the token is removed from the position \(c_{b}\) and the process \(bp_{2}\) (\(bp_{1}\), respectively) is locked. In accordance with the transformed reachable marking graph (Figure 9), the state \(S_{31}\) (\(S_{13}\)) is the last state of the chosen dangerous segment. Hence, the lock can be lifted after the activation of  
Figure 8: Reachable marking graph of original Petri net. Figure 9: Transformed reachable marking graph of Petri net. the transition \(t_{4}\) (\(t_{10}\), respectively). To this end, the position \(c_{b}\) must be the output position for the transitions \(t_{4}\) and \(t_{10}\), as is illustrated in \[T_{\min}(S)=\min\{t_{i}(S)\}, \tag{9}\]0  
The transformed reachable marking graph (Figure 9) contains the position \(c_{b}\) in all states except for the ones corresponding to dangerous segments. The states \(S_{12}\), \(S_{13}\), \(S_{21}\) and \(S_{31}\), which are dangerous in the original graph, become safe lock states; the state \(S_{11}\) becomes the conflict state. In addition, the forbidden states \(S_{22}\), \(S_{32}\), \(S_{23}\) and \(S_{33}\) turn out to be unreachable in the transformed graph. The simulation of the transformed Petri net over 100 steps have testified to the efficiency of this well-timed forced locking procedure; see the simulation results in \[T_{\min}(S)=\min\{t_{i}(S)\}, \tag{9}\]1  
\[T_{\min}(S)=\min\{t_{i}(S)\}, \tag{9}\]2 Transformed execution model for two parallel BPs: simulation results. \[T_{\min}(S)=\min\{t_{i}(S)\}, \tag{9}\]3 Initial state of execution model for two parallel BPs with well-timed forced locking. The second approach to eliminate the dead states and interlocks of processes is to allocate the additional resources required for their simultaneous execution (Figure 12). In this case, the positions \(c_{1}\) and \(c_{2}\) have single tokens, which corresponds to two units of homogeneous resource. Next, the third approach to eliminate the dead states and interlocks of processes is to capture simultaneously all the resources required for a process (Figure 13). For lifting the interlock of the first process, a position \(c_{21}\) is added to the original network that holds the second resource. \[T_{\min}(S)=\min\{t_{i}(S)\}, \tag{9}\]4 Execution model for two parallel BPs with allocation of additional resources: simulation results. \[T_{\min}(S)=\min\{t_{i}(S)\}, \tag{9}\]5 Execution model for two parallel BPs with monopolistic capture of resources: simulation results. The last (fourth) approach to eliminate the dead states and interlocks is to arrange the capture of resources. Serial numbers are assigned for all types of resources and a capture discipline is defined for all processes. In the transformed model, this approach is implemented by reassigning serial numbers for resources and specifying choice rules for the transitions \(t_{2}\), \(t_{4}\), and \(t_{8}\), \(t_{10}\) (Figure 14). The developed models eliminate the interlocks of parallel processes. The methodology of colored Petri nets is used to analyze the complete state space of the model in order to improve the reliability of the computing system and also to satisfy the requirements.