## 3 Method
### Timed Colored Petri Net Model
\begin{table}
\begin{tabular}{c l} \hline
**Transition** & **Description of Transitions** \\ \hline \(t_{1}\) & The transition aims at modeling the check of the worker \\ \(t_{2}\) & The transition aims at modeling the check of the material \\ \(t_{3}\) & The transition aims at modeling requesting the worker \\ \(t_{4}\) & The transition aims at modeling requesting the material \\ \(t_{5}\) & The transition aims at modeling the machine processing and publishing a logistics task \\ \(t_{6}\) & The transition aims at modeling the quality detection \\ \(t_{7}\) & The transition aims at modeling the selection of the AGV \\ \(t_{8}\) & The transition aims at modeling the temporary storage \\ \(t_{9}\) & The transition aims at modeling the selected AGV going to the start point \\ \(t_{10}\) & The transition aims at modeling the reprocessing or the scarp \\ \(t_{11}\) & The transition aims at modeling the rejection of the AGV \\ \(t_{12}\) & The transition aims at modeling picking pallet and loading \\ \(t_{13}\) & The transition aims at modeling the selected AGV going to the destination \\ \(t_{14}\) & The transition aims at modeling the unloading \\ \hline \end{tabular}
\end{table} 
Table 1: Transitions in Figure 3.  
Figure 3: The timed colored Petri net model for self-adaptive collaborative production-logistics systems. Figure 3 shows the TCPN model of the self-adaptive collaboration method. This model refers to the basic cycle of production-logistics systems, which consists of twenty-three places and fourteen transitions. Conditional statement expressions are assigned to the directed arcs \(a_{1}\), \(a_{2}\), \(a_{3}\), \(a_{4}\), \(a_{5}\), \(a_{6}\), \(a_{7}\), and \(a_{8}\). The cycle starts with checking workers and materials to be processed in production cells. Transition \(t_{1}\) denotes the check of workers while transition \(t_{2}\) denotes the check of materials. If the workers or materials are not ready, they will be requested. Otherwise, the materials will be processed on the machine. Transition \(t_{5}\) describes machine processing as well as publishing a logistics task. The two processes are performed at the same time. The remaining time of the current operation of the machine is calculated and considered as a critical parameter for selecting an AGV. While a logistics task is published, all AGVs actively request the task. A token in the place \(p_{9}\) represents the status information of an AGV, including current location and remaining space, which are collected by embedded devices or sensors. Thus, the machine can perceive the status of the AGV. Transition \(t_{6}\) represents the quality detection of the WIP after machine processing. Unqualified WIP will be reprocessed or abandoned based on the detection standards. Transition \(t_{10}\) denotes the reprocessing or the scarp. If the WIP is unqualified and needs to be reprocessed or abandoned, this cycle ends and the next cycle begins. Only the qualified one will be sent to the out-buffer of the production cell and wait to be transported to the next production cell. Transition \(t_{7}\) represents selection of an AGV. The nearest AGV with remaining