Cross-Departmental Collaboration Approach for Earthquake Emergency Response Based on Synchronous Intersection between Traditional and Logical Petri Nets
Abstract
:1. Introduction
- (1)
- Traditional and logical Petri nets with better representation capability are applied to the field of earthquake emergency management;
- (2)
- The synchronization composition of traditional Petri nets is extended from the synchronization of transitions to the synchronization between logical and traditional transitions in traditional and logical Petri nets, and the intersection operation of logical functions of corresponding transitions is presented. For the first time, the logical function is extracted for traditional transitions, and the definition of synchronous transition unit and the calculation method of its logical functions are proposed;
- (3)
- The synchronous intersection operation between traditional and logical Petri nets fills the research gap. It also solves the coordination problem of the earthquake emergency departments;
- (4)
- For the superior department, a new logical Petri net can be obtained by modeling the workflow of its subordinate units between traditional and logical Petri nets and performing synchronous intersection operations. Then, we can more directly observe the workflow of each department and judge which work needs the cooperation of the two departments.
2. Related Work
2.1. Business Process Management and Process Mining
2.2. Traditional and Logical Petri Nets
2.3. Sharing Composition and Synchronous Composition
2.4. Emergency Management and Cross-Organizational Collaboration
- (1)
- At present, the main model of emergency management is constructed using traditional Petri nets, which leads to many limitations in modeling complex situations.
- (2)
- The application of logical Petri nets in earthquake emergency management is still a gap, and its value has not been fully utilized.
- (3)
- The research on cross-departmental collaboration is still more dependent on traditional Petri nets than on logical Petri nets.
- (4)
- In the composition of logical Petri nets, due to its complexity, the current research focus is mainly on the sharing composition. Therefore, the synchronous composition of logical Petri nets, which has the significance of cross-organizational, cross-departmental collaboration research, has not achieved research results.
2.5. Solution
3. Preliminaries
- (1)
- For, if,, ti is enabled at M, then ti can be fired, it can be denoted by M[ti>.
- (2)
- When ti is fired under the marking M, a new marking M′ is created, and it can be denoted by M[ti>M′. If, and, then; if, and, then; else,.
- (1)
- P is a finite set of places on LPN;
- (2)
- T is a finite set of transitions on LPN,, where
- (a)
- denotes the set of traditional transitions of LPN, whose firing rules are consistent with those of the transitions in traditional Petri nets, with specific reference to the contents of Definition 1;
- (b)
- denotes the set of logical input transitions of LPN; for, the firing of ti is constrained by the logical input functionof ti for its place, and. For, if, ti is enabled at M, then ti can be fired, it can be denoted by M[ti>; When ti is fired under the marking M, a new marking M′ is created, and it can be denoted by M[ti>M′. For,and; for,;
- (c)
- denotes the set of logical output transitions of LPN; for, the firing result is constrained by the logical output functionof ti for its place, and. For, ifand,is enabled at M, thencan be fired, it can be denoted by M[ti>; when ti is fired under the marking M a new marking M′ is created, and it can be denoted by M[ti>M′. For,and; for,;
- (3)
- is a finite set of directed arcs on LPN;
- (4)
- I is a mapping from a set of logical input transitions to a logical input function, for,;
- (5)
- O is a mapping from a set of logical output transitions to a logical output function, for,;
- (6)
- is a mapping from a set of transitions to a set of activities;
- (7)
- is a marking function on LPN,represents the number of tokens in p.
4. Synchronous Intersection of Traditional and Logical Petri Nets
4.1. Definition of Synchronous Intersection
- For, the logical input function is;
- For, the logical output function is;
- Forin traditional Petri nets, its logical functions are extracted in the same way as the way forin logical Petri nets. In addition, obtaining functions for the synchronous transition unit can be done by intersecting the logical functions of the two transitions that have not been merged before.
4.2. Computation of Synchronous Intersection
4.2.1. Synchronous Intersection Operation of Traditional Transitions
- (1)
- The set of activities composition
- (2)
- The set of places composition
- (3)
- The set of transitions composition
- (4)
- The set of directed arcs composition
- (5)
- Mapping I composition
- (6)
- Mapping O composition
- (7)
- Marking composition
- (8)
- Mapping composition
4.2.2. Synchronous Intersection Operation of Traditional and Logical-Input Transitions
- (1)
- The set of transitions composition
- (2)
- The logical input functions composition
- (3)
- Mapping I composition
- (4)
- Mapping O composition
- (1)
- Reachable marking functions about PN5
- (2)
- Reachable marking functions about LPN6
- (3)
- Synchronous intersection operation of PN5 and LPN6
4.2.3. Synchronous Intersection Operation of Traditional and Logical-Output Transitions
- (1)
- The set of transitions composition
- (2)
- Mapping I composition
- (3)
- The logical output functions composition
- (4)
- Mapping O composition
- (1)
- Reachable marking functions about PN9
- (2)
- Reachable marking functions about LPN10
- (3)
- Synchronous intersection operation of PN9 and LPN10
5. Simulation Experiments
5.1. Emergency Planning Restatement
5.2. EOI Model and Its Reachable Markings
5.3. STD Model and Its Reachable Markings
5.4. Synchronous Intersection of PN12 and LPN13
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Tian, Y.; Pang, X.; Su, Y.; Han, D.; Du, Y. Cross-Departmental Collaboration Approach for Earthquake Emergency Response Based on Synchronous Intersection between Traditional and Logical Petri Nets. Electronics 2023, 12, 1207. https://doi.org/10.3390/electronics12051207
Tian Y, Pang X, Su Y, Han D, Du Y. Cross-Departmental Collaboration Approach for Earthquake Emergency Response Based on Synchronous Intersection between Traditional and Logical Petri Nets. Electronics. 2023; 12(5):1207. https://doi.org/10.3390/electronics12051207
Chicago/Turabian StyleTian, Yinhua, Xiaowen Pang, Yan Su, Dong Han, and Yuyue Du. 2023. "Cross-Departmental Collaboration Approach for Earthquake Emergency Response Based on Synchronous Intersection between Traditional and Logical Petri Nets" Electronics 12, no. 5: 1207. https://doi.org/10.3390/electronics12051207