## 5 Conclusions and Future Works  
To address the research questions posed in the introduction, the following conclusions can be drawn based on the results and discussions presented in this article:  
* The system efficiently implements real-time delivery of promotional advertisements using the Haversine formula to calculate user proximity to shopping centers. The API developed in Laravel processes mobile device coordinates and sends relevant offers when the user is within a 600 m radius. * The integration of Petri nets provides significant benefits for modeling the asynchronous and concurrent behaviors of the mobile application. The Petri net model enables an accurate representation of interactions between network requests, message delivery, and user proximity detection, optimizing the user experience. * The use of Petri nets allows identifying and optimizing bottlenecks in the interaction flow. The network structure facilitates visualization of potential improvement areas in communication flow, leading to greater efficiency in real-time promotion delivery. The design and implementation of the mobile application for real-time delivery of promotional advertisements has proven to be an effective and efficient solution for communication between shopping centers and users. Through the use of the Haversine formula and geolocation, a system has been established that accurately detects user proximity, allowing the API, developed with Laravel, to send relevant information at timely moments. Modeling the system's behavior with Petri nets has been crucial to understanding and optimizing the asynchronous and concurrent nature of interactions. This approach ensures a smooth user experience by minimizing response times and maximizing the relevance of delivered promotions, creating a seamless, uninterrupted user experience. The Petri net structure has facilitated the identification of potential bottlenecks and has proven invaluable for ensuring the liveness and boundedness of the system, meaning that all transitions remain available at any time without exceeding a reasonable limit on resources. This contributes to the robustness and stability of the system--key elements for applications that require real-time interactions. The combination of modern technologies, such as Kotlin for the mobile application and Laravel for the backend, with Petri net modeling has proven to be an effective and scalable solution, paving the way for future expansions and improvements in the functionality of similar applications. In conclusion, this research not only highlights the feasibility of the implemented system but also lays the foundation for future applications in proximity marketing. The integration of formal models, such as Petri nets, in mobile application and web service development offers a valuable approach to improving the efficiency and effectiveness of similar systems in the future. Regarding limitations to consider, the following are highlighted:  
* Standard Petri nets, as used in this study, lack the ability to learn or adapt to dynamic changes in behavioral patterns. * The API may face scalability issues, particularly if the number of requests increases significantly. * The mobile application may encounter compatibility problems with older Android versions or devices with limited hardware capabilities. Regarding future work, the following aspects are proposed:  
* Enhancing the Petri net structure by integrating neural components to enable learning capabilities, allowing the system to deliver promotions based on user interests. * Implementing load distribution technologies to optimize system performance under high demand. * Conducting tests on a variety of devices to ensure compatibility and optimizing the code for devices with limited hardware resources. * The share button enables promotions to reach a broader audience. As future work, it is suggested to integrate tracking metrics to evaluate the real-time impact of shared promotions.