## 3 Proposed Model
### Model Phases
Latency refers to the delay incurred in transmitting data packets from the source to the destination, encompassing factors such as propagation delay, processing delay, and queuing delay. Acceptable latency is crucial for ensuring timely communication and responsiveness in various applications, particularly those requiring real-time or near-real-time data exchange. The competitive latency performance of the proposed algorithm suggests its suitability for scenarios where efficient communication with minimal delay is essential, contributing to improved user experience and system reliability. Figure 8: Overhead ratio with respect to number of users. Figure 7: Delivery probability with respect to number of users. Note: Since some of the nodes travel between the cities, varying the transmission speed and the buffer size of all the nodes does not lead to a remarkable changes in delivery probability, overhead and latency; this is why these simulations are not discussed here. ### Varying the number of copies of the messages. Figure 10 shows that increasing the number of copies of messages between fourand sixgives the highest delivery probability. Increasing the number of copies beyond sixincreases the messages' processing and transmission time and thus decreases the delivery probability. The local maximum point in delivery probability signifies a saturation effect, where the benefits of additional message replication are offset by the escalating overhead. At this point, further increases in the number of copies no longer yield significant improvements in delivery probability due to the diminishing returns and increasing network congestion. Figure 10: Delivery probability with respect to number of copies (DakNet scenario). Figure 9: Latency with respect to number of users. ## 5 Conclusions

In this paper, we have introduced a novel probabilistic routing model for opportunistic networks. The new solution leverages nodes'meeting probabilities to dynamically route packets towards their destinations, effectively addressing the unique challenges posed by the absence of complete paths and rapidly changing connectivity in opportunistic networks. By incorporating historical data, specifically the meeting times between nodes, the model establishes controlled and efficient routing strategies, aiming to connect disjointed nodes within the network. Additionally, the proposed model integrates cross-layer optimization

Figure 14: Overhead ratio case, WiFi-direct. Figure 13: Delivery probability case, WiFi-direct. Table
20.0 Latency case, WiFi-direct. techniques, combining optimization strategies spanning multiple protocol layers. This integration aims to enhance the energy efficiency, adaptability, the reliability of message delivery within the network. Moreover, an efficient message detection scheme is introduced to alleviate high overhead by selectively deleting messages from buffers during congestion. Extensive simulations have demonstrated the effectiveness of our proposed solution. Our results indicate that the new model achieves the highest delivery probability among prominent DTN routing protocols while maintaining acceptable and controlled overhead. As a result, the latency incurred remains within acceptable bounds, primarily attributed to the negotiation and table exchange processes between connected nodes. As a conclusion, the proposed model's applicability extends to IoT applications deployed in challenging environments, contributing to enhancing connectivity and efficiency in such deployments. Conceptualization, A.K. and B.Z. ; methodology, A.K. and B.Z. ; software, A.K. and B.Z. ; validation, A.K. and B.Z. ; formal analysis, A.K. and B.Z. ; investigation, A.K. and B.Z. ; resources, A.K. and B.Z. ; data curation, A.K. and B.Z. ; writing--original draft preparation, A.K. and B.Z. ; writing--review and editing, A.K. and B.Z. ; visualization, A.K. and B.Z. ; supervision, A.K. and B.Z. ; project administration, A.K. and B.Z. ; funding acquisition, A.K. and B.Z. All authors have read and agreed to the published version of the manuscript.