# A Mathematical-Based Model for Estimating the Path Duration of the DSDV Routing Protocol in MANETs
###### Abstract  
Mobile Ad Hoc Networks (MANETs) are kind of wireless networks where the nodes move in decentralized environments with a highly dynamic infrastructure. Many well-known routing protocols have been proposed, with each having its own design mechanism and its own strengths and weaknesses and most importantly, each protocol being mainly designed for specific applications and scenarios. Most of the research studies in this field used simulation testbeds to analyze routing protocols. Very few contributions suggested the use of analytical studies and mathematical approaches to model some of the existing routing protocols. In this research, we have built a comprehensive mathematical-based model to analyze the Destination-Sequenced Distance Vector protocol (DSDV), one of the main widely deployed proactive protocols and studied its performance on estimating the path duration based on the concepts of the probability density function and the expected values to find the best approximation values in real scenarios. We have tested the validity of the proposed model using simulation scenarios implemented by the Network Simulator tool (NS3). The results extracted from both the mathematical model and the simulation have shown that the path duration is inversely proportional to both the speed of the node and the hop count. Furthermore, it had shown that the path duration estimated from the DSDV protocol is less than the actual path duration, due to the implementation of the settling time concept and keeping the \"periodic routes' update\" parameter at a constant level, despite the fact that the node's speed reduces the effective path utilization. m 2022 11 23 2022 20  
of other nodes can establish a direct communication link, otherwise they cooperate with intermediate nodes to manage the connection. MANETs have many interesting applications that fulfill human needs. Examples of such applications are military fields, emergency situations and natural disasters, etc. In such applications, it is extremely impossible to rely on fixed infrastructures due to their absence or their high implementation costs [4; 5]. Routing information in MANETs is a big issue, and puts several challenges to researchers on how to design suitable routing protocols to handle them. Therefore, many routing protocols have been developed that are compatible with the characteristics and the dynamic nature of these networks. Existing routing protocols have their own design mechanisms to improve some of the MANET performance metrics. Among the most important metrics are throughput, Packet Delivery Ratio (PDR), routing overhead and end-to-end delay [5; 6]. These metrics are interrelated and interdependent; this means that working to improve one often leads to negatively affecting others. Routing protocols in MANETs are broadly classified into three categories: proactive, reactive or hybrid [7; 8]. In proactive-based routing, every node manages its own routing table/s to store the routing information for all connected nodes. To keep the routing information constantly updated, the nodes exchange update messages frequently or periodically. This method makes routing information available whenever needed, but at the same time, increases routing overhead. Examples of this category are Fisheye State Routing protocol (FSR) [9] and Optimized Link State Routing protocol (OLSR) [10]. In reactive protocols, the nodes do not retain routing information--instead, they broadcast route requests to the destination node on demand. This step is only performed when data routing is required, which increases the throughput, but also increases the end-to-end delay. Ad Hoc On-demand Distance Vector (AODV) [11] and Dynamic Source Routing (DSR) [12] are well-known routing protocols belonging to this category. Hybrid protocols like Zone Routing Protocol (ZRP) [13] and Temporally-Ordered Routing Algorithm (TORA) [14] utilize the positive characteristics of both mechanisms (proactive and reactive) to improve the performance of the routing process.