# A Mathematical-Based Model for Estimating the Path Duration of the DSDV Routing Protocol in MANETs
## 4 Model Analysis and Discussion  
To validate the proposed mathematical-based model and study the effect of the DSDV protocol on its path duration estimation, we have built two simulation scenarios (Table 1). In the first scenario, we selected a simulation area of 1000 \(\times\) 1000 m\({}^{2}\) and the node's signal range of 250 m and the mobility of the nodes and their velocities are selected using the  
Figure 8: Path duration from node A to node F showing the least links’ durations between all paths. RWP model. The velocity of each step is increased by 5 m/s, (5, 10, 15,... ). In the second scenario, we kept the scenario dimension as in the first one (1000 \(\times\) 1000 m\({}^{2}\)), and fixed the nodes' velocities at 10 m/s. The distribution of the movement of the nodes are kept random. The initial value of the signal range is 100 m, and this increases by 10 m in each step. The change in the signal range means a change in the hop count, which is needed to reach the destination node. Meanwhile, the node with a short-range signal requires more hops to reach the destination node. Table 1 summarizes these settings. Figure 9 illustrates the relationship between the node velocity and the path duration. It is observed that the path duration decreases with the increase in the node's speed, and it is significantly reduced when the speed exceeds 10 m/s. It is also noted that the actual path duration is longer than the DSDV path duration, and this difference increases by increasing the nodes' velocity. Furthermore, we found out that the analysis of the DSDV path duration is less than the actual path duration, since the DSDV protocol needs to wait for a time period (settling time) before rebroadcasting the routing information. During the waiting period, the nodes keep moving, and consequently the path duration of the DSDV protocol will be decreased. The nodes that install the DSDV instance periodically update their routing information. In the case the interval between the current and next update periods is longer than the path duration to the final destination, the node loses the connection to the destination node before the routing information is updated. Thus, the period between both update intervals is not fully utilized. Figure 10 shows the relationship between the utilization ratio of the path duration and the velocity of the node. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Scenario 1** & **Scenario 2** \\ \hline Simulation area & 1 km \(\times\) 1 km & 1 km \(\times\) 1 km \\ Signal range (radius) & 250 m & 100, 110, 120,... \\ Nodes’ velocity & 5, 10, 15,..., 30 m/s & 10 m/s \\ Mobility model & Random Waypoint & Random Waypoint \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The settings of the two implemented scenarios of the mathematical model parameters. Figure 9: The path duration vs. and the node velocity. From Figure 10, it is assumed that the periodic update time is 15 s, which is the default value used by the NS3 simulation environment. It is observed that the utilization rate of the DSDV path duration decreases as the velocity of the nodes increases. This is because the path duration decreases with the increase in nodes' velocity, while the periodic update remains constant. Figure 11 illustrates the relationship between the number of hops and the path duration. It is shown that the path duration is inversely proportional to the hop count, and it is considerably decreased when the hop count is greater 4. It is also noted that the actual path duration (Model) is greater than the observed DSDV path duration (NS3), and this difference increases with increasing the hop count metric. Furthermore, the path duration decreases more than the calculated path duration when the number of hops increases, and this can be attributed to the increase in the amount of data that must be exchanged by the nodes to update their records.