# A Mathematical-Based Model for Estimating the Path Duration of the DSDV Routing Protocol in MANETs
###### Abstract
Due to the permanent movement of the nodes, their connections' links are continuously broken. All the metrics mentioned above are affected by the age of the links established between nodes. This means that the path duration between any source-destination communication's link might affect the performance metrics of the routing protocols. In the case the path duration is too long, there is greater throughput, greater PDR and lower routing overhead and vice versa. The path duration mainly depends on three parameters: speed of the node, direction of movement, and range of transmission signals. Destination Sequenced Distance Vector (DSDV) [15; 16] is a well-known MANET routing protocol, which has been extensively used by the researchers to enhance its performance. Many recent extended versions of this protocol were developed, such as Proactive Routing Protocol for Multi-Channel Wireless Ad Hoc Networks (DSDV-MC) [17], Hash-MAC-DSDV [18], Intelligent Promising Support DSDV (IPS DSDV) [19] and others are appearing on the horizon. It is a proactive loop-free distance vector routing protocol where the nodes periodically forward data packets based on their routing information. Upon receiving the data, the neighboring nodes update their routing tables accordingly. In this case, the required updates will be inserted into the routing table in various settings, e.g., when any required information for a specific destination is missing from the routing table, when the current update message contains a larger sequence number or when the update message with a similar sequence number contains a shorter connection path (smaller hop count). A new update in the routing table will be instantly forwarded to the neighboring nodes and the routing information will be periodically rebroadcast again to reach the convergence state. Figure 1 shows an example scenario of this process. In this scenario, node (A) represents a new device that joined the network recently, so the routing table of node (A) shows only its routing information. All nodes periodically exchange the contents of their routing tables, and each record in the table contains the identity of the node, the number of hops and the sequence number of the record. When node (B) receives the updates from node (A), it increases the hop count to the destination by 1, and adds the new updates to its routing table. In the next periodic update, node (B) forwards its updated routing table to the other neighbors. The DSDV routing table contains the following five fields:  
* Next hop: refers to the next node to be visited along the path from the source to the final destination. * Metric: represents the number of nodes involved in packets' forwarding along the path from the source to the destination. * Sequence number: a unique identifier given to each update message to distinguish between new and old updates. * Settling time: the amount of elapsed time set by the node before broadcasting the incoming updates (this timer will be reset for each update). * Hold down time: the amount of time that determines the lifetime of the record, i.e., marking the record as expiry to consider broken connection. Since the link and path durations play a crucial role in designing high-efficiency routing protocols, this is mainly due to their direct impact on throughput, end-to-end delay and routing overhead; having their values estimated in advance for a given network scenario can help in the optimal selection of other network parameters such as Time to Live (TTL)--a predetermined value that controls the lifetime of a given packet--and an optimal packet length, which minimizes the overall packet loss. However, the prediction of these durations for a given path is a challenging issue, as the estimation process mainly depends on several dynamic parameters such as node velocity, node direction, network size and number of nodes. Furthermore, due to the mobility nature of MANETs, the connectivity graph may change frequently, i.e., active links which are currently available might not be available at other times.