# A Mathematical-Based Model for Estimating the Path Duration of the DSDV Routing Protocol in MANETs
## 2 Related Work
using the Newton divided difference method. In this method, each node determines its links' breakage time, and forwards this information to other nodes in advance. Based on this information, the route discovery process will be initiated earlier to find alternate routes. The proposed approach was implemented on AODV routing protocol. Compared to the generic AODV, the results of the new proposal showed that packet loss and average end-to-end delay were significantly reduced and data packet delivery ratio was increased. [PERSON], [PERSON] [27] suggested an analytical model to estimate the average path duration in multihop routing using the Random Way Point (RWP) model. This work considered the node density as a network parameter and studied its impact on the path duration. The results have shown that the average path duration can be analytically predicted for the shortest path routing. Moreover, they showed that the analytical prediction of the average path duration parameter is beneficial in optimizing the routing functionalities such as TTL of a given routing protocol. [PERSON], et al. [28] conducted a study to examine the duration probability and availability of routing paths that are subjected to frequent disconnections and link failures caused by the mobility nature of mobile nodes. This study specifically focused on the scenarios where the mobile nodes move according to the RWP model and derived the approximate and actual expressions of these probabilities to select the optimal routes in terms of path availability. It also proposed an approach to find the best routes of reactive routing protocols to improve the efficiency and reduce the routing overhead. [PERSON], et al. [29] developed an analytical model to predict both the link duration and the path duration in multi-hop WSNs. The developed model was tested using 50 simulation scenarios with various transmission and mobility conditions on two simulation platforms (NS2 and MATLAB). They found out that both the predicted and measured results are consistent with the simulation results estimated by the analytical equations derived from the analytical model. [PERSON], et al. [30] developed a new routing algorithm to increase the link duration, improve routing stability and reduce the overall control overhead in high-mobility MANET scenarios. Compared to the existing reactive routing protocols, which consider only disjoint paths, a new discovery concept called non-disjoint paths was introduced in this approach. This study also introduced an approach to find the best estimation of the link lifetime without the need for Global Positioning System (GPS) services. The new approaches were simulated and the traffic overhead analysis showed good performance with promising results. [PERSON], et al. [31] developed another approach to examine the effect of some path duration statistics (PDFs) that vary according to some network parameters such as relative node speed, hop count, transmission range and mobility model. The obtained results argued that at low mobility speeds, some mobility models may induce multimodal distributions that affect some characteristics such as mobility constraints, spatial map and traffic pattern, while at moderate to high velocities, the exponential distribution can provide good path duration approximation for a number of mobility models. [PERSON] and [PERSON] [32] proposed a hybrid location-based prediction model to estimate the probable locations of mobile nodes with respect to their neighborhoods based on spatial and temporal characteristics. They developed a multi-path routing protocol considering the estimated probability of nodes' locations with path diversion, in order to improve the routing performance and reduce packets' overhead. In summary, to the best of the authors' knowledge, mathematical modeling of proactive routing protocols to estimate the link and path durations are at developing stages.