# A Mathematical-Based Model for Estimating the Path Duration of the DSDV Routing Protocol in MANETs
## 2 Related Work  
Although the routing process in MANETs is very hot research area, it is clearly shown in the literature that the majority of the contributions used simulation testbeds to implement and validate the developed routing protocols, compared to the mathematical models that have been developed so far. Existing mathematical models examined some of the reactive routing protocols that have adopted very specific conditions to build the mathematical models and this is due to the fact that the adoption of a mathematical model that considers all MANET's factors make the mathematical model very complex. A brief description of each model is given below. [PERSON], et al. [20] proposed a new statistical-based scheme named Least-Square Quadratic Polynomial Regression-Based-Link Failure (LSQPR-LFE) to estimate the link failure time in MANETs. It builds an optimal error quadratic model between packet arrival time and node distance considering signal levels of the delivered packets. The link failure time was calculated by obtaining the moment at which the maximum communication range will be reached. Several simulations scenarios were implemented to test the accuracy of the proposed scheme, considering various mobility models, node density and node velocity. In their proposed model, [PERSON] and [PERSON] [21] analyzed the path duration using three parameters: node speed, signal level and node density. The main assumption is that the next hop is selected using a function of the Least Remaining Distance (LRD) to the final destination. [PERSON], et al. [22] proposed a routing protocol called Route Stability-based QoS routing (RSQR) to estimate the probability of link failures based on two parameters: node mobility and signal strength. It determines mobility speeds and relative positions of nodes without requiring any geographical information for nodes. It first uses the signal strength values from the MAC sublayer to compute link stability. Next, it uses less control overhead without enforcing a periodic pilot packet exchange to compute link stability values. [PERSON], et al. [23] developed a new a routing scheme titled Mobility, Residual energy, and Link quality Aware Multipath (MRLAM) to address the potential drawbacks of MANETs in the areas of link quality, battery consumption and mobility nature. In this routing scheme, a Q-Learning algorithm was implemented to manage the process of selecting the optimal set of intermediate nodes based on link quality, mobility and energy level parameters of a given scenario, positive and negative rewards are assigned to each node accordingly. Compared to other routing protocols, the proposed routing scheme showed a significant improvement in the overall performance in terms of consumed energy, end-to-end delay, packet loss ratio and convergence time. [PERSON], et al. [24] analyzed path and link lifetime in one-dimensional vehicle wireless networks. They assumed a uniform distribution of velocity and lognormal headway distance. The study analyzed the effect of mobility of the vehicles and the transmission range on the average lifetime of the link. They also performed the Kolmogorov-Smirnov test to find the best PDF fits for the link duration. The results have shown that the PDF of link duration can be estimated to be lognormal. [PERSON], et al. [25] conducted some experiments on two exiting statistical models: Autoregressive Integrated Moving Average (ARIMA); and multilayer perceptron (MLP) to predict the path length between a transmitter-receiver pair. They applied three different mobility models to collect path length data: the Random Way Point mobility model (RWP); the Manhattan Grid Mobility Model (MHG); and the Reference Point Group Mobility Model (RPGM). AODV routing protocol was used to evaluate the accuracy of the statistical models. The results showed that MLP-based neural network models outperform the ARIMA model in prediction accuracy. [PERSON], et al. [26] developed a prediction method to estimate the link availability based on the signal strength.