<span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Wireless devices have been equiping extensive services over recent years. Since most of these devices are randomly distributed, a fundamental trade-off to be addressed is the transmission rate, latency, and packet loss of the ad hoc route selection in device to device (D2D) networks. Therefore, this paper introduces a notion of weighted transmission rate and total delay, as well as the probability of packet loss. By designing optimal transmission algorithms, this proposed algorithm aims to select the best path for device-to-device communication that maximizes the transmission rate while maintaining minimum delay and packet loss. Using the Lagrange optimization method, the lagrangian optimization of rate, delay, and the probability of packet loss algorithm (LORDP) is modeled. For practical designation, we consider the fading effect of the wireless channels scenario. The proposed optimal algorithm is modeled to compute the optimal cost objective function and represents the best possible solution for the corresponding path. Moreover, a simulation for the optimized algorithm is presented based on optimal cost objective function. Simulation results establish the efficiency of the proposed LORDP algorithm</span><span>.</span><span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Wireless devices have been equiping extensive services over recent years. Since most of these devices are randomly distributed, a fundamental trade-off to be addressed is the transmission rate, latency, and packet loss of the ad hoc route selection in device to device (D2D) networks. Therefore, this paper introduces a notion of weighted transmission rate and total delay, as well as the probability of packet loss. By designing optimal transmission algorithms, this proposed algorithm aims to select the best path for device-to-device communication that maximizes the transmission rate while maintaining minimum delay and packet loss. Using the Lagrange optimization method, the lagrangian optimization of rate, delay, and the probability of packet loss algorithm (LORDP) is modeled. For practical designation, we consider the fading effect of the wireless channels scenario. The proposed optimal algorithm is modeled to compute the optimal cost objective function and represents the best possible solution for the corresponding path. Moreover, a simulation for the optimized algorithm is presented based on optimal cost objective function. Simulation results establish the efficiency of the proposed LORDP algorithm</span>
Intuitions About Lagrangian Optimization