On the Analytical Calculation of the Probability Distribution of End-to-End Delay in a Two-Way Highway VANET

In several papers, analytical calculations of the mean value of the end-to-end delay in highway vehicular ad-hoc networks (VANETs) have been presented. Unfortunately, none of these papers presented calculations of the probability distribution of this delay, which is necessary to give probabilistically guaranteed upper bounds on the end-to-end delay in such VANETs. In a previous paper, we introduced the first analytical framework for the calculation of the probability distribution, and not only the mean, of the end-to-end delay in multi-lane one-way highway VANETs. This made it possible to provide guarantees of transmission in a given time frame with known confidence. In this paper, that previous work is extended to two-way multi-lane highways by taking into consideration vehicles travelling in both directions. The probability distribution of the end-to-end delay is calculated herein and its dependence on system parameters, such as speed distributions in the two directions, communication range, and vehicle densities, are analyzed. Computer simulations are used to verify the analytical model. The good agreement between simulation results and the analytical calculations demonstrates the correctness and accuracy of the proposed analytical model.