In this paper, we analyze the delay of the message delivery from a vehicle to a downstream vehicular gateway in a sparse vehicle ad hoc network (VANET). Several research efforts have previously been devoted to the calculations of the rehealing delay in the restoration of a network disconnection; however, most of them focus only on the delivery of upstream messages. In this paper, we analyze the end-to-end delay of downstream message deliveries. This analysis is essential for many applications, e.g., aggressive driving identification, that requires regular collection of vehicle data, such as speed, location, etc. In our analysis, we calculate the first two moments of the rehealing delay, then utilize the central limit theorem (CLT) to derive the end-to-end delay distribution. Simulation results confirm that our analysis is very accurate for both the mean and the variance of the rehealing delay. It is observed from numerical results that opposite-directional traffic intensity plays a more important role in deciding the end-to-end delay than same-directional traffic intensity, and that comparing between up- and down-stream message deliveries, the former has a slightly shorter delay than the latter when traffic intensity is low, but they are comparable when it is high.
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