The delay incurred during which messages are transmitted by a vehicle to its downstream vehicles in a vehicle ad hoc network (VANET) is analyzed in this paper. In related works the recovery delay of rebuilding network disconnection has been calculated; however, most of them only consider upstream message transmissions. This work continues our previous research but uses a different analytical method. It is because our previous calculation method, in which the central limit theorem is used, is suitable for long distance message transmissions. When message transmissions are short-distance, previous analysis may lack good accuracy. Therefore, the recovery delay probability distribution for repairing a single network disconnection will first be calculated in this paper. Since the calculations include the sum of random variables, Laplace transform and its inverse transform will be used. Numerical results show that our analysis is very accurate.