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In a vehicular delay tolerant network, the problem of scheduling the traffic from a roadside unit to passing-by vehicles is studied. A cost function is associated with a scheduled transmission. And if a delay bound is violated, a penalty cost is charged. The optimal stopping theory is applied to decide when the roadside unit should schedule its accumulated traffic to a passing-by vehicle such that the rate of cost is minimized. It is shown that the optimal scheduling strategy is a pure-threshold strategy, i.e., upon a vehicle arrival, if the queueing delay at the roadside unit is above a threshold, it is optimal to schedule a transmission via the vehicle. Simulation results validate the effectiveness of the derived optimal rule.