Hopping on an earlier flight: Optimal waiting with multiple flights

When should travellers leave for the airport? This paper develops a model for optimal airport arrival timing when travellers face uncertain travel times and can potentially board earlier flights. We show that access to earlier flights creates a “recourse option†that fundamentally changes optimal behaviour. While earlier flights always reduce the probability of missing one’s scheduled departure, they may paradoxically increase expected waiting time when travellers adjust their arrival strategies. Using renewal theory and a high-frequency (small-headway) limit, we show that with frequent service the expected residual waiting approaches half the headway between departures (up to lower-order terms). We connect the problem to newsvendor theory, showing how the fixed penalty for missing flights (rather than linear costs) leads to distinct optimality conditions. Our results explain why rational travellers should occasionally miss flights and provide practical guidelines for airlines designing standby policies and for travellers making departure decisions.