关于步行与等待的说明
A Note on Walking Versus Waiting
摘要：
这种数学娱乐扩展了最近一篇论文的分析，该论文询问当旅行者在公共汽车站并且不知道下一辆公共汽车的时间时，最好建议他等待或开始向目的地步行。详细的分析和解决方案提供了一个非常一般的类的概率分布的公交车到达时间，和解决方案的特点是在一个功能类似的风险率在可靠性理论。本说明还审议了中途停靠问题。研究发现，即使车头时距不太长，最优策略也不总是最懒的。对于常见的特殊情况下，人们知道（统一）的车头时距，但不确切的时间表，它表明，应该等待，如果车头时距是小于步行时间（少巴士旅行时间），步行，如果车头时距是两倍以上。在这两者之间，等待或步行可能会更好，这取决于一个人是否有信心能够赶上路过的公共汽车。
英文摘要：
This mathematical recreation extends the analysis of a recent paper, asking when a traveller at a bus stop and not knowing the time of the next bus is best advised to wait or to start walking toward the destination. A detailed analysis and solution is provided for a very general class of probability distributions of bus arrival time, and the solution characterised in terms of a function analogous to the hazard rate in reliability theory. The note also considers the question of intermediate stops. It is found that the optimal strategy is not always the laziest, even when headways are not excessively long. For the common special case where one knows the (uniform) headway but not the exact timetable, it is shown that one should wait if the headway is less than the walking time (less bus travel time), and walk if the headway is more than twice this much. In between it may be better to wait or to walk, depending on one's confidence in being able to catch up to a passing bus.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
