Randomness affecting the operation of public transport systems generates significant increments in waiting times. A strategy to deal with this randomness is bus injection, in which buses are kept in specific points along the route ready to be dispatched when an event such as an extremely long headway occurs. In this work, a stochastic model based on the second moment of the headways distribution is developed to determine if one or more buses are worth reserving for injection in a public transport service. A single stop approach is initially used to determine an expression for the optimal headway threshold triggering the injection. Then, a model for the complete service is developed and used to determine when the empty bus should be injected within the headway once the decision to inject it has been taken. We show that the bus should be injected approximately when 57% of the headway has passed. Simulations with real data are used to test the proposed model, proving its accuracy in terms of measuring the impact on waiting times. The results show that reserving a bus to be injected can be better than operating the entire fleet continuously.

影响公共交通系统运行的随机性会大大增加等待时间。一种应对这种随机性的策略是公交车注入，在这种情况下，公交车会被放置在沿路线的特定位置，以便在发生诸如极长车速之类的事件时进行调度。在这项工作中，建立了基于车距分布第二时刻的随机模型，以确定在公共交通服务中是否值得保留一辆或多辆公交车。一站式方法最初用于确定触发注射的最佳车距阈值的表达式。然后，开发出用于完整服务的模型，并用于确定一旦决定将空母线何时应在车距内注入。我们表明，应该在大约57％的行驶距离通过后注入公交车。使用真实数据进行的仿真用于测试所提出的模型，从而在测量对等待时间的影响方面证明了其准确性。结果表明，保留要注入的公交车比连续运行整个车队更好。