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已有的求解股道分配问题的方法很少探讨强壮性，得到的股道分配方案中会有一些瓶颈. 要对这些瓶颈进行局部优化，就需要一定的方法来探测这些瓶颈. 本文首先利用Petri网技术将一个股道分配方案转换成可执行的动态模型，然后对每一项列车作业进行扰动分析，并利用全部列车的出发晚点时间来识别瓶颈. 最后，对一个衔接6个方向的车站平面图和一个持续时间约30分钟的股道分配方案进行分析，结果发现最小缓冲时间为21秒；方案中存在两处瓶颈，缓冲时间分别为57秒和44秒，这表明最小缓冲时间所对应的列车作业区域不一定是方案的瓶颈. 这种方法为强壮性优化以及多方案比选提供了技术支持.

Bottlenecks Detection of Track Allocation Schemes at Rail Stations by Petri Nets

Robustness of the track allocation problem is rarely addressed in literatures and the obtained track allocation schemes (TAS) embody some bottlenecks. Therefore,an approach to detect bottlenecks is needed to support local optimization. First a TAS is transformed to an executable model by Petri nets. Then distrubances ananlysis is performed using the model and the indicators of the total trains' departure delays are collected to detect bottlenecks when each train suffers an disturbance. Finally,the results of the tests based on a rail hub linking six lines and a TAS about thirty minutes show that the the minimum buffer time is 21 seconds and there are two bottlenecks where the buffer times are 57 and 44 seconds respectively,and it indicates that the bottlenecks do not certainly locate at the area where there is minimum buffer time. The proposed approach can further support selection of multi schemes and robustness optimization.