Crossover conflict never happens for trains which use the same track. A crossover conflict happens in events which occur consecutively. These properties can be rephrased in terms of graph theory as crossover conflicts do not happen between two nodes n1 and n2 such that there exists a path from n1 to n2 or from n2 to n1. Order interchangeable node sets for departing order decision are found as a set which consists of a local train and express trains which are overtaking and which are likely to overtake the local train. Figure 2 shows an example of a train schedule, and in Figure 3, a train schedule network with node order interchangeable sets created from the schedule of Figure 2 is depicted.
Nodes connected by dotted lines are order interchangeable node sets.
Conclusions We have introduced an idea to express a train schedule by a PERT network with order interchangeable node sets. We have also developed a new train traffic simulation method called hybrid simulation using this network and a knowledge base for change of train orders. We believe that ours is an effective simulation method combining a mathematical programming method and a knowledge-based method, and this approach is quite useful to develop a practical expert system. Tokyo 185, Japan.