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1 Introduction ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 1 1. 1 Developments of high-speed railway in China ¡­¡­¡­¡­¡­¡­ 1 1. 2 Aim and relevance of the book ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 3 1. 3 Literature review ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 7 1. 4 Contributions and outline of the book ¡­¡­¡­¡­¡­¡­¡­¡­¡­ 17 2 Appropriate timetable mode for China¡äs high-speed railway ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 20 2. 1 Non-cyclic timetable ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 20 2. 2 Cyclic timetable ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 25 2. 3 " Cyclic + non-cyclic" timetable ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 35 3 Definition of adding train paths problem ¡­¡­¡­¡­¡­¡­¡­¡­¡­ 43 3. 1 Model assumptions ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 43 3. 2 Objectives in ATP problem ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 46 3. 3 Modeling requirements ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 49 4 Mathematical model for adding train paths problem ¡­¡­¡­¡­ 56 4. 1 A general ATP model ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 56 4. 2 Extensions of the ATP problem model ¡­¡­¡­¡­¡­¡­¡­¡­ 66 4. 3 Objectives functions ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 74 4. 4 Experimental studies ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 78 5 Integration of train-set circulation and adding train paths problem ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 95 5. 1 The use of train-set in china¡äs HSR ¡­¡­¡­¡­¡­¡­¡­¡­¡­ 95 5. 2 Terminology and literature ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 97 5. 3 Special features of train-set planning in the ATP problem ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 102 5. 4 Formulation for train-set routing in adding paths problem ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­ 105