FROM RAILWAY RESOURCE PLANNING TO TRAIN OPERATION a brief survey of complementary formalisations Martin Penicka* Department of Applied Mathematics‚ Faculty of Transportation Sciences‚ Czech Technical University‚ Na Florenci 25‚ CZ-11000 Prague penicka@fd.cvut.cz Dines Bjørner* Department of Computer Science‚ School of Computing‚ National University of Singapore‚ 3 Science Drive 2‚ Singapore 117543 E–Mail: bjorner@comp.nus.edu.sg‚ URL: http://www.comp.nus.edu.sg/cs/ Abstract From seasonal planning via day-to-day train operation to real-time monitoring and control of trains‚ software applications are becoming increasingly integrated. Timetabling implies train traffic. Train staff rosters and train car maintenance are initially derived from timetables and influences future timetables. In this extended abstract we shall sketch a formal model of Railway Nets‚ Timetables‚ Rosters‚ Maintenance‚ Station Interlocking‚ Line Direction Agree- ment and Automatic Line Signaling. The last three formal models are based on four integrated formal techniques (RAISE‚ Petri Nets‚ Live Sequence Charts and State Charts). The formal sketches are all “backed-up” by either a publication or a research report. Keywords: Railways‚ Planning‚ Timetabling‚ Rostering‚ Control‚ Interlocking‚ Signalling‚ RAISE‚ Petri Nets‚ Live Sequence Charts‚ State Charts‚ Technique Integration 1. Railway System A railway system can be modelled as a function from time (T) to states of a railway net (N), to states of all rolling stock (RS), to its timetable (TT), to states of all passengers (P) and freight (F). *This paper was written while the authors were at Inst. of Informatics & Modelling‚ Technical University of Denmark‚ DK-2800 Kgs. Lyngby‚ Denmark. The first author gratefully acknowledges support from the EU 5FP Network of Excellence Programme: CoLogNET: Computational Logic Network