Kronecker Algebra-based Deadlock Analysis for Railway Systems

Deadlock analysis for railway systems differs in several aspects from deadlock analysis in computer science. While the problem of deadlock analysis for standard computer systems is well-understood, multi-threaded embedded computer systems pose new challenges. A novel approach in this area can easily be applied to deadlock analysis in the domain of railway systems. The approach is based on Kronecker algebra. A lazy implementation of the matrix operations even allows analysing exponentially sized systems in a very efficient manner. The running time of the algorithm does not depend on the problem size but on the size of the solution. While other approaches suffer from the fact that additional constraints make the problem and its solution harder, our approach delivers its results faster if constraints are added. In addition, our approach is complete and sound for railway systems, i.e., it generates neither false positives nor false negatives.

[1]  Johann Blieberger,et al.  Shared Memory Concurrent System Verification using Kronecker Algebra , 2011, ArXiv.

[2]  Yong Cui.  Simulation based hybrid model for a partially automatic dispatching of railway operation , 2010 .

[3]  A. J. Taylor,et al.  Line Block Prevention In Rail Line Dispatch And Simulation Models , 1983 .

[4]  Marc Davio,et al.  Kronecker products and shuffle algebra , 1981, IEEE Transactions on Computers.

[5]  Peter Buchholz,et al.  Efficient Computation and Representation of Large Reachability Sets for Composed Automata , 2002, Discret. Event Dyn. Syst..

[6]  Brigitte Plateau.  On the stochastic structure of parallelism and synchronization models for distributed algorithms , 1985, SIGMETRICS 1985.

[7]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[8]  Gianfranco Ciardo,et al.  A data structure for the efficient Kronecker solution of GSPNs , 1999, Proceedings 8th International Workshop on Petri Nets and Performance Models (Cat. No.PR00331).

[9]  Michal Žarnay,et al.  SOLVING DEADLOCK STATES IN MODEL OF RAILWAY STATION OPERATION USING COLOURED PETRI NETS , 2008 .

[10]  Maged M. Dessouky,et al.  Modeling train movements through complex rail networks , 2004, TOMC.

[11]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[12]  Richard Bellman,et al.  Introduction to matrix analysis (2nd ed.) , 1997 .

[13]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[14]  Johann Blieberger,et al.  Timing Analysis of Concurrent Programs , 2012, WCET.

[15]  Alessandro Giua,et al.  A deadlock prevention method for railway networks using monitors for colored Petri nets , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[16]  Peter Henderson,et al.  A lazy evaluator , 1976, POPL.

[17]  Wilfried Imrich,et al.  Topics in Graph Theory: Graphs and Their Cartesian Product , 2008 .

[18]  Brigitte Plateau,et al.  Stochastic Automata Network For Modeling Parallel Systems , 1991, IEEE Trans. Software Eng..

[19]  Gerhard Küster.  On the Hurwitz Product of Formal Power Series and Automata , 1991, Theor. Comput. Sci..

[20]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

[21]  Arie Shoshani,et al.  System Deadlocks , 1971, CSUR.