Kronecker Algebra-based Deadlock Analysis for Railway Systems
Downloads
Downloads
Stallings, W.: Operating Systems, 4th Ed., Upper Saddle River, New Jersey: Prentice-Hall, 2001
Coffman, E. G. J., Elphick, M. J. and Shoshani, A.: “System deadlocks,” ACM Computing Surveys, Vol. 3, No. 2, pp. 67-78,
Dijkstra, E. W.: “Een algorithme ter voorkoming van de dodelijke omarming (EWD-108)”.
Mittermayr, R. and Blieberger, J.: “Shared Memory Concurrent System Verification using Kronecker Algebra”, 2011. [Online]. Available: http://arxiv.org/abs/1109.5522.
Miller, J.: “Earliest Known Uses of Some of the Words of Mathematics”, 2011. [Online]. Available: http://jeff560.tripod.com/k.html. [Accessed 26 Sept. 2011]
Bellman, R.: Introduction to Matrix Analysis, Classics in Applied Mathematics, 2nd Ed., Society for Industrial and Applied Mathematics, 1997
Graham, A.: Kronecker Products and Matrix Calculus with Applications, New York: Ellis Horwood Ltd., 1981
Davio, M. “Kronecker Products and Shuffle Algebra”, IEEE Trans. Computers, Vol. 30, No. 2, pp. 116-125, 1981
Hurwitz, A.: “Zur Invariantentheorie”, Math. Annalen, Vol. 45, pp. 381-404, 1894
Plateau, B. and Atif, K.: “Stochastic Automata Network For Modeling Parallel Systems”, IEEE Trans. Software Eng., Vol. 17, No. 10, pp. 1093-1108, 1991
Küster, G.: “On the Hurwitz Product of Formal Power Series and Automata”, Theor. Comput. Science, Vol. 83, No. 2, pp. 261-273, 1991
Imrich, W., Klavzar, S. and Rall, D. F.: Topics in Graph Theory: Graphs and Their Cartesian Product, A K Peters Ltd, 2008
Knuth, D. E.: Combinatorial Algorithms, The Art of Computer Programming, Vol. 4A, Addison-Wesley, 2011
Dijkstra, E. W.: “A note on two problems in connexion with graphs”, Numerische Mathematik, Vol. 1, pp. 269-271, 1959
Fredman, M. L. and Tarjan, R. E.: “Fibonacci heaps and their uses in improved network optimization algorithms”, in 25th Annual Symposium on Foundations of Computer Science, 1984
Henderson, P. and Morris, J. J. H.: “A Lazy Evaluator”, in Proceedings of the 3rd ACM SIGACT-SIGPLAN symposium on Principles on programming languages, 1976
Buchholz, P. and Kemper, P.: “Efficient Computation and Representation of Large Reachability Sets for Composed Automata”, Discrete Event Dynamic Systems, Vol. 12, No. 3, pp. 265-286, 2002
Mittermayr, R. and Blieberger, J.: Timing Analysis of Concurrent Programs, In Proc. of 12th Int. Workshop on Worst-Case Execution Time Analysis, 2012
Plateau, B.: “On the Stochastic Structure of Parallelism and Synchronization Models for Distributed Algorithms”, ACM SIGMETRICS, Vol. 13, pp. 147-154, 1985
Ciardo, G. and Miner, A. S.: “A Data Structure for the Efficient Kronecker Solution of GSPNs”, in Proc. 8th Int. Workshop on Petri Nets and Performance Models (PNPM'99), 1999
Cui, Y.: Simulation-Based Hybrid Model for a Partially-Automatic Dispatching of Railway Operation, I. f. E. u. Verkehrswesen, Ed., Universität Stuttgart: PhD thesis, 2010
Martin, U.: Verfahren zur Bewertung von Zug- und Rangierfahrten bei der Disposition, TU Braunschweig: PhD thesis, 1995
Pachl, J.: Steuerlogik für Zuglenkanlagen zum Einsatz unter stochastischen Betriebsbedingungen, TU Braunschweig: PhD thesis, 1993
Petersen, E. and Taylor, A.: “Line Block Prevention in Rail Line Dispatch”, INFOR Journal, Vol. 21, No. 1, pp. 46-51, 1983
Mills, G., Pudney, P. J., White, K. and Hewitt, J.: “The effects of deadlock avoidance on rail network capacity and performance”, in Proc. of the 2003 mathematics-in-industry study group, 2003
Lu, Q., Dessouky, M. and Leachman, R. C.: “Modeling Train Movements Through Complex Rail Networks”, ACM Transactions on Modeling and Computer Simulation, Vol. 14, No. 1, pp. 48-75, 2004
Fanti, M. P., Giua, A. and Seatzu, C.: “A deadlock prevention method for railway networks using monitors for colored Petri nets”, in Proc. of Int. Conf. on Systems, Man and Cybernetics, 2003
Zarnay, M.: “Solving deadlock states in model of railway station operation using coloured Petri nets”, in Proceedings of Symposium FORMS/FORMAT, 2008
Zehfuss, J. G.: “Ueber eine gewisse Determinante,” Zeitschrift für Mathematik und Physik, Vol. 3, pp. 298-301, 1858