The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Baccelli, François. Ergodic theory of stochastic Petri networks. Ann. Probab. 20 (1992), no. 1, 375--396. MR1143426 (93a:68110)
  2. Baccelli, François Louis; Cohen, Guy; Olsder, Geert Jan; Quadrat, Jean-Pierre. Synchronization and linearity.An algebra for discrete event systems.Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Ltd., Chichester, 1992. xx+489 pp. ISBN: 0-471-93609-X MR1204266 (94b:93001)
  3. F. Baccelli and D. Hong. Tcp is max-plus linear and what it tells us on its throughput. In SIGCOMM 00:Proceedings of the conference on Applications, Technologies, Architectures and Protocols for Computer Communication, pages 219--230. ACM Press, 2000.
  4. Baccelli, François; Liu, Zhen. On a class of stochastic recursive sequences arising in queueing theory. Ann. Probab. 20 (1992), no. 1, 350--374. MR1143425 (93c:60137)
  5. Bousch, Thierry; Mairesse, Jean. Finite-range topical functions and uniformly topical functions. Dyn. Syst. 21 (2006), no. 1, 73--114. MR2200765 (2006k:26020)
  6. H. Braker. Algorithms and Applications in Timed Discrete Event Systems. PhD thesis, Delft University of Technology, Dec 1993.
  7. Cohen, Guy; Dubois, Didier; Quadrat, Jean-Pierre; Viot, Michel. A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing. IEEE Trans. Automat. Control 30 (1985), no. 3, 210--220. MR0778424 (86c:93002)
  8. Cohen, Joel E. Subadditivity, generalized products of random matrices and operations research. SIAM Rev. 30 (1988), no. 1, 69--86. MR0931278 (89g:60300)
  9. de Kort, A. F.; Heidergott, B.; Ayhan, H. A probabilistic $(max,+)$ approach for determining railway infrastructure capacity. European J. Oper. Res. 148 (2003), no. 3, 644--661. MR1976565
  10. Gaubert, Stéphane; Mairesse, Jean. Modeling and analysis of timed Petri nets using heaps of pieces. IEEE Trans. Automat. Control 44 (1999), no. 4, 683--697. MR1684424 (99m:68139)
  11. Griffiths, Robert B. Frenkel-Kontorova models of commensurate-incommensurate phase transitions. Fundamental problems in statistical mechanics VII (Altenberg, 1989), 69--110, North-Holland, Amsterdam, 1990. MR1103829 (92c:82042)
  12. Heidergott, Bernd. A characterisation of $(max,+)$-linear queueing systems. Queueing Systems Theory Appl. 35 (2000), no. 1-4, 237--262. MR1782609 (2001h:90014)
  13. Heidergott, Bernd; Oldser, Geert Jan; van der Woude, Jacob. Max plus at work.Modeling and analysis of synchronized systems: a course on max-plus algebra and its applications.Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, 2006. xii+213 pp. ISBN: 978-0-691-11763-8; 0-691-11763-2 MR2188299 (2006g:93079)
  14. D. Hong. Lyapunov exponents: When the top joins the bottom. Technical Report RR-4198, INRIA, http://www.inria.fr/rrrt/rr-4198.html, 2001.
  15. Mairesse, Jean. Products of irreducible random matrices in the $(max,+)$ algebra. Adv. in Appl. Probab. 29 (1997), no. 2, 444--477. MR1450939 (98k:60165)
  16. G. Merlet. Produits de matrices al'eatoires : exposants de Lyapunov pour des matrices al'eatoires suivant une mesure de Gibbs, th'eor`emes limites pour des produits au sens max-plus. PhD thesis, Universit'e de Rennes, 2005. http://tel.archives-ouvertes.fr/tel-00010813.
  17. G. Merlet. Law of large numbers for products of random matrices in the (max,+) algebra. Technical report, Keio University, http://hal.archives-ouvertes.fr/ccsd-00085752, 2006.
  18. J.-M. Vincent. Some ergodic results on stochastic iterative discrete events systems. Discrete Event Dynamic Systems, 7(2):209--232, 1997.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.