Applications of non-Markovian stochastic Petri nets

Performance Evaluation Review

Volumn 26, Issue 2, 1998, Pages 15-27

  Fricks, Ricardo M ^a   Puliafito, Antonio ^b   Telek, Miklós ^c   Trivedi, Kishor S ^d  

^a PONTIFICAL CATHOLIC UNIVERSITY OF PARANÁ   (Brazil)

^b UNIVERSITY OF CATANIA   (Italy)

^c BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^d Duke University   (United States)

Author keywords

Markov regenerative processes; Numerical analysis; Preemption policies; Stochastic Petri Nets

Indexed keywords

EID: 1842551208     PISSN: 01635999     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/288197.288204     Document Type: Article

References (42)

1. M. Ajmone Marsan, G. Conte, and G. Balbo, "A class of generalized stochastic Petri net for the performance evaluation of multiprocessor systems," ACM Transaction on Computer Systems, vol. 2, no. 2, pp. 93-122, May 1984.
2. G. Ciardo, A. Blakemore, P.F. Chimento, J.K. Muppala, and K.S. Trivedi, "Automatic generation and analysis of markov reward models using stochastic reward nets," in Linear Algebra, Markov Chains, and Queueing Models, IMA Volumes in Mathematics and its Applications, C. Meyer and R.J. Plemmons, Eds., Heidelberg, Germany, 1992, vol. 48, Springer-Verlag.
3. Kishor S. Trivedi, Probability & Statistics with Reliability, Queueing, and Computer Science Applications, Prentice-Hall, NJ, USA, 1982.
4. D.R. Cox, "The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables," Proceedings of the Cambridge Philosophical Society, vol. 51, no. 3, pp. 433-441, 1955.
5. R.F. Botta, C.M. Harris, and W.G. Marchai, "Characterizations of generalized hyperexponential distribution functions," Communications in Statistics - Stochastic Models, vol. 3, no. 1, pp. 115-148, 1987.
6. M.F. Neuts, "Renewal process of phase type," Naval Research Logistics Quartely, vol. 25, no. 3, pp. 445-454, 1978.
7. E. Çinlar, Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, NJ, USA, 1975.
8. V.G. Kulkarni, Modeling and Analysis of Stochastic Systems, Chapman & Hall, London, UK, 1995.
9. J. B. Dugan, K. S. Trivedi, R. M. Geist, and V.F. Nicola, "Extended stochastic Petri nets: Applications and analysis," Performance, pp. 507-519, 1984.
10. M. Ajmone Marsan and G. Chiola, "On Petri nets with deterministic and exponentially distributed firing times," Lecture Notes on Computer Science, vol. 266, pp. 132-145, 1987.
11. Aldo Cumani, "ESP - a package for the evaluation of stochastic Petri nets with phase-type distributed transition times," in Proceedings of International Workshop on Timed Petri Nets, Torino, Italy, July 1-3, 1985, pp. 144-151.
12. H. Choi, V.G. Kulkarni, and K.S. Trivedi, "Markov regenerative stochastic Petri nets," Performance Evaluation, vol. 20, pp. 337-357, 1994.
13. M. Telek, A. Bobbio, and A. Puliafito, "Steady state solution of MRSPN with mixed preemption policies," in 2nd Int. Performance and Dependability Symposium, Urbana-Champaign, IL, 1996, pp. 106-115, IEEE CS Press.
14. R. Marie and K. S. Trivedi, "A note on the effect of preemptive policies on the stability of a priority queue," Information Processing Letters, vol. 24, pp. 397-401, 1987.
15. M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani, "The effect of execution policies on the semantics and analysis of stochastic Petri nets," IEEE Transactions on Software Engineering, vol. SE-15, pp. 832-846, 1989.
16. A. Bobbio, V.G. Kulkarni, A. Puliafito, M. Telek, and K. Trivedi, "Preemptive repeat identical transitions in Markov regenerative stochastic petri nets," in Proceedings of the 6th International Workshop on Petri Nets and Performance Models - PNPM'95, Durham, NC, USA, October 3-6 1995, pp. 113-122.
17. J.A. Couvillon, R. Freire, R. Johnson, W.D. Obal, M.A. Qureshi, M. Rai, W. Sanders, and J.E. Tvedt, "Performability modeling with UltrasSAN," IEEE Software, vol. 8, pp. 69-80, September 1991.
18. C. Lindemann, "DSPNexpress: a software package for the efficient solution of deterministic and stochastic Petri nets," Performance Evaluation, vol. 22, pp. 3-21, 1995.
19. D.R. Cox, Renewal Theory, Methuen & Co. Ltd, London, England, 1967.
20. William Feller, An Introduction to Probability Theory and Its Applications, 2nd ed., John Wiley & Sons, New York, NY, USA, 1966.
21. R. German and C. Lindemann, "Analysis of stochastic Petri nets by the method of supplementary variables," Performance Evaluation, vol. 20, no. 1-3, pp. 317-335, May 1994.
22. S. Garg, A. Puliafito, M. Telek, and K. Trivedi, "Analysis of preventive maintenance in transactions based software systems," IEEE Transactions on Computers, vol. 47, pp. 96-107, January 1998.
23. A. Bobbio and M. Telek, "Markov regenerative SPN with nonoverlapping activity cycles," in Proceedings of the 1st Annual IEEE International Computer Performance & Dependability Symposium - IPDS'95, Erlangen, Germany, April 24-26 1995, pp. 124-133.
24. M. Telek, Some Advanced Reliability Modeling Techniques, C.Sc/Ph.D. thesis, Hungarian Academy of Science, Budapest, Hungary, 1994.
25. Harold Davis Thayer, The Theory of The Volterra Integral Equation of the Second Kind, Bloomington, Indiana, USA, 1930.
26. Reinhard German, "Transient analysis of deterministic and stochastic Petri nets by the method of supplementary variables," in Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems Conference - MASCOTS'95, Durham, NC, USA, January 18-20, 1995, pp. 394-398.
27. R. German, D. Logothetis, and K.S. Trivedi, "Transient analysys of Markov regenerative stochastic Petri nets: A comparison of approaches," in Proceedings of the 6th International Workshop on Petri Nets and Performance Models, Durham, NC, USA, October 3-6 1995, pp. 103-111.
28. M. Telek, A. Bobbio, L. Jereb, A. Puliafito, and K.S. Trivedi, "Steady state analysis of Markov regenerative SPN with age memory policy," in Lecture Notes in Computer Science, H. Beilner and F. Bause, Eds., 1995, vol. 977, pp. 165-179.
29. H. Brunner and P.J. van der Houwen, The Numerical Solution of Volterra Equations, North-Holland, New York, NY, USA, 1986.
30. Peter Linz, Analytical and Numerical Methods for Volterra Equations, vol. 7, SIAM Studies in Applied Mathematics, Philadelphia, PA, USA, 1985.
31. R. Fricks, M. Telek, A. Puliafito, and K. Trivedi, "Markov renewal theory applied to performability evaluation," in State-of-the Art in Performance Modeling and Simulation. Modeling and Simulation of Advanced Computer Systems: Applications and Systems, Kallol Bagchi and George Zobrist, Eds., Newark, NJ, EUA, 1997, pp. 193-236, Gordon and Breach Publishers.
32. D. Logothetis and K. Trivedi, "Dependability evaluation of the double counter-rotating ring with concentrator attachments," ACM/IEEE Transactions on Networks, vol. 2, no. 5, pp. 520-532, October 1994.
33. D. Logothetis and K. Trivedi, "Time-dependent behavior of redundant systems with deterministic repair," in Computations with Markov Chains, W. J. Stewart, Ed., Norwell, MA, USA, 1995, pp. 135-150, Kluwer Academic Publishers.
34. D. Logothetis and K. Trivedi, "The effect of detection and restoration times for error recovery in communication networks," Journal of Network and Systems Management, vol. 5, no. 2, pp. 173-195, June 1997.
35. V. Mainkar and K. Trivedi, "Approximate analysis of priority scheduling systems using stochastic reward nets," in Proceedings of the 13th International Conference on Distributed Computing Systems - ICDCS'93, Pittsburgh, PA, USA, May 1993, pp. 466-473.
36. M. Telek and A. Pfening, "Performance analysis of Markov regenerative reward models," Performance Evaluation, vol. 27 & 28, pp. 1-18, 1996.
37. G. Ciardo, J. Muppala, and K. Trivedi, "Spnp: Stochastic petri net package," in Proc. Int. Workshop on Petri Nets and Performance Models, Los Alamitos, CA, USA, December 1989, IEEE Computer Society Press, pp. 142-150.
38. H. Choi, V.G. Kulkarni, and K. Trivedi, "Transient analysis of deterministic and stochastic Petri nets," in Proceedings of the 14-th International Conference on Application and Theory of Petri Nets, Chicago, June 1993.
39. G. Ciardo and C. Lindemann, "Analysis of deterministic and stochastic Petri nets," in Proceedings International Workshop on Petri Nets and Performance Models - PNPM93 IEEE Computer Society, 1993, pp. 160-169.
40. D.L. Jagerman, "An inversion technique for the Laplace transform," The Bell System Technical Journal, vol. 61, pp. 1995-2002, October 1982.
41. A. Bobbio, A. Puliafito, M. Scarpa, and M. Telek, "Webspn: A web-accessible petri net tool," in Proceedings of the Int. Conf. on WEB based Modeling and Simulation, San Diego, CA, USA, January 11-14 1998.
42. C. Fröberg, Introduction to Numerical Analysis, 2nd. ed., Addison-Wesley Publishing Company, Reading, MA, USA, 1969.