Response-Time Models and Timeliness Hazard Rate

Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


In tagged customer approach, an arbitrary message/customer is picked as the tagged message/customer and its passage through the network (closed queuing, with finite steady-state distribution) is tracked. By this method, the problem of computing the response time distribution of the tagged customer is transformed into time to absorption distribution of a finite-state, continuous time Markov chain (CTMC), conditioned on the state of the system upon entry. Using the arrival theorem of Sevcik and Mitrani [8], distribution of the other customers in the network at the instant of arrival of tagged customer can be established. This allows obtaining the unconditional response time distribution.


Sensor Node Timeliness Failure Network Channel Network Delay Continuous Time Markov Chain 


  1. 1.
    Wesly WC, Chi-Man S, Kin KL (1991) Task response time for real-time distributed systems with resource contentions. IEEE Trans Softw Eng 17(10):1076–1092CrossRefGoogle Scholar
  2. 2.
    Diaz JL, Gracia DF, Kim K, Lee C-Gun, Bello LL, Lopez JM, Min SL, and Mirabella O (2002) Stochastic analysis of periodic real-time systems. In: Proceedings of the 23rd IEEE real-time systems symposium (RTSS’02)Google Scholar
  3. 3.
    Diaz JL, Lopez JM, Gracia DF (2002) Probabilistic analysis of the response time in a real time system. In: Proceedings of the 1st CARTS workshop on advanced real-time technologies, OctoberGoogle Scholar
  4. 4.
    Mitrani I (1985) Response time problems in communication networks. J R Statist Soc (Series B) 47(3):396-406 MathSciNetMATHGoogle Scholar
  5. 5.
    Muppala JK, Varsha M, Trivedi KS, Kulkarni VG (1994) Numerical computation of response-time distributions using stochastic reward nets. Ann Oper Res 48:155–184MATHCrossRefGoogle Scholar
  6. 6.
    Trivedi KS, Ramani S, Fricks R (2003) Recent advances in modeling response-time distributions in real-time systems. Proc IEEE 91:1023–1037CrossRefGoogle Scholar
  7. 7.
    Muppala JK, Trivedi KS (1991) Real-time systems performance in the presence of failures. IEEE Comp Mag 37–47Google Scholar
  8. 8.
    Sevick KC, Mitrani I (1981) The distribution of queueing network states at input and output instants. J ACM 28(2):353–471Google Scholar
  9. 9.
    Tindell K, Burns A, Wellings AJ (1995) Calculating controller area network (CAN) message response times. Control Eng Prac 3(2):1163–1169 CrossRefGoogle Scholar
  10. 10.
    Tindell KW, Hansson H, Wellings AJ (1994) Analyzing real-time communications: controller area network (CAN). In: Proceeding of real-time symposium, pp 259–263, DecemberGoogle Scholar
  11. 11.
    Nolte T, Hansson H, Norstrom C (2002) Minimizing can response-time jitter by message manipulation. In: Proceedings of the 8th real-time and embedded technology and application symposium (RTAS’02)Google Scholar
  12. 12.
    Trivedi KS (1982) Probability & Statistics with Reliability, Queueing, and Computer Science Applications. Prentice-Hall, Englewood CliffsGoogle Scholar
  13. 13.
    Nolte T, Hansson H, Norstrom C (2003) Probabilistic worst-case response-time analysis for the controller area network. In: Proceedings of the 9th real-time and embedded technology and application symposium (RTAS’03)Google Scholar
  14. 14.
    Law M, Kelton WD (2000) Simulation Modeling and Analysis. McGraw Hill, New YorkGoogle Scholar
  15. 15.
    Nolte T, Hansson H, Norstrom C, Punnekkat S (2001) Using bit-stuffing distributions in can analysis. In: IEEE/IEE real-time embedded systems workshop (RTES’01), DecemberGoogle Scholar
  16. 16.
    Hansson H, Norstrom C, Punnekkat S (2000) Integrating reliability and timing analysis of can-based systems. In: Proceedings of WCFS’2000-3rd IEEE international workshop on factory communication systems, pp 165–172, SeptemberGoogle Scholar
  17. 17.
    Lindgren M, Hansson H, Norstrom C, Punnekkat S (2000) Deriving reliability estimates of distributed real-time systems by simulation. In: Proceeding of 7th international conference on real-time computing system and applications, pp 279–286Google Scholar
  18. 18.
    Tipsuwan Y, Chow M-Y (2003) Control methodologies in networked control systems. Control Eng Prac 11(10):1099-1111CrossRefGoogle Scholar
  19. 19.
    Johnson BW (1989) Design and analysis of fault-tolerant digital systems. Addison Wesley, ReadingGoogle Scholar
  20. 20.
    Cox DR, Miller HD (1970) The theory of stochastic processes. Methuen, LondonGoogle Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology Bombay (IITB)Powai, MumbaiIndia
  2. 2.Department of Civil EngineeringIndian Institute of Technology Bombay (IITB)Powai, MumbaiIndia

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