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Automobile System Safety Based on the Model for Stochastic Networks with Dependent Service Times

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

Broadband wireless data transmission network for providing of automobile transport system safety is considered. The network operates under IEEE802.11n-2012 protocol that guarantees high-speed transmission of multimedia information from stationary and mobile automatic systems of traffic control. The model of stochastic network with dependent service time and processor sharing discipline for the problem solution is used. Product-form representation for the model steady-state probabilities is presented.

The paper have been supported by RFBR grants number 13-07-00737.

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References

  1. J.R. Jackson, Networks of waiting lines. Oper. Res. 5, 518–521 (1957). No. 4

    Article  Google Scholar 

  2. J.R.J. Job, Shop-like queueing systems. Manag. Sci. 10, 131–142 (1963). No. 1

    Article  Google Scholar 

  3. W.J. Gordon, G.F. Newell, Closed queueing systems with exponential servers. Oper. Res. 15(2), 254–265 (1967)

    Article  MATH  Google Scholar 

  4. F. Baskett, K.H. Chandy, R.R. Muntz, F.G. Palacios, Open, closed and mixed networks of queues with different classes of customers. J. ACM 22(22), 248–260 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  5. F.P. Kelly, Network of queues. Adv. Appl. Probab. 8, 416–432 (1976). No. 2

    Article  MATH  Google Scholar 

  6. F.P. Kelly, Reversibility and Stochastic Networks (Wiley, Chichester, 1979)

    MATH  Google Scholar 

  7. G.P. Basharin, A.L. Tolmachev, Queueing networks theory and their applications to the analysis of computer communication systems, in Itogi Nauki Techniki. Teoria Veroatn. Matem. Statist. Techn. Kibern. M.: VINITI, vol. 21 (1983), pp. 3–120

    Google Scholar 

  8. M.Ya. Kelbert, Yu.M. Sukhov, Mathematical problems of the network theory with queues, in Itogi Nauki Techniki. Teoria Veroatn. Matem. Statist. Techn. Kibern. M.: VINITI, vol. 26 (1988), pp. 3–96

    Google Scholar 

  9. R.J. Boucherie, Product Form in Queueing Networks (Thesis Publishers, Amsterdam, 1992)

    Google Scholar 

  10. N.M. van Dijk, Queueing Networks and Product Forms. A System Approach (Wiley, New York, 1993)

    Google Scholar 

  11. R. Serfozo, Introduction to Stochastic Networks (Springer, New York, 1999). 300 pp.

    Book  MATH  Google Scholar 

  12. V. Vishnevsky, Encyclopedia of WiMAX. Way to 4G (Technospera, Moscow, 2009). 472 pp.

    Google Scholar 

  13. R.L. Dobrushin, Yu.M. Sukhov, Asymptotic investigation of star-type networks with message commutation and large number of lines. Probl. Inf. Transm. 12, 70–94 (1976). No. 1

    MATH  Google Scholar 

  14. M.Ya. Kelbert, Yu.M. Sukhov, On a class of star-type communication networks with package commutation. Probl. Inf. Transm. 15, 53–72 (1979). No. 4

    MathSciNet  Google Scholar 

  15. J.M. Harrison, A.J. Lemoin, Note on networks on infinity server queues. J. Appl. Probab. 18, 561–567 (1981). No. 2

    Article  MATH  MathSciNet  Google Scholar 

  16. A.L. Tolmachev, Queueing network with regenerative service mechanism. Probl. Inf. Transm. 22, 59–68 (1986). No. 2 (in Russian)

    MathSciNet  Google Scholar 

  17. V.V. Rykov, Two approach to decomposition of the complex hierarchical stochastic systems. Continuously interacting subsystems. Autom. Remote Control 10, 91–104 (1997)

    MathSciNet  Google Scholar 

  18. V.V. Rykov, Two approach to decomposition of the complex hierarchical stochastic systems. Aggregative interacting systems. Autom. Remote Control 12, 140–149 (1997)

    MathSciNet  Google Scholar 

  19. V.V. Rykov, On decomposition of hierarchical computer communication network. Appl. Math. Inform. 2, 110–125 (1996)

    Google Scholar 

  20. A.V. Pechinkin, V.V. Rykov, On product form for open queuing systems with dependent service times, in Proceedings of the International Workshop (IPPI, Moscow, 1998), pp. 34–48

    Google Scholar 

  21. A.V. Pechinkin, V.V. Rykov, On decomposition of closed networks with dependent service times. Autom. Remote Control 60, 1568–1576 (1999). No. 11

    MATH  MathSciNet  Google Scholar 

  22. A.V. Pechinkin, V.V. Rykov, Product form for open queueing networks with dependent service times, in Proceedings of the International Conference: Distributed Computer Communication Networks. Theory and Applications (Institute for Information Transmission Problems RAS, Moscow, 1997), pp. 171–178

    Google Scholar 

  23. V.M. Vishnevsky, A new generation of safety systems on roads and their applications in intellectual transport systems. Inf. Technol. Comput. Syst. 4, 17–26 (2013) (in Russian)

    Google Scholar 

  24. D. Revuz, Markov Chains (North-Holland, Amsterdam, 1984)

    MATH  Google Scholar 

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Correspondence to Vladimir Vishnevsky .

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Vishnevsky, V., Rykov, V. (2015). Automobile System Safety Based on the Model for Stochastic Networks with Dependent Service Times. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_81

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