Skip to main content

Part of the book series: Applied Probability ((APPLIEDPROB,volume 1))

Abstract

Mathematical modeling, like painting or photography, is an art, requiring proper balance between composition and the ability to convey a message. A good mathematical model, aiming to present an idealistic image of a real-life situation, should be accurate as well as selective in its description, and should use mathematical tools worthy of the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brémaud, P. (1980) Point Processes and Queues (Martingale Dynamics). Springer-Verlag, Berlin.

    Google Scholar 

  2. Cherry, E. C. (ed) (1956) Information Theory. Butterworth, London.

    MATH  Google Scholar 

  3. Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities, 2nd edn. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  4. Chung, K. L. and Rao, M. (1980) Equilibrium and energy. Prob. Math. Statist. (Wroclaw) 1, 99–108.

    MathSciNet  MATH  Google Scholar 

  5. Cohen, J. W. (1969) The Single Server Queue (2nd edn 1982 ). North-Holland, Amsterdam.

    Google Scholar 

  6. Doob, J. L. (1984) Classical Potential Theory and its Probabilistic Counterpart. Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  7. Glover, J. (1983) Topics in energy and potential theory. In Seminar on Stochastic Processes, Birkhauser, Basel, 195–202.

    Google Scholar 

  8. Goursat, E. (1914) Kurs analizy matematycznej, Vol. 1 ( Polish translation ). Warsaw.

    Google Scholar 

  9. Gzyl, H. (1980) Infinitesimal generators of time changed processes. Ann. Prob. 8, 716–726.

    Article  MathSciNet  MATH  Google Scholar 

  10. Jackson, W. (ed) (1953) Communication Theory. Butterworth, London.

    Google Scholar 

  11. Keilson, J. (1979) Markov Chain Models—Rarity and Exponentiality. Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  12. Kühn, P. (1973) The impact of queueing theory on the optimization of communications and computer systems. Proc. XX TIMS, Tel Aviv, ed. E. Shlifer, Jerusalem Academic Press, Jerusalem, 2, 554–568.

    Google Scholar 

  13. Pogorzelski, W. (1946) Analiza matematyczna,Vols 1–4. Warsaw.

    Google Scholar 

  14. Pogorzelski, W. (1953) Rowania calkowe i ich zastosowania. PWN, Warsaw.

    Google Scholar 

  15. Pollaczek, F. (1963) Summary of Théorie analytique. University of Maryland Technical Report BN-323.

    Google Scholar 

  16. Prabhu, N. U. (ed) (1975) Applied probability: Its nature and scope. Stoch. Proc. Appl. 3, 253–255.

    Article  MathSciNet  Google Scholar 

  17. Saaty, T. L. and Alexander, J. M (1981) Thinking with Models. Pergamon Press, Oxford.

    MATH  Google Scholar 

  18. Savage, L. J. (1962) The Foundations of Statistical Inference. Methuen, London.

    Google Scholar 

  19. Smith, W. L. (1958) Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 293–294.

    Google Scholar 

  20. Syski, R. (1953) The theory of congestion in lost-call systems. ATE Jnl 9, 182–215.

    Google Scholar 

  21. Syski, R. (1955) Analogies between the congestion and communication theories. ATE Jnl 11, 220–243 (Summary in Teleteknik, Copenhagen 1 (1957), 124–125.

    Google Scholar 

  22. Syski, R. (1958) Professor Neyman in London (in Polish). J. Inst. Polish Engrs in Great Britain 18, January, p. 23.

    Google Scholar 

  23. Syski, R. (1959) On the role of mathematics in technology (in Polish). Technika i Nauka (London) 6, 1–3.

    Google Scholar 

  24. Syski, R. (1960) Reply to a letter (in Polish). Technika i Nauka (London) 8, 45–46.

    Google Scholar 

  25. Syski, R. (1960) Introduction to Congestion Theory in Telephone Systems. Oliver and Boyd, Edinburgh. (Revised reprint 1985, North-Holland, Amsterdam. )

    Google Scholar 

  26. Syski, R. (1962) Congestion in telephone exchanges. [2], pp. 85–98.

    Google Scholar 

  27. Syski, R. (1965) Markovian queues. In Proc. Symp. Congestion Theory, ed. W. L. Smith and W. E. Wilkinson, University of North Carolina Press, Chapel Hill, 170–227.

    Google Scholar 

  28. Syski, R. (1967) Pollaczek method in queueing theory. In Queueing Theory, ed. R. Cruon, English Universities Press, London, pp. 33–60.

    Google Scholar 

  29. Syski, R. (1973) Queueing theory symposium: Introduction and summary Proc. XX TIMS, Tel Aviv, ed. E. Shlifer, Jerusalem Academic Press, Jerusalem, 2, 507–508.

    Google Scholar 

  30. Syski, R. (1973) Queues and potentials. Proc. XX TIMS, Tel Aviv, ed. E. Shlifer, Jerusalem Academic Press, Jerusalem, 2, 547–554.

    Google Scholar 

  31. Syski, R. (1973) Potential theory for Markov chains. In Probabilistic Methods in Applied Mathematics 3, ed. A. T. Bharucha-Reid, Academic Press, New York, 213–276.

    Google Scholar 

  32. Syski, R. (1975) Energy of Markov chains (abstract). Adv. Appl. Prob. 7, 254255.

    Google Scholar 

  33. Syski, R. (1979) Energy of Markov chains. Adv. Appl. Prob. 11, 542–575.

    Article  MathSciNet  MATH  Google Scholar 

  34. Syski, R. (1979) Random Processes: A First Look. Dekker, New York.

    MATH  Google Scholar 

  35. Syski, R. (1980) Stochastic processes and their applications (in Polish). Technika i Nauka (London) 46, 33–42.

    Google Scholar 

  36. Syski, R. (1982) Phase-type distributions and perturbation model. Applicationes Math. (Wroclaw) 17, 377–399.

    MathSciNet  MATH  Google Scholar 

  37. Syski, R. (1984) Markovian queues in teletraffic theory. In Fundamentals of Teletraffic Theory, USSR Academy of Sciences, Moscow, 430–440.

    Google Scholar 

  38. Syski, R. (1985) Markovian queues. Chapter 11 of the reprint of [25].

    Google Scholar 

  39. Zagórski, W. (1957) Wicher wolnosci (English translation: Seventy Days ). Muller, London.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Applied Probability Trust

About this chapter

Cite this chapter

Syski, R. (1986). Markovian Models—An Essay. In: Gani, J. (eds) The Craft of Probabilistic Modelling. Applied Probability, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8631-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-8631-5_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8633-9

  • Online ISBN: 978-1-4613-8631-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics