Non-Markovian Queueing Systems

  • László Lakatos
  • László Szeidl
  • Miklós Telek


The M/G/1 queueing system is similar to the M/M/1 queueing system and the only difference is that the service time is not exponential. First we mention some ideas, most of which were described in the previous chapter in connection with an M/M/1 system.


  1. 1.
    Borovkov, A.A.: Stochastic Processes in Queueing Theory. Applications of Mathematics. Springer, New York (1976)Google Scholar
  2. 2.
    Borovkov, A.A.: Asymptotic Methods in Queueing Theory. Wiley, New York (1984)zbMATHGoogle Scholar
  3. 3.
    Ceric, V., Lakatos, L.: Measurement and analysis of input data for queueing system models used in system design. Syst. Anal. Model. Simul. 11, 227–233 (1993)zbMATHGoogle Scholar
  4. 4.
    Cox, D.R.: The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proc. Camb. Philos. Soc. 51, 433–440 (1955)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gnedenko, B.V., Kovalenko, I.N.: Introduction to Queueing Theory, 2nd edn. Birkhauser Boston Inc., Cambridge (1989)CrossRefGoogle Scholar
  6. 6.
    Henderson, W.: Alternative approaches to the analysis of the M/G/1 and G/M/1 queues. J. Operat. Res. Soc. Jpn. 15, 92–101 (1972)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kendall, D.G.: Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math. Stat. 24, 338–354 (1953)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Khinchin, A.: Mathematisches über die Erwartung vor einem öffentlichen Schalter. Rec. Math. 39, 72–84 (1932). Russian, with German summaryGoogle Scholar
  9. 9.
    Kleinrock, L.: Queuing Systems, Volume 1: Theory. Wiley Interscience, New York (1975)zbMATHGoogle Scholar
  10. 10.
    Lakatos, L.: A note on the Pollaczek-Khinchin formula. Ann. Univ. Sci. Budapest. Sect. Comput. 29, 83–91 (2008)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Lindley, D.V.: The theory of queues with a single server. Math. Proc. Camb. Philos. Soc. 48, 277–289 (1952)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Medgyessy, P., Takács, L.: Probability Theory. Tankönyvkiadó, Budapest (1973). In HungarianGoogle Scholar
  13. 13.
    Palm, C.: Methods of judging the annoyance caused by congestion. Telegrafstyrelsen 4, 189–208 (1953)Google Scholar
  14. 14.
    Takács, L.: Investigation of waiting time problems by reduction to Markov processes. Acta Math. Acad. Sci. Hung. 6, 101–129 (1955)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Takács, L.: The distribution of the virtual waiting time for a single-server queue with Poisson input and general service times. Oper. Res. 11, 261–264 (1963)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Takács, L.: Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York (1967)zbMATHGoogle Scholar
  17. 17.
    Tijms, H.: Stochastic Models, An Algorithmic Approach. Wiley, New York (1994)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • László Lakatos
    • 1
  • László Szeidl
    • 2
  • Miklós Telek
    • 3
  1. 1.Eotvos Lorant UniversityBudapestHungary
  2. 2.Obuda UniversityBudapestHungary
  3. 3.Technical University of BudapestBudapestHungary

Personalised recommendations