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Ergodicity and steady state existence. Continuity of stationary distributions of queueing characteristics

  • A. Brandt
  • P. Franken
  • B. Lisek
Stationarity And Ergodicity 2
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 60)

Keywords

Weak Solution Service Time Interarrival Time Ergodic Property Single Server Queue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Borovkov A.A. (1972), Continuity theorems for multi-server loss systems, Teor. Veroyat. Primenen. 17, 458–468 (in Russian).Google Scholar
  2. Borovkov A.A. (1978), Ergodic and stability theorems for one class of stochastic equations and their applications, Teor. Veroyat. Primenen. 23, 241–262 (in Russian).Google Scholar
  3. Borovkov A.A. (1980), Asymptotic Methods in Queueing Theory (in Russian), Nauka, Moscow.Google Scholar
  4. Brandt A. (1982a), On stationary waiting times and limiting behaviour of queues with many servers I. The general G/G/m/∞ case (to appear in EIK).Google Scholar
  5. Brandt A. (1982b), On stationary waiting times and limiting behaviour of queues with many servers II. The G/GI/m/∞ case (to appear in EIK).Google Scholar
  6. Brandt A. and Lisek B. (1981), On the continuity of G/GI/m queues (to appear in Math. Operationsforsch. Statist., Ser. Statistics).Google Scholar
  7. FKAS (Franken P., König D., Arndt U. and Schmidt V.) (1981), Queues and Point Processes, Akademie-Verlag, Berlin (J. Wiley, 1983).Google Scholar
  8. Franken P. (1970), Ein Stetigkeitssatz für Verlustsysteme, Operationsforschung und Math. Statistik II, 9–23, Akademie-Verlag, Berlin.Google Scholar
  9. Franken P. (1982), The Point Process Approach to Queueing Theory and Related Topics, Seminarbericht Nr. 43, Sektion Mathematik, Humboldt-Universität zu Berlin, G.D.R.Google Scholar
  10. Franken P. and Lisek B. (1982), On Wald's identity for dependent variables, Z. Wahrscheinlichkeitstheorie verw. Geb. 60, 143–150.Google Scholar
  11. Kiefer J. and Wolfowitz J. (1955), On the theory of queues with many servers, Trans. Amer. Math. Soc. 78, 1–18.Google Scholar
  12. Lisek B. (1979), Construction of stationary state distributions for loss systems, Math. Operationsforsch. Statist., Ser. Statistics 10, 561–581.Google Scholar
  13. Lisek B. (1981), Stability theorems for queueing systems without delay, Elektron. Informationsverarb. Kybernetik 17, 259–278.Google Scholar
  14. Lisek B. (1982), A method for solving a class of recursive stochastic equations, Z. Wahrscheinlichkeitstheorie verw. Geb. 60, 151–161.Google Scholar
  15. Lisek B. (1983), A method for solving a class of recursive stochastic equations II. (paper in preparation).Google Scholar
  16. Loynes R.M. (1962), The stability of a queue with non-independent inter-arrival and service times, Proc. Cambridge Philos. Soc. 58, 497–520.Google Scholar
  17. Nawrotzki K. (1978), Einige Bemerkungen zur Verwendung der Palmschen Verteilung in der Bedienungstheorie, Math. Operationsforsch. Statist., Ser. Optimization 9, 241–253.Google Scholar
  18. Rolski T. (1981), Stationary Random Processes Associated with Point Processes, Lecture Notes in Statistics 5, Springer-Verlag, New York, Heidelberg, Berlin.Google Scholar
  19. Wirth K.-D. (1982), On stationary queues with batch arrivals, Elektron. Informationsverarb. Kybernetik 18, 603–619.Google Scholar
  20. Wirth K.-D. (1983), A new approach to queues with warm up times (submitted to Elektron. Informationsverarb. Kybernetik).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • A. Brandt
    • 1
  • P. Franken
    • 1
  • B. Lisek
    • 1
  1. 1.Humboldt-Universität, Sektion MathematikBerlinGerman Democratic Republic

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