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Original Articles

Asymptotic Analysis of Loss Probabilities in GI/M/m/n Queueing Systems as n Increases to Infinity

Pages 379-393 | Received 01 May 2005, Accepted 01 Apr 2006, Published online: 09 Feb 2016

References

  • Abramov, V. M. (1997). On a property of a refusals stream. Journal of Applied Probability, 34, 800–805.
  • Abramov, V. M. (2002). Asymptotic analysis of the GI/M/1/n queueing system as increases to infinity. Annals of Operations Research, 112, 35–41.
  • Abramov, V. M. (2004). Asymptotic behavior of the number of lost messages. SIAM Journal on Applied Mathematics, 64, 746–761.
  • Abramov, V. M. (2005). Optimal control of a large dam. arXiv:math/PR 0512118.
  • Bharucha-Reid, A. T. (1960). Elements of the Theory of Markov Processes and Their Application. McGraw-Hill, New York.
  • Borovkov, A. A. (1976). Stochastic Processes in Queueing Theory. Springer-Verlag, Berlin.
  • Brockmeyer, E., HalstrÖm, H. L. and Jensen, A. (1948). The Life and the Works of A.K.Erlang. The Copenhagen Telephone Company, Copenhagen.
  • Choi, B. D. and Kim, B. (2000). Sharp results on convergence rates for the distribution of the GI/M/c/K queues as K tends to infinity. Journal of Applied Probability, 37, 1010–1019.
  • Choi, B. D., Kim, B., Kim, J. and Wee, I.-S. (2003). Exact convergence rate for the distributions of GI/M/1/K queue as K tends to infinity. Queueing Systems, 44: 125–136.
  • Choi, B. D., Kim, B. and Wee, I.-S. (2000). Asymptotic behavior of loss probability in GI/M/1/K queue as tends to infinity. Queueing Systems, 36, 437–442.
  • Cohen, J. W. (1957). The full availability group of trunks with an arbitrary distribution of interarrival times and negative exponential holding time distribution. Simon Stevin, 31, 169–181.
  • Kim, B. and Choi, B. D. (2003). Asymptotic analysis and simple approximation of the loss probability of the GI X /M/c/K queue. Performance Evaluation, 54, 331–356.
  • Kleinrock, L. (1975). Queueing Systems. Volume 1: Theory. John Wiley, New York.
  • Miyazawa, M. (1990). Complementary generating functions for the M X /GI/1/k and GI/M Y/1/k queues and their application to the comparison for loss probabilities. Journal of Applied Probability, 27, 682–692.
  • Palm, C. (1943). Intensitätschwankungen im Fernsprechverkehr. Ericsson Technics, 44, 1–189.
  • Pollaczek, F. (1953). Generalisation de la theorie probabiliste des systemes telephoniques sans dispositif d’attente. Comptes Rendus de l’Academie des Sciences (Paris), 236, 1469–1470.
  • Postnikov, A. G. (1979–1980). Tauberian Theory and Its Application. Trudy Matematicheskogo Instituta Steklova 2 (1979) 1–147 (In Russian). Engl. transl. in: Procedings of the Steklov Mathematical Institute 2 (1980) 1–137.
  • Ramalhoto, M. F. and Gomez-Corral, A. (1998). Some decomposition formulae for M/M/r/r + d queues with constant retrial rate. Stochastic Models, 14, 123–145.
  • Sevastyanov, B. A. (1957). An ergodic theorem for Markov processes and its application to telephone systems with refusals. Theory of Probability and Its Applications, 2, 104–112.
  • Simonot, F. (1998). A comparison of the stationary distributions of GI/M/c/n and GI/M/c . Journal of Applied Probability, 35, 510–515.
  • Subhankulov, M.A. (1976). Tauberian Theorems with Remainder. Nauka, Moscow. (In Russian)
  • Takács, L. (1957). On a probability problem concerning telephone traffic. Acta Mathematika Academia Scientiarum Hungaricae, 8, 319–324.
  • Takács, L. (1962). Introduction to the Theory of Queues. Oxford University Press, New York/London.
  • Takács, L. (1967). Combinatorial Methods in the Theory of Stochastic Processes. John Wiley, New York.
  • Whitt, W. (2004). Heavy-traffic limits for loss proportions in single-server queues. Queueing Systems, 46, 507–536.
  • Whitt, W. (2005). Heavy-traffic limits for the G/H* 2 /n/m queue. Mathematics of Operations Research, 30, 1–27.

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