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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 53570, 15 pages

Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes

1Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain
2Department of Industrial and Manufacturing Engineering and Business, Kettering University, Flint 48439, MI, USA

Received 28 February 2005; Revised 11 May 2005; Accepted 20 June 2005

Copyright © 2006 Jesus R. Artalejo and Srinivas R. Chakravarthy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. V. Anisimov and J. R. Artalejo, “Analysis of Markov multiserver retrial queues with negative arrivals,” Queueing Systems. Theory and Applications, vol. 39, no. 2-3, pp. 157–182, 2001. View at Zentralblatt MATH · View at MathSciNet
  2. J. R. Artalejo and S. R. Chakravarthy, “Algorithmic analysis of the MAP/PH/1retrial queue,” submitted.
  3. J. R. Artalejo and S. R. Chakravarthy, “Computational analysis of the maximal queue length in the MAP/M/cretrial queue,” submitted.
  4. J. R. Artalejo, A. Economou, and A. Gomez-Corral, “Applications of maximum queue length to call centers management,” to appear in Computers & Operations Research.
  5. S. R. Chakravarthy, “The batch Markovian arrival process: A review and future work,” in Advances in Probability Theory and Stochastic Processes, A. Krishnamoorthy, N. Raju, and V. Ramaswami, Eds., pp. 21–39, Notable Publications, New Jersey, 2000.
  6. D. J. Houck and W. S. Lai, “Traffic modeling and analysis of hybrid fiber-coax systems,” Computer Networks and ISDN Systems, vol. 30, no. 8, pp. 821–834, 1998.
  7. G. K. Janssens, “The quasi-random input queueing system with repeated attempts as a model for a collision-avoidance star local area network,” IEEE Transactions on Communications, vol. 45, no. 3, pp. 360–364, 1997.
  8. G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, SIAM, Pennsylvania; American Statistical Association, Virginia, 1999. View at Zentralblatt MATH · View at MathSciNet
  9. D. M. Lucantoni, “New results on the single server queue with a batch Markovian arrival process,” Communications in Statistics. Stochastic Models, vol. 7, no. 1, pp. 1–46, 1991. View at Zentralblatt MATH · View at MathSciNet
  10. M. A. Marsan, G. de Carolis, E. Leonardi, R. Lo Cigno, and M. Meo, “Efficient estimation of call blocking probabilities in cellular mobile telephony networks with customer retrials,” IEEE Journal on Selected Areas in Communications, vol. 19, no. 2, pp. 332–346, 2001.
  11. M. F. Neuts, “The distribution of the maximum length of a Poisson queue during a busy period,” Operations Research, vol. 12, no. 2, pp. 281–285, 1964. View at Zentralblatt MATH · View at MathSciNet
  12. M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, vol. 2 of Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, Maryland, 1981. View at Zentralblatt MATH · View at MathSciNet
  13. M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications, vol. 5 of Probability: Pure and Applied, Marcel Dekker, New York, 1989. View at Zentralblatt MATH · View at MathSciNet
  14. R. F. Serfozo, “Extreme values of birth and death processes and queues,” Stochastic Processes and their Applications, vol. 27, no. 2, pp. 291–306, 1988. View at Zentralblatt MATH · View at MathSciNet
  15. H. Shimonishi, T. Takine, M. Murata, and H. Miyahara, “Performance analysis of fast reservation protocol in ATM networks with arbitrary topologies,” Performance Evaluation, vol. 27-28, pp. 41–69, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. P. Tran-Gia and M. Mandjes, “Modeling of customer retrial phenomenon in cellular mobile networks,” IEEE Journal on Selected Areas in Communications, vol. 15, no. 8, pp. 1406–1414, 1997.