Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics and Decision Sciences
Volume 2007, Article ID 51801, 13 pages
http://dx.doi.org/10.1155/2007/51801
Research Article

Correlations in Output and Overflow Traffic Processes in Simple Queues

Department of Management, University of Canterbury, Christchurch 8140, New Zealand

Received 11 April 2007; Accepted 8 August 2007

Academic Editor: Paul Cowpertwait

Copyright © 2007 Don McNickle. 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. D. C. Boes, “Note on the output of a queuing system,” Journal of Applied Probability, vol. 6, no. 2, pp. 459–461, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. D. N. Shanbhag and D. G. Tambouratzis, “Erlang's formula and some results on the departure process for a loss system,” Journal of Applied Probability, vol. 10, no. 1, pp. 233–240, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. B. Cooper, Introduction to Queueing Theory, Edward Arnold, London, UK, 2nd edition, 1981. View at Zentralblatt MATH
  4. W. Whitt, “Approximating a point process by a renewal process—I: two basic methods,” Operations Research, vol. 30, no. 1, pp. 125–147, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. L. Albin, “Approximating a point process by a renewal process—II: superposition arrival processes to queues,” Operations Research, vol. 32, no. 5, pp. 1133–1162, 1984. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. L. Albin and S.-R. Kai, “Approximation for the departure process of a queue in a network,” Naval Research Logistics Quarterly, vol. 33, no. 1, pp. 129–143, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. A. Johnson, “Markov MECO: a simple Markovian model for approximating nonrenewal arrival processes,” Communications in Statistics. Stochastic Models, vol. 14, no. 1-2, pp. 419–442, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. I. J. B. F. Adan and V. G. Kulkarni, “Single-server queue with Markov-dependent inter-arrival and service times,” Queueing Systems, vol. 45, no. 2, pp. 113–134, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Heindl, “Decomposition of general queueing networks with MMPP inputs and customer losses,” Performance Evaluation, vol. 51, no. 2–4, pp. 117–136, 2003, special issue on queueing networks with blocking, Kouvatsos and Balsamo, eds. View at Publisher · View at Google Scholar
  10. R. L. Disney and P. C. Kiessler, Traffic Processes in Queueing Networks: A Markov Renewal Approach, vol. 4 of Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, Md, USA, 1987. View at Zentralblatt MATH · View at MathSciNet
  11. E. Çinlar, “Markov renewal theory,” Advances in Applied Probability, vol. 1, pp. 123–187, 1969. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet