Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 291402, 6 pages
http://dx.doi.org/10.1155/2015/291402
Research Article

On Some Compound Random Variables Motivated by Bulk Queues

Maritime Faculty, University of Montenegro, Dobrota 36, 85330 Kotor, Montenegro

Received 3 June 2015; Revised 2 August 2015; Accepted 9 August 2015

Academic Editor: Hua Fan

Copyright © 2015 Romeo Meštrović. 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. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1, John Wiley & Sons, New York, NY, USA, 3rd edition, 1968.
  2. B. Dragović, N.-K. Park, N. Đ. Zrnić, and R. Meštrović, “Mathematical models of multiserver queuing system for dynamic performance evaluation in port,” Mathematical Problems in Engineering, vol. 20112, Article ID 710834, 19 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. G. M. Gontijo, G. S. Atuncar, F. R. B. Cruz, and L. Kerbache, “Performance evaluation and dimensioning of GIX/M/c/N systems through kernel estimation,” Mathematical Problems in Engineering, vol. 2011, Article ID 348262, 20 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Lee, “Discrete-Time bulk queueing system with variable service capacity depending on previous service time,” Mathematical Problems in Engineering, vol. 2015, Article ID 482179, 6 pages, 2015. View at Publisher · View at Google Scholar
  5. R. Liu, “Probabilistic decomposition method on the server indices of an Mξ/G/1 vacation queue,” Journal of Applied Mathematics, vol. 2014, Article ID 241636, 9 pages, 2014. View at Publisher · View at Google Scholar
  6. D. R. Manfield and P. Tran-Gia, “Analysis of a finite storage system with batch input arising out of message packetization,” IEEE Transactions on Communications, vol. 30, no. 3, pp. 456–463, 1982. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Mezghiche and L. Tadj, “Note on a binomial schedule for an MX/G/1 queueing system with an unreliable server,” ISRN Probability and Statistics, vol. 2013, Article ID 508045, 6 pages, 2013. View at Publisher · View at Google Scholar
  8. D. G. Kendall, “Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain,” The Annals of Mathematical Statistics, vol. 24, no. 3, pp. 338–354, 1953. View at Publisher · View at Google Scholar
  9. C. A. Charalambides, Combinatorial Methods in Discrete Distributions, John Wiley & Sons, Hoboken, NJ, USA, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  10. L. D. Minkova, “The Pólya-Aeppli process and ruin problems,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2004, no. 3, pp. 221–234, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. E. Peköz and S. M. Ross, “Compound random variables,” Probability in the Engineering and Informational Sciences, vol. 18, no. 4, pp. 473–484, 2004. View at Google Scholar · View at Scopus
  12. W. Feller, “On a general class of ‘contagious’ distributions,” The Annals of Mathematical Statistics, vol. 14, no. 4, pp. 389–400, 1943. View at Publisher · View at Google Scholar
  13. J. Gurland, “A generalized class of contagious distributions,” Biometrics, vol. 14, no. 2, pp. 229–249, 1957. View at Publisher · View at Google Scholar
  14. G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, Addison-Wesley, Reading, Mass, USA, 1976.
  15. N. L. Johnson, S. Kotz, and A. W. Kemp, Univariate Discrete Distributions, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, New York, NY, USA, 3rd edition, 2005. View at MathSciNet
  16. N. Haydn and S. Vaienti, “The compound Poisson distribution and return times in dynamical systems,” Probability Theory and Related Fields, vol. 144, no. 3-4, pp. 517–542, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Thomas, “A generalization of Poisson's binomial limit for use in ecology,” Biometrika, vol. 36, no. 1-2, pp. 18–25, 1949. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus