skip to main content
10.1145/1837856.1837859acmotherconferencesArticle/Chapter ViewAbstractPublication PagesqtnaConference Proceedingsconference-collections
research-article

On the distribution of the successful and blocked events in retrial queues with finite number of sources

Published:24 July 2010Publication History

ABSTRACT

This paper deals with a multiservice retrial queue with finite population, where the input process is characterized by the fact that each idle source generates arrivals independently and with the same exponentially distributed inter-arrival time of rate a. As a consequence of the retrial feature, the flow of repeated attempts is superimposed on the stream of primary arrivals, so both type of events become undistinguished. In this paper some aspects of this problem are considered. The distributions of the successful primary arrivals and retrials during a busy period are studied. Then, the transient behavior of these performance descriptors is investigated.

References

  1. J. Abate and W. Whitt, "Numerical inversion of Laplace transforms of probability distributions", ORSA Journal on Computing, vol. 7, pp. 36--43, 1995.Google ScholarGoogle ScholarCross RefCross Ref
  2. A. S. Alfa and K. S. Isotupa, "An M/PH/k retrial queue with finite number of sources", Computers and Operations Research, vol. 31, pp. 1455--1464, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. J. Amador and J. R. Artalejo, "On the distribution of the successful and blocked events in the M/M/c retrial queue: a computational approach", Applied Mathematics and Computation vol. 190, pp. 1612--1626, 2007.Google ScholarGoogle ScholarCross RefCross Ref
  4. J. Amador and J. R. Artalejo, "The M/G/1 retrial queue: new descriptors of the customer's behavior", Journal of Computational and Applied Mathematics, vol. 223, pp. 15--26, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. J. Amador and J. R. Artalejo, "Transient analysis of the successful and blocked events in retrial queues", Telecommunication Systems, vol 41, pp. 255--265, 2009.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. J. R. Artalejo and A. Gómez-Corral, Retrial queueing systems: a computational approach. Springer, Berlin, 2008.Google ScholarGoogle Scholar
  7. A. M. Cohen, Numerical methods for Laplace transform inversion, Springer, New York, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. J. Medhi, Stochastic Models In Queueing Theory, Academic Press, Amsterdam, 1985. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. P. Wüchner, J. Sztrik and H. Meer, "Finite source M/M/S retrial queue with search for balking and impatient customers from the orbit", Computer Network, vol. 53, 1264--1273, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. J. Sztrik, Finite source queuing systems and their applications. A Bibliography, 2001. Available at http://irh.inf.unideb.hu/user/jsztrik/research/fsqreview.pdf.Google ScholarGoogle Scholar

Index Terms

  1. On the distribution of the successful and blocked events in retrial queues with finite number of sources

          Recommendations

          Comments

          Login options

          Check if you have access through your login credentials or your institution to get full access on this article.

          Sign in
          • Published in

            cover image ACM Other conferences
            QTNA '10: Proceedings of the 5th International Conference on Queueing Theory and Network Applications
            July 2010
            213 pages
            ISBN:9781450302128
            DOI:10.1145/1837856

            Copyright © 2010 ACM

            Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

            Publisher

            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 24 July 2010

            Permissions

            Request permissions about this article.

            Request Permissions

            Check for updates

            Qualifiers

            • research-article

          PDF Format

          View or Download as a PDF file.

          PDF

          eReader

          View online with eReader.

          eReader