Skip to main content
Log in

Main Probability Characteristics of the Queuing System Gκ|G|1

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For the queuing system G κ|G|1 with batch arrivals of calls, we present the distributions of the following characteristics: the length of a busy period, queue length in transient and stationary modes of the queuing system, total idle time of the queuing system, virtual waiting time to the beginning of the service, input stream of calls, output stream of served calls, etc.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. N. U. Prabhu, Stochastic Storage Processes [Russian translation], Mir, Moscow (1984).

  2. I. I. Ezhov and V. F. Kadankov, “On the distribution of the maximum of the difference of independent renewal processes with discrete time,” Ukr. Mat. Zh., 50, No. 10, 1426–1432 (1998).

    Google Scholar 

  3. A. A. Borovkov, Probability Processes in Queuing Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  4. F. D. Gakhov and Yu. I. Cherskii, Equations of Convolution Type [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  5. D. V. Lindley, “The theory of queues with a single server,” Proc. Cambridge Phil. Soc., 48, No. 2, 277–287 (1952).

    Google Scholar 

  6. I. I. Ezhov, “On the distribution of the queue length in the classical system G?G?1 with discrete time,” Dokl. Akad. Nauk Rossii, 332, No. 4, 408–410 (1993).

    Google Scholar 

  7. I. I. Ezhov and V. F. Kadankov, “On the distribution of the number of calls in the queuing system \(D_{\eta} |D_{\xi}^{\kappa}|\)1,” Ukr. Mat. Zh., 52, No. 8, 1075–1081 (2000).

    Google Scholar 

  8. I. I. Ezhov and V. F. Kadankov, “Boundary functionals for the difference of nonordinary renewal processes with discrete time,” Ukr. Mat. Zh., 52, No. 10, 1345–1356 (2000).

    Google Scholar 

  9. I. I. Ezhov and V. F. Kadankov, “Boundary functionals for a semicontinuous difference of renewal processes with discrete time,” Ukr. Mat. Zh., 45, No. 12, 1710–1713 (1993).

    Google Scholar 

  10. I. I. Ezhov and V. F. Kadankov, “On the generating function of the time of first hitting the boundary by a semicontinuous difference of independent renewal processes with discrete time,” Ukr. Mat. Zh., 52, No. 4, 553–561 (2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ezhov, I.I., Kadankov, V.F. Main Probability Characteristics of the Queuing System Gκ|G|1. Ukrainian Mathematical Journal 53, 1626–1644 (2001). https://doi.org/10.1023/A:1015239809693

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015239809693

Keywords

Navigation