Skip to main content
Log in

BMAP/G/1/∞ system with last come first served probabilistic priority

  • Queueing Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to the BMAP/G/1/∞ single-server queuing system with batch Markov arrivals, arbitrary servicing, finite-capacity buffer, and last come first served probabilistic priority. Equations for determination of the stationary probabilities of states and stationary characteristics associated with the time of customer sojourn in the system were determined.

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. Pechinkin, A.V., On an Invariant Queuing System, Math. Oper. Statist., Ser. Optim., 1983, vol. 14, no. 3, pp. 433–444.

    MATH  MathSciNet  Google Scholar 

  2. Schrage, L. and Miller, L., The Queue M/G/1 with the Shortest Remaining Processing Time Discipline, Oper. Res., 1966, vol. 14, pp. 670–684.

    Article  MATH  MathSciNet  Google Scholar 

  3. Schrage, L., A Proof of the Optimality of the Shortest Remaining Processing Time Discipline, Oper. Res., 1968, vol. 16, pp. 687–690.

    Article  MATH  Google Scholar 

  4. Schassberger, R., The Steady-State Appearance of the M/G/1 Queue under the Discipline of Shortest Remaining Processing Time, Adv. Appl. Probab., 1990, vol. 22, pp. 456–479.

    Article  MATH  MathSciNet  Google Scholar 

  5. Grishechkin, S.A., On a Relationship between Processor-Sharing Queues and Cramp-Mode-Jagers Branching Processes, Adv. Appl. Probab., 1992, vol. 24, pp. 653–698.

    Article  MATH  MathSciNet  Google Scholar 

  6. Pechinkin, A.V., Nonstationary Characteristics of the Queuing System with the SRPT Discipline, Vestn. Ross. Univ. Druzhby Narodov, Ser. Prikl. Mat. Inf., 1996, no. 1, pp. 77–85.

  7. Pechinkin, A.V., MAP/G/1/∞ System with the SRPT Discipline, Teor. Veroyatn. Primen., 2000, vol. 45, no. 3, pp. 589–595.

    MathSciNet  Google Scholar 

  8. Nagonenko, V.A., On the Characteristics of One Nonstandard Queuing System. I, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1981, no. 1, pp. 187–195.

  9. Nagonenko, V.A., On the Characteristics of One Nonstandard Queuing System. II, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1981, no. 3, pp. pp. 91–99.

  10. Nagonenko, V.A. and Pechinkin, A.V., On High Load in the System with the Last Come First Served Probabilistic Priority, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1982, no. 1, pp. 86–94.

  11. Nagonenko, V.A. and Pechinkin, A.V., On Low Load in the System with the Last Come First Served Probabilistic Priority, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1984, no. 6, pp. 86–94.

  12. Tatashev, A.G., An Invariant-discipline Queueing System, Autom. Remote Control, 1992, no. 7, pp. 1034–1037.

  13. Tatashev, A.G., Queuing System with Batch Arrival and Inversive Discipline, Kibern. Sist. Anal., 1995, no. 6, pp. 163–165.

  14. Tatashev, A.G., One Inversive Servicing Discipline in the System with Batch Arrival, Avtomat. Vychisl. Tekh., 1995, no. 1, pp. 53–59.

  15. Tatashev, A.G., One Inversive Servicing Discipline in Single-server System with Customers of Different Types, Avtom. Telemekh., 1999, no. 7, pp. 177–181.

  16. Tatashev, A.G., Single-server System with Inversive Servicing Discipline and Customers of Different Types, Kibern. Sist. Anal., 2000, no. 3, pp. 170–174.

  17. Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queuing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.

    Google Scholar 

  18. Pechinkin, A.V. and Svishcheva, T.A., MAP/G/1/r System with Last Come First Served Probabilistic Priority, Vestn. Ross. Univ. Druzhby Narodov, Ser. Prikl. Mat. Inf., 2002, no. 1, pp. 80–89.

  19. Pechinkin, A.V. and Svishcheva, T.A., MAP/G/1/∞ System with Last Come First Served Probabilistic Priority, Vestn. Ross. Univ. Druzhby Narodov, Ser. Prikl. Mat. Inf., 2003, no. 1, pp. 109–118.

  20. Milovanova, T.A., BMAP/G/1/r System with Last Come First Served Probabilistic Priority, Inform. Protsessy, 2007, no. 2, pp. 153–167.

  21. Milovanova, T.A., Stationary Characteristics Related to the Time of Customer Sojourn in the BMAP/G/1/r/LCFS PP System, Inform. Protsessy, 2007, no. 4, pp. 411–424.

  22. Bocharov, P.P., D’Apice, C., Pechinkin, A.V., and Salerno, S., Queueing Theory, Utrecht: VSP, 2004.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © T.A. Milovanova, 2009, published in Avtomatika i Telemekhanika, 2009, No. 5, pp. 155–168.

This work was supported by the Russian Foundation for Basic Research, project no. 06-07-89056.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Milovanova, T.A. BMAP/G/1/∞ system with last come first served probabilistic priority. Autom Remote Control 70, 885–896 (2009). https://doi.org/10.1134/S0005117909050142

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117909050142

PACS number

Navigation