Skip to main content
SpringerLink
Log in

Analysis of B M A P/M S P/1 Queue

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

The analysis for the B M A P/M S P/1 queueing system is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution at random epoch. We obtain the steady-state system-length distributions at various epochs as well as of the actual sojourn-time distribution of an arbitrary customer in an arriving batch.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abate J, Choudhury GL, Whitt W (1994) Asymptotics for steady-state tail probabilities in structured Markov queueing models. Stoch Model 10(1):99–143

    Article  MathSciNet  MATH  Google Scholar 

  • Albores-Velasco FJ, Tajonar-Sanabria FS (2004) Analysis of the G I/M S P/c/r queueing system. Information Theory and Information Processing 4(1):46–57

    Google Scholar 

  • Alfa AS, Xue J, Ye Q (2000) Perturbation theory for the asymptotic decay rates in the queues with Markovian arrival process and/or Markovian service process. Queueing Systems 36(4):287–301

    Article  MathSciNet  MATH  Google Scholar 

  • Bocharov PP, D’Apice C, Pechinkin A, Salerno S (2003) The stationary characteristics of the G/M S P/1/r queueing system. Autom Remote Control 64(2):288–301

    Article  MathSciNet  MATH  Google Scholar 

  • Chakravarthy S (1993) Analysis of a finite M A P/G/1 queue with group services. Queueing Systems 13(4):385–407

    Article  MathSciNet  MATH  Google Scholar 

  • Chaudhry ML (1965) Correlated queueing. J Canadian Operational Research Society 3:142–151

    MathSciNet  MATH  Google Scholar 

  • Chaudhry ML (1966) Limited space queueing with arrivals correlated. Journal of the Royal Naval Scientific Service 21:272–278

    Google Scholar 

  • Chaudhry ML (1991) QPACK Software Package. A & A Publications, 395 Carrie Cresc, Kingston, Ontario, K7M 5X7 Canada

  • Chaudhry ML, Harris CM, Marchal WG (1990) Robustness of rootfinding in single-server queueing models. INFORMS J Comput 2:273–286

    Article  MATH  Google Scholar 

  • Chaudhry ML, Templeton JGC (1983) A First Course in Bulk Queues. John Wiley & Sons, New York

    MATH  Google Scholar 

  • Chaudhry ML, Samanta SK, Pacheco A (2012) Analytically explicit results for the G I/C-\(MSP/1/\infty \) queueing system using roots. Probability in the Engineering and Informational Sciences 26(2):221–244

    Article  MathSciNet  MATH  Google Scholar 

  • Dudin AN, Klimenok VI (1996) Queueing system with passive servers. J Appl Math Stoch Anal 9(2):185–204

    Article  MathSciNet  MATH  Google Scholar 

  • Gail HR, Hantler SL, Taylor BA (1996) Spectral analysis of M/G/1 and G/M/1 type Markov chains. Adv Appl Probab 28:114–165

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta UC, Banik AD (2007) Complete analysis of finite and infinite buffer G I/M S P/1 queue - A computational approach. Oper Res Lett 35:273–280

    Article  MathSciNet  MATH  Google Scholar 

  • Horváth A, Horváth G, Telek M (2010) A joint moments based analysis of networks of M A P/M A P/1 queues. Perform Eval 67(9):759–778

    Article  Google Scholar 

  • Janssen A, Leeuwaarden J (2005) Analytic computation schemes for the discrete time bulk service queue. Queueing Systems 50:141–163

    Article  MathSciNet  MATH  Google Scholar 

  • Lucantoni DM (1991) New results on the single server queue with a batch Markovian arrival process. Stoch Model 7:1–46

    Article  MathSciNet  MATH  Google Scholar 

  • Machihara F (1999) A B M A P/S M/1 queue with service times depending on the arrival process. Queueing Systems 33:277–291

    Article  MathSciNet  MATH  Google Scholar 

  • Neuts MF (1979) A versatile Markovian point process. J Appl Probab 16:764–779

    Article  MathSciNet  MATH  Google Scholar 

  • Ozawa T (2006) Sojourn time distributions in the queue defined by a general QBD process. Queueing Systems 53(4):203–211

    Article  MathSciNet  MATH  Google Scholar 

  • Pacheco A, Tang LC, Prabhu NU (2009) Markov-Modulated Processes and Semiregenerative Phenomena. World Scientific, Singapore

    MATH  Google Scholar 

  • Riska A, Smirni E (2002) Exact aggregate solutions for M/G/1-type Markov processes. In: Proceedings Int. Conf. on Measurement and Modeling of Computer Systems (ACM SIGMETRICS 2002). ACM Press, Marina Del Rey, pp 86-96

  • Samanta SK, Gupta UC, Sharma RK (2007) Analyzing discrete-time D- B M A P/G/1/N queue with single and multiple vacations. Eur J Oper Res 182(1):321–339

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang Q, Heindl A, Smirni E (2005) Characterizing the B M A P/M A P/1 departure process via the ETAQA truncation. Stoch Model 21(2-3):821–846

    Article  MathSciNet  MATH  Google Scholar 

  • Tijms HC (2003) A First Course in Stochastic Models, John Wiley and Sons

Download references

Author information

Authors and Affiliations

  1. CEMAT and Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001, Lisboa, Portugal

    S. K. Samanta & A. Pacheco

  2. Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, Ontario, Canada, K7K 7B4

    M. L. Chaudhry

Authors
  1. S. K. Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. L. Chaudhry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Pacheco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Pacheco.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samanta, S.K., Chaudhry, M.L. & Pacheco, A. Analysis of B M A P/M S P/1 Queue. Methodol Comput Appl Probab 18, 419–440 (2016). https://doi.org/10.1007/s11009-014-9429-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-014-9429-0

Keywords

Mathematics Subject Classification (2010)

Search

Navigation