IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v10y2019i1d10.1007_s13198-018-0731-z.html
   My bibliography  Save this article

On two node tandem queueing model with time dependent service rates

Author

Listed:
  • K. Srinivasa Rao

    (Andhra University)

  • J. Durga Aparajitha

    (Andhra University)

Abstract

Queueing is a phenomenon associated with congestion. For controlling congestion and to utilize the resources optimally the queueing models are developed. In queueing models, it is customary to consider that the arrival and service processes are stable and follows a Poisson process. But in many systems the service process is time dependent and it can be well characterized by non-homogeneous Poisson process. This paper introduces a tandem queueing model with non-homogeneous Poisson service process. The system performance is analysed by deriving the system performance measure such as, average content of the queues, average waiting time of a customer in the queue and in the system, the throughput of transmitters, and the variance of the number of customers in the system. The effect of various changes in parameter on the system performance measures is carried through sensitivity analysis. It is observed that the time dependent service rate has significant influence on the system performance measures. This model can accurately predict the performance measures, when the service rates are time dependent. Several of the earlier models become particular cases of this model.

Suggested Citation

  • K. Srinivasa Rao & J. Durga Aparajitha, 2019. "On two node tandem queueing model with time dependent service rates," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(1), pages 19-34, February.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:1:d:10.1007_s13198-018-0731-z
    DOI: 10.1007/s13198-018-0731-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-018-0731-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13198-018-0731-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Atchuta Rao Sadu & K. Srinivas Rao & K. Nirupama Devi, 2017. "Forked queueing model with load dependent service rate and bulk arrivals," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 30(1), pages 1-32.
    2. Avi Mandelbaum & William A. Massey, 1995. "Strong Approximations for Time-Dependent Queues," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 33-64, February.
    3. A.V.S. Suhasini & K. Srinivasa Rao & P. Rajasekhara Reddy, 2014. "Queueing model with non-homogeneous bulk arrivals having state-dependent service rates," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 21(1), pages 84-99.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Avi Mandelbaum & Kavita Ramanan, 2010. "Directional Derivatives of Oblique Reflection Maps," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 527-558, August.
    2. Yongjiang Guo & Yunan Liu & Renhu Pei, 2018. "Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback," Annals of Operations Research, Springer, vol. 264(1), pages 157-191, May.
    3. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    4. Jabari, Saif Eddin & Liu, Henry X., 2013. "A stochastic model of traffic flow: Gaussian approximation and estimation," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 15-41.
    5. Avishai Mandelbaum & Petar Momčilović, 2008. "Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 561-586, August.
    6. Yongjiang Guo & Xiyang Hou & Yunan Liu, 2021. "A functional law of the iterated logarithm for multi-class queues with batch arrivals," Annals of Operations Research, Springer, vol. 300(1), pages 51-77, May.
    7. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    8. Wanyang Dai, 2024. "Stochastic Differential Games and a Unified Forward–Backward Coupled Stochastic Partial Differential Equation with Lévy Jumps," Mathematics, MDPI, vol. 12(18), pages 1-46, September.
    9. Tan, Xiaoqian & Knessl, Charles & Yang, Yongzhi (Peter), 2013. "On finite capacity queues with time dependent arrival rates," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2175-2227.
    10. Kerry Fendick & Ward Whitt, 2022. "Heavy traffic limits for queues with non-stationary path-dependent arrival processes," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 113-135, June.
    11. Gianmarco Bet & Remco van der Hofstad & Johan S. H. van Leeuwaarden, 2019. "Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 821-864, August.
    12. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    13. Ward Whitt & Wei You, 2019. "Time-Varying Robust Queueing," Operations Research, INFORMS, vol. 67(6), pages 1766-1782, November.
    14. Junfei Huang & Boaz Carmeli & Avishai Mandelbaum, 2015. "Control of Patient Flow in Emergency Departments, or Multiclass Queues with Deadlines and Feedback," Operations Research, INFORMS, vol. 63(4), pages 892-908, August.
    15. Morgan, Lucy E. & Barton, Russell R., 2022. "Fourier trajectory analysis for system discrimination," European Journal of Operational Research, Elsevier, vol. 296(1), pages 203-217.
    16. Wang, Haiyan & Olsen, Tava Lennon & Liu, Guiqing, 2018. "Service capacity competition with peak arrivals and delay sensitive customers," Omega, Elsevier, vol. 77(C), pages 80-95.
    17. Allan, Andrew L. & Liu, Chong & Prömel, David J., 2021. "Càdlàg rough differential equations with reflecting barriers," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 79-104.
    18. R. Sudhesh & R. Sebasthi Priya & R. B. Lenin, 2016. "Analysis of N-policy queues with disastrous breakdown," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 612-634, October.
    19. Jamol Pender, 2017. "Sampling the Functional Kolmogorov Forward Equations for Nonstationary Queueing Networks," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 1-17, February.
    20. Ad Ridder, 2022. "Rare-event analysis and simulation of queues with time-varying rates," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 545-547, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:ijsaem:v:10:y:2019:i:1:d:10.1007_s13198-018-0731-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.