IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v331y2023i2d10.1007_s10479-022-05036-0.html
   My bibliography  Save this article

Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting

Author

Listed:
  • Alexander Dudin

    (Belarusian State University
    RUDN University)

  • Valentina Klimenok

    (Belarusian State University)

Abstract

Queueing systems where certain inventory items are required to provide service to a customer have become popular in the literature from early 1990th. Such systems are similar to those models analysed in the literature models with paired customers, assembly-like queues, passenger–taxi models, etc. During the last few years they are considered in the context of modelling operation of the nodes of a wireless sensor network with energy harvesting. Distinguishing feature of the model considered in this paper, besides the suggestion that arrival flow of customers is described by the Markovian arrival process, is the assumption about a general distribution of the service time while only exponential or phase-type distribution was previously assumed in the existing literature. We apply the well-known technique of M/G/1 type Markov chains and semi-regenerative processes to obtain the ergodicity criterion in a transparent form, stationary distribution of the system under study and the Laplace–Stieltjes transform of the sojourn time distribution. This creates an opportunity to formulate and solve various optimization problems. A number of numerical examples illustrate the computational tractability of the theoretical results and illustrate the behavior of the system performance measures depending on its parameters.

Suggested Citation

  • Alexander Dudin & Valentina Klimenok, 2023. "Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting," Annals of Operations Research, Springer, vol. 331(2), pages 839-866, December.
    • Handle: RePEc:spr:annopr:v:331:y:2023:i:2:d:10.1007_s10479-022-05036-0
    DOI: 10.1007/s10479-022-05036-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-05036-0
    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/s10479-022-05036-0?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. Eline Cuypere & Koen Turck & Dieter Fiems, 2018. "A queueing model of an energy harvesting sensor node with data buffering," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 67(2), pages 281-295, February.
    2. Erol Gelenbe, 2015. "Synchronising Energy Harvesting and Data Packets in a Wireless Sensor," Energies, MDPI, vol. 8(1), pages 1-14, January.
    3. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Dmitry Kozyrev, 2021. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation," Mathematics, MDPI, vol. 9(4), pages 1-29, February.
    4. Srinivas R. Chakravarthy & B. Madhu Rao, 2021. "Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities," Mathematics, MDPI, vol. 9(10), pages 1-26, May.
    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. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.
    2. Ciro D’Apice & Maria Pia D’Arienzo & Alexander Dudin & Rosanna Manzo, 2023. "Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers," Mathematics, MDPI, vol. 11(21), pages 1-34, November.
    3. Ming He & Sheng Wang & Xiang Zhong & Mingjie Guan, 2019. "Study of a Piezoelectric Energy Harvesting Floor Structure with Force Amplification Mechanism," Energies, MDPI, vol. 12(18), pages 1-10, September.
    4. Sujit Kumar Samanta & Kousik Das, 2023. "Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.
    5. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    6. Mohammed B. Abazeed & Mohammed Ali & Ali Alqahtani, 2023. "Optimizing Energy Consumption and QoS in WMSNs Using Queueing Theory," Sustainability, MDPI, vol. 15(18), pages 1-13, September.
    7. Doo Il Choi & Dae-Eun Lim, 2020. "Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations," Sustainability, MDPI, vol. 12(6), pages 1-15, March.
    8. Chris Blondia, 2021. "A queueing model for a wireless sensor node using energy harvesting," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 77(2), pages 335-349, June.
    9. Srinivas R. Chakravarthy & Serife Ozkar, 2024. "A Queueing Model with BMAP Arrivals and Heterogeneous Phase Type Group Services," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-30, December.
    10. Kousik Das & Sujit Kumar Samanta, 2023. "Computational analysis of $$GI^{[X]}/D$$ G I [ X ] / D - $$MSP^{(a,b)}/1$$ M S P ( a , b ) / 1 queueing system via RG-factorization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 1-39, August.

    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:annopr:v:331:y:2023:i:2:d:10.1007_s10479-022-05036-0. 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.