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A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra

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  • Thulaseedharan Salini Sinu Lal

    (Department of Mathematics, St. Stephens College, Kollam District, Pathanapuram 89695, Kerala, India)

  • Varghese Chaukayil Joshua

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, Kerala, India)

  • Vladimir Vishnevsky

    (V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia)

  • Dmitry Kozyrev

    (V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia)

  • Achyutha Krishnamoorthy

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, Kerala, India)

Abstract

The model discussed in this paper provides an efficient mechanism for the selection and allocation of available limited spectra for transmission of heterogeneous data in a network. The data packets (customers), belonging to different classes, arrive according to a batch marked the Markovian arrival process (BMMAP). The inventory considered is of multi-type (different types of channels becoming available) and are generated according to a marked Markovian arrival process (MMAP). The number of distinct types of inventory and that of the customers are the same. Arriving customers are allowed to wait in finite buffers of each category which are reserved for distinct classes of customers except for the most general class, which is provided with an infinite waiting space. The number of servers also equals the number of distinct types of inventory. When items of a particular type arrive in the inventory, the service starts, providing the buffer of customers of the corresponding class is non-empty. The service can be viewed as a selection process with Coxian distributed service times. The system is analyzed using the matrix analytic method and performance measures are obtained. The model is illustrated with suitable numerical examples.

Suggested Citation

  • Thulaseedharan Salini Sinu Lal & Varghese Chaukayil Joshua & Vladimir Vishnevsky & Dmitry Kozyrev & Achyutha Krishnamoorthy, 2022. "A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:714-:d:757749
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    References listed on IDEAS

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    1. P.L.M. Nyen & J.W.M. Bertrand & H.P.G. Ooijen & N.J. Vandaele, 2006. "A heuristic to control integrated multi-product multi-machine production-inventory systems with job shop routings and stochastic arrival, set-up and processing times," Springer Books, in: George Liberopoulos & Chrissoleon T. Papadopoulos & Barış Tan & J. M. Smith & Stanley B. Gershwin (ed.), Stochastic Modeling of Manufacturing Systems, pages 253-288, Springer.
    2. Zhao, Ning & Lian, Zhaotong, 2011. "A queueing-inventory system with two classes of customers," International Journal of Production Economics, Elsevier, vol. 129(1), pages 225-231, January.
    3. Liu, Mingwu & Feng, Mengying & Wong, Chee Yew, 2014. "Flexible service policies for a Markov inventory system with two demand classes," International Journal of Production Economics, Elsevier, vol. 151(C), pages 180-185.
    4. Serife Ozkar & Umay Uzunoglu Kocer, 2021. "Two-commodity queueing-inventory system with two classes of customers," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 234-256, March.
    5. A. Krishnamoorthy & R. Manikandan & B. Lakshmy, 2015. "A revisit to queueing-inventory system with positive service time," Annals of Operations Research, Springer, vol. 233(1), pages 221-236, October.
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