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

Thulaseedharan Salini Sinu Lal, Varghese Chaukayil Joshua, Vladimir Vishnevsky, Dmitry Kozyrev and Achyutha Krishnamoorthy
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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
Achyutha Krishnamoorthy: Centre for Research in Mathematics, CMS College, Kottayam 686001, Kerala, India

Mathematics, 2022, vol. 10, issue 5, 1-11

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.

Keywords: queueing inventory; batch marked markovian arrival process; coxian distribution; matrix analytic method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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