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Infinite-Server Queue Model \(MMAP_{k}(t)|G_{k}|\infty \) with Time Varying Marked Map Arrivals of Customers and Occurrence of Catastrophes

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Book cover Computer Networks (CN 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1231))

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Abstract

In the present paper, the infinite-server queue model \(MMAP_{k}(t)|G_{k}|\infty \) in transient MMAP random environment with time varying marked MAP arrival of k types of customers subject to catastrophes is considered. The transient joint probability generating functions (PGF) of the number of different types of customers present in the model at moment t and the number of different types of customers departing from the system in the time interval (0, t] are found. The Laplace-Stieltjes transform (LST) of total volume of customers being in service at moment t is defined. The basic differential equations for joint probability generating functions of the number of busy servers and served customers for transient and stationary random environment are obtained.

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Acknowledgement

This work was supported by “Data Science Program with Career Support and Connections to Industry,” NSF Award 1842386 grant.

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Authors and Affiliations

  1. University of California San Diego, San Diego, CA, USA

    Ruben Kerobyan

  2. California State University Northridge, Northridge, CA, USA

    Khanik Kerobyan, Carol Shubin & Phu Nguyen

Authors
  1. Ruben Kerobyan
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  2. Khanik Kerobyan
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  3. Carol Shubin
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  4. Phu Nguyen
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Corresponding author

Correspondence to Ruben Kerobyan .

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Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Piotr Gaj

  2. Gdańsk University of Technology, Gdańsk, Poland

    Wojciech Gumiński

  3. Silesian University of Technology, Gliwice, Poland

    Andrzej Kwiecień

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Kerobyan, R., Kerobyan, K., Shubin, C., Nguyen, P. (2020). Infinite-Server Queue Model \(MMAP_{k}(t)|G_{k}|\infty \) with Time Varying Marked Map Arrivals of Customers and Occurrence of Catastrophes. In: Gaj, P., Gumiński, W., Kwiecień, A. (eds) Computer Networks. CN 2020. Communications in Computer and Information Science, vol 1231. Springer, Cham. https://doi.org/10.1007/978-3-030-50719-0_13

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  • DOI: https://doi.org/10.1007/978-3-030-50719-0_13

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  • Online ISBN: 978-3-030-50719-0

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