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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

  • Ruben KerobyanEmail author
  • Khanik Kerobyan
  • Carol Shubin
  • Phu Nguyen
Conference paper
  • 51 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 1231)

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.

Keywords

Marked MAP Infinite-server queue Catastrophes MMAP random environment 

Notes

Acknowledgement

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

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Ruben Kerobyan
    • 1
    Email author
  • Khanik Kerobyan
    • 2
  • Carol Shubin
    • 2
  • Phu Nguyen
    • 2
  1. 1.University of California San DiegoSan DiegoUSA
  2. 2.California State University NorthridgeNorthridgeUSA

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