Advances and Applications in Statistics

The Advances and Applications in Statistics is an internationally recognized journal indexed in the Emerging Sources Citation Index (ESCI). It provides a platform for original research papers and survey articles in all areas of statistics, both computational and experimental in nature.

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ANALYSIS OF BATCH ARRIVAL DIFFERENTIATED VACATION QUEUE WITH SERVER WORKING BREAKDOWN AND REPAIRS

Authors

  • K. Vijaya
  • B. Deepa
  • A. Kalaivani

Keywords:

steady state batch arrival, Markovian queue, differentiated vacations, single server network channel, server working breakdown and repair

DOI:

https://doi.org/10.17654/0972361725059

Abstract

We formulate and analyze a stochastic queueing network mathematical model with Markovian batch arrival differentiated vacation, server working breakdown and repair. In this queueing model, customers arrive in bulk as stated by Poisson distribution. While the customer is receiving service, the server may breakdown.  At the time of failure, the server continues the service process with slower service rate instead of stopping the service. We proved this queueing model with numerical examples which illustrate the applicability of our findings and perception into optimal system design. Performance metrics, such as the average number of customers in the system and various measures are discussed. For this model, the probability-generating functions of the system size distributions in steady state are obtained. The cost analysis of this model based on service expenses is discussed.

Received: May 26, 2025
Revised: June 19, 2025
Accepted: July 15, 2025

References

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[12] B. Deepa, K. Kalidass and K. Vijaya, Cost analysis approach-the queues with working breakdowns and interruptions, Comm. Appl. Nonlinear Anal. 31 (2024), 44-60.

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[18] A. A. Bouchentouf, M. Boualem, L. Yahiaoui and H. Ahmad, A multi-station unreliable machine model with working vacation policy and customers’ impatience, Quality Technology and Quantitative Management 19(6) (2022), 766-796.

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[20] Srinivas R. Chakravarthy, Shruti and Rakhee Kulshrestha, A queueing model with server breakdowns, repairs, vacations, and backup server, Operations Research Perspectives 7 (2020), 100131.

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Published

12-08-2025

Issue

Vol. 92 No. 9 (2025)

Section

Articles

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Copyright (c) 2025 Pushpa Publishing House, Prayagraj, India

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How to Cite

ANALYSIS OF BATCH ARRIVAL DIFFERENTIATED VACATION QUEUE WITH SERVER WORKING BREAKDOWN AND REPAIRS. (2025). Advances and Applications in Statistics , 92(9), 1319-1343. https://doi.org/10.17654/0972361725059

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