Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server

Sudhesh R. (), Mohammed Shapique A. () and Dharmaraja S. ()
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Sudhesh R.: Anna University
Mohammed Shapique A.: IFET College of Engineering
Dharmaraja S.: Indian Institute of Technology Delhi

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2485-2508

Abstract: Abstract An M/M/1 dual-stage vacation queueing system with a system disaster is analysed in this paper. This work is motivated by the dual-stage sleep mode mechanism in the MAC (Media Access Control) and the physical layer of a WiMAX system with Denial of Service. In this model, the server switches to two types of vacation called stage-I and stage-II vacation. Disaster can occur at any stage of the system and subsequent repair is considered. For this system, explicit expressions for transient and steady-state probabilities are computed. Further, performance indices like the mean, variance of the system size, the probability that the server is on vacation mode and busy mode, and system throughput have been computed. Finally, numerical illustrations are presented to understand the effect of the parameters on the system performance.

Keywords: Single server; WiMAX networks; Dual-stage vacation; Disaster; Repairable server; Transient probabilities (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-022-09926-5

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