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This paper analyses the <italic>M</italic>/<italic>M</italic>(<italic>a</italic>,<italic>b</italic>)/1/<italic>MWV</italic> queuing model with various types of breakdowns. During peak times, the system has breakdown due to server unavailability. The model considers system with two types of breakdowns. The system may breakdown in two different ways during busy and working vacation stages. Customer arrives to the system with parameter <italic>λv </italic>which follows Poisson distribution and server provides service in regular busy period with parameter <italic>µrb </italic>and under the multiple working vacations it provides service with parameter <italic>µwv </italic>with exponential distribution. In this model batches of customers are served under General Bulk Service Rule. The system may breakdown at any time. The breakdown that occurs during working vacation is denoted as <italic>βv</italic>1 and the breakdown during busy state is denoted as <italic>βv</italic>2. The steady-state equation, the performance of measures for the system and particular cases of described model are derived. Finally, a real life example demonstrated the validity of the model in a proper way.
</abstract>

This paper analyses the M/M(a,b)/1/MWV queuing model with various types of breakdowns. During peak times, the system has breakdown due to server unavailability. The model considers system with two types of breakdowns. The system may breakdown in two different ways during busy and working vacation stages. Customer arrives to the system with parameter λv which follows Poisson distribution and server provides service in regular busy period with parameter µrb and under the multiple working vacations it provides service with parameter µwv with exponential distribution. In this model batches of customers are served under General Bulk Service Rule. The system may breakdown at any time. The breakdown that occurs during working vacation is denoted as βv1 and the breakdown during busy state is denoted as βv2. The steady-state equation, the performance of measures for the system and particular cases of described model are derived. Finally, a real life example demonstrated the validity of the model in a proper way.

Performance study of the <italic>M</italic>/<italic>M</italic>(<italic>a</italic>,<italic>b</italic>)/1/<italic>MWV</italic> queuing system with types of breakdowns

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution 4.0 International License.

Performance study of the /(,)/1/ queuing system with types of breakdowns

This paper analyses the M/M(a,b)/1/MWV queuing model with various types of breakdowns. During peak times, the system has breakdown due to server...

Performance study of the M/M(a,b)/1/MWV queuing system with types of breakdowns

Published Online: Jan 06, 2024

Page range: 23 - 38

DOI: https://doi.org/10.2478/jamsi-2023-0008

Keywords
Busy period, Multiple Working vacations (MWV), Working state

© 2023 P. Lidiya et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Performance study of the M/M(a,b)/1/MWV queuing system with types of breakdowns

Published Online: Jan 06, 2024

Page range: 23 - 38

DOI: https://doi.org/10.2478/jamsi-2023-0008

KeywordsBusy period, Multiple Working vacations (MWV), Working state

© 2023 P. Lidiya et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Busy period, Multiple Working vacations (MWV), Working state