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Cost Optimization of the Queueing System with Degrading Service Rate, Bernoulli Vacation, and a Regular Vacation After Fixed Services

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Abstract

Due to the continuous work, degradation in the working capacity of machines and servers is an inevitable phenomenon. To analyze this type of situation in queueing systems, we considered the degradation in the service rate of the server. For the maintenance purpose, vacation is given after completion of a threshold number of services. After maintenance, the server will start working in the fresh mode, that is, with the initial service rate. The impatient behavior of customers and unreliability of the server are also included, which make our model more realistic. We derived the stability condition for this model and found out the steady state probabilities using matrix geometric method. All the system performance measures are calculated. An expected cost function is constructed and is optimized using the particle swarm optimization method. Effects of degrading service rate as well as breakdown rate and vacation rate are studied on the key measures and the expected cost function.

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Acknowledgements

The authors would like to thank the Editor-in-Chief and the anonymous referees of the journal for their valuable suggestions and comments which help a lot in improving the quality and clarity of the paper. First author is also thankful to CSIR (Council of Scientific and Industrial Research), India for the financial support, file number is 09/1131(0007)/2017-EMR-I.

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  1. Department of Mathematics, Central University of Rajasthan, Ajmer, India, 305817

    Alka Choudhary, Nitin Mahla & Dinesh C. Sharma

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  1. Alka Choudhary
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Correspondence to Alka Choudhary.

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Choudhary, A., Mahla, N. & Sharma, D.C. Cost Optimization of the Queueing System with Degrading Service Rate, Bernoulli Vacation, and a Regular Vacation After Fixed Services. Int. J. Appl. Comput. Math 8, 124 (2022). https://doi.org/10.1007/s40819-022-01319-z

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