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Time-Dependent Analytical and Computational Study of an M/M/1 Queue with Disaster Failure and Multiple Working Vacations

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Mathematical Analysis and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 381))

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Abstract

An M/M/1 working vacation (WV) queueing model with disaster failure is considered to examine time-dependent behavior. When the system is in busy mode, it can fail such that all the customers in the system are flushed out and never returns; such type of failure is known as disaster failure. The server is allowed to go for a WV after each busy period for a random duration of time. In the duration of WV, the server reduces the service rate rather than halting the service. After completing the vacation period, the server can take any number of vacation until he found some customers waiting in the queue; this vacation policy is known as multiple vacation policy. The transient analytical formulae for the queue size distributions are formulated by solving Chapman–Kolmogorov equations using continued fractions, modified Bessel function and probability generating function methods. Moreover, various queueing performance measures are given, and real-time performance is evaluated by computing the performance measures numerically.

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Acknowledgements

The author (Rakesh Kumar Meena) is thankful to the institute of Eminence (IoE) cell, Banaras Hindu University for providing a reserach grant with project reference number IoE (6031) to carry out the present research wok.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Madhu Jain & Mayank Singh

  2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India

    Rakesh Kumar Meena

Authors
  1. Madhu Jain
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  2. Mayank Singh
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  3. Rakesh Kumar Meena
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Correspondence to Mayank Singh .

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Editors and Affiliations

  1. Faculty of Economy, Ibn Zohr University, Agadir, Morocco

    Ouayl Chadli

  2. Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur, India

    Sourav Das

  3. Mathematics, University of Central Florida, Orlando, FL, USA

    Ram N. Mohapatra

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    A. Swaminathan

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Jain, M., Singh, M., Meena, R.K. (2021). Time-Dependent Analytical and Computational Study of an M/M/1 Queue with Disaster Failure and Multiple Working Vacations. In: Chadli, O., Das, S., Mohapatra, R.N., Swaminathan, A. (eds) Mathematical Analysis and Applications. Springer Proceedings in Mathematics & Statistics, vol 381. Springer, Singapore. https://doi.org/10.1007/978-981-16-8177-6_21

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