American Journal of Theoretical and Applied Statistics

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Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation

Received: 04 December 2014    Accepted: 05 December 2014    Published: 11 March 2015
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Abstract

In the present paper, mathematical modeling for analyzing a Markovian queueing system with two heterogeneous servers and working vacation has been demonstrated. Keeping in view queueing situations in real life problems, here we consider service policy that initially both the heterogeneous servers take vacation when there are no customers waiting for service in the queue; however, after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. Busy period analysis for the working vacation model with heterogeneous servers has been worked out. Performance measures of the Markovian queueing system with varying parameters have been explored under steady state using matrix geometric method. Finally, based on sensitivity analysis of the performance measures, conclusive observations have been focused.

DOI 10.11648/j.ajtas.s.2015040201.11
Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2-1, March 2015)

This article belongs to the Special Issue Scope of Statistical Modeling and Optimization Techniques in Management Decision Making Process

Page(s) 1-10
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Markovian queue, working vacation (WV), Bernoulli vacation, heterogeneous servers, algorithmic approach, matrix geometric solution, steady state performance measures

References
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Author Information
  • Department of Pure & Applied Mathematics and Statistics, School of Science & Technology, The University of Fiji, Lautoka, Fiji Islands; Vision Institute of Technology Aligarh, U.P. Technical University, Lucknow ,India

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    Vishwa Nath Maurya. (2015). Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation. American Journal of Theoretical and Applied Statistics, 4(2-1), 1-10. https://doi.org/10.11648/j.ajtas.s.2015040201.11

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    ACS Style

    Vishwa Nath Maurya. Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation. Am. J. Theor. Appl. Stat. 2015, 4(2-1), 1-10. doi: 10.11648/j.ajtas.s.2015040201.11

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    Vishwa Nath Maurya. Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation. Am J Theor Appl Stat. 2015;4(2-1):1-10. doi: 10.11648/j.ajtas.s.2015040201.11

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  • @article{10.11648/j.ajtas.s.2015040201.11,
      author = {Vishwa Nath Maurya},
      title = {Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {2-1},
      pages = {1-10},
      doi = {10.11648/j.ajtas.s.2015040201.11},
      url = {https://doi.org/10.11648/j.ajtas.s.2015040201.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.s.2015040201.11},
      abstract = {In the present paper, mathematical modeling for analyzing a Markovian queueing system with two heterogeneous servers and working vacation has been demonstrated. Keeping in view queueing situations in real life problems, here we consider service policy that initially both the heterogeneous servers take vacation when there are no customers waiting for service in the queue; however, after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. Busy period analysis for the working vacation model with heterogeneous servers has been worked out. Performance measures of the Markovian queueing system with varying parameters have been explored under steady state using matrix geometric method. Finally, based on sensitivity analysis of the performance measures, conclusive observations have been focused.},
     year = {2015}
    }
    

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    AB  - In the present paper, mathematical modeling for analyzing a Markovian queueing system with two heterogeneous servers and working vacation has been demonstrated. Keeping in view queueing situations in real life problems, here we consider service policy that initially both the heterogeneous servers take vacation when there are no customers waiting for service in the queue; however, after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. Busy period analysis for the working vacation model with heterogeneous servers has been worked out. Performance measures of the Markovian queueing system with varying parameters have been explored under steady state using matrix geometric method. Finally, based on sensitivity analysis of the performance measures, conclusive observations have been focused.
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