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.
| Published in |
American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2-1)
This article belongs to the Special Issue Scope of Statistical Modeling and Optimization Techniques in Management Decision Making Process |
| DOI | 10.11648/j.ajtas.s.2015040201.11 |
| 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), 2015. Published by Science Publishing Group |
Markovian queue, working vacation (WV), Bernoulli vacation, heterogeneous servers, algorithmic approach, matrix geometric solution, steady state performance measures
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APA Style
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
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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Download@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://article.sciencepublishinggroup.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}
}
TY - JOUR T1 - Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation AU - Vishwa Nath Maurya Y1 - 2015/03/11 PY - 2015 N1 - https://doi.org/10.11648/j.ajtas.s.2015040201.11 DO - 10.11648/j.ajtas.s.2015040201.11 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 1 EP - 10 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.s.2015040201.11 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. VL - 4 IS - 2-1 ER -
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