Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 2-1, March 2015, Pages: 1-10
Received: Dec. 4, 2014; Accepted: Dec. 5, 2014; Published: Mar. 11, 2015
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Author
Vishwa Nath Maurya, 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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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.
Keywords
Markovian queue, working vacation (WV), Bernoulli vacation, heterogeneous servers, algorithmic approach, matrix geometric solution, steady state performance measures
To cite this article
Vishwa Nath Maurya, Mathematical Modelling and Steady State Performance Analysis of a Markovian Queue with Heterogeneous Servers and Working Vacation, American Journal of Theoretical and Applied Statistics. Special Issue: Scope of Statistical Modeling and Optimization Techniques in Management Decision Making Process. Vol. 4, No. 2-1, 2015, pp. 1-10. doi: 10.11648/j.ajtas.s.2015040201.11
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