Journal of Statistical Theory and Practice

, Volume 11, Issue 1, pp 41–62 | Cite as

Waiting time of bulk arrival unreliable queue with balking and Bernoulli feedback using maximum entropy principle

  • Charan Jeet SinghEmail author
  • Sandeep Kaur
  • Madhu Jain


This article deals with an MX/G/1 unreliable queueing system with Bernoulli feedback and discouraging behavior of the units arriving at the service system. The maximum entropy principle is used to study the queueing indices of the system. The flow of the units is in batches with varying arrival rates and depends on the joining probabilities of the units in different system states. The server renders the essential as well as optional service on demand to the units that join the system. The server may break down while rendering any stage of the service. In order to recover the failed server, multiphase repair is required. The entropy function is constructed in terms of several known constraints and the maximum entropy principle is used to obtain the approximate waiting time. We perform a comparative study of the exact waiting time obtained by the supplementary variable technique and the approximate waiting time derived by using maximum entropy principle by taking the numerical illustration. A sensitivity analysis is also carried out to validate the analytical results.


Bernoulli feedback bulk arrival maximum entropy optional service supplementary variable unreliable server 


60K25 68M20 


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The authors are thankful to the editor of the journal and the reviewers for their valuable suggestions for the improvement of this article.


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© Grace Scientific Publishing, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsGuru Nanak Dev UniversityAmritsarIndia
  2. 2.Department of Applied SciencesKhalsa College of Engineering & TechnologyIndia
  3. 3.Department of MathematicsIndian Institute of TechnologyRoorkeeIndia

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