On a BMAP/G/1 Retrial System with Two Types of Search of Customers from the Orbit

  • Alexander DudinEmail author
  • T. G. Deepak
  • Varghese C. Joshua
  • Achyutha Krishnamoorthy
  • Vladimir Vishnevsky
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


A single server retrial queueing model, in which customers arrive according to a batch Markovian arrival process (BMAP), is considered. An arriving batch, finding server busy, enters an orbit. Otherwise one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit try to reach the server subsequently and the inter-retrial times are exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms are switched-on. Thus, when the server is idle, a competition takes place between primary customers, the customers coming by retrial and the two types of searches. It is assumed that if the type II search reaches the service facility ahead of the rest, all customers in the orbit are taken for service simultaneously, while in the other two cases, only a single customer is qualified to enter the service. We assume that the service times of the four types of customers namely, primary, repeated and those by the two types of searches are arbitrarily distributed with different distributions. Steady state analysis of the model is performed.


Batch Markovian arrival process Orbit Retrials Customers search Group service 



This work has been financially supported by the Russian Science Foundation and the Department of Science and Technology (India) via grant No 16-49-02021 (INT/RUS/RSF/16) for the joint research project by the V.A. Trapeznikov Institute of Control Problems of the Russian Academy Sciences and the CMS College Kottayam.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alexander Dudin
    • 1
    Email author
  • T. G. Deepak
    • 2
  • Varghese C. Joshua
    • 3
  • Achyutha Krishnamoorthy
    • 3
  • Vladimir Vishnevsky
    • 4
  1. 1.Department of Applied Mathematics and Computer ScienceBelarusian State UniversityMinskBelarus
  2. 2.Department of MathematicsIndian Institute of Space Science and TechnologyThiruvananthapuramIndia
  3. 3.Department of MathematicsCMS CollegeKottayamIndia
  4. 4.Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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