On Finite Buffer BMAP/G/1 Queue with Queue Length Dependent Service

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)


This paper deals with the analysis of a finite buffer queueing system where customers are arriving according to the batch Markovian arrival process (BMAP). The service time is considered to be generally distributed and is dependent on the queue length at service initiation epoch. The stationary queue length distribution at various epoch is obtained using the embedded Markov chain technique and the supplementary variable technique. A computational procedure has been discussed by considering phase-type service time distribution. Finally, some numerical results are given to show the numerical compatibility of the analytical results. Also a comparative study is carried out to establish the fact that our model may help in optimizing system performance by controlling the service rate depending on the state of the system.


Batch Markovian arrival process Blocking probability Congestion Queue length dependent service 



The authors thank the anonymous referee for their valuable comments. The second author acknowledges the Department of Science and Technology (DST), Govt. of India, for the partial financial support under the project grant \(SB/FTP/MS-048/2013\).


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (BHU)VaranasiIndia
  2. 2.Department of MathematicsBMS Institute of Technology & Management, (Affiliated to VTU, Belgaum-18)Yelahanka, BengaluruIndia

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