Two-Level Control Policy of an Unreliable Queueing System with Queue Size-Dependent Vacation and Vacation Disruption

  • S. P. NiranjanEmail author
  • V. M. Chandrasekaran
  • K. Indhira
Conference paper
Part of the Trends in Mathematics book series (TM)


The objective of the paper is to analyse two-level control policy of an MXG(a, b)∕1 queueing system with fast and slow vacation rates and vacation disruption. In the service completion epoch, if the queue length is less than ‘a’, then the server leaves for a vacation. In this model depending upon the queue length, the server is allowed to take two types of vacation called fast vacation and slow vacation. Addressing this in the service completion epoch, if the queue length ψ(say) is less than β where β < a − 1, then the server leaves for slow vacation. On the other hand, if ψ > ζ, where a − 1 ≥ ζ > β during service completion, then the server leaves for fast vacation. During slow vacation if the queue length reaches the value ζ, then the server breaks the slow vacation and switches over to fast vacation. Also if the queue length attains the threshold value ‘a’ during fast vacation, then the server breaks the fast vacation too and moves to tune-up process to start the service. After tune-up process service will be initiated only if ψ ≥ N(N > b). For the designed queueing system probability, generating function of the queue size at an arbitrary time epoch is obtained by using supplementary variable technique. Various performance characteristics will also be derived with suitable numerical illustrations. Cost-effective analysis is also carried out in the paper.



This work was supported by the “NBHM DAE, Government of India” and “Ref.No.2∕48(6)∕2015∕NBHM(R.P)∕R&D11∕14129”.


  1. 1.
    Haridass, M., Nithya, R.P.: Analysis of a bulk queueing system with server breakdown and vacation interruption. International Journal of Operations Research.12(3), 069–090 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ke, J.C.: Modified T Vacation Policy for an M/G/1 Queueing System with an Unreliable Server and start-up. Mathematical and Computer Modelling.41, 1267–1277 (2005)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Lee, H.W., Lee, S.S., Chae, K.C.: A Fixed-Size Batch Service Queue With Vacations. Journal of Applied Mathematics and Stochastic Analysis.9(2), 205–219 (1996)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Neuts, M.F.: A general class of bulk queues with Poisson input. Ann.Math. Statis. 38, 759–770 (1967).MathSciNetCrossRefGoogle Scholar
  5. 5.
    Niranjan, S.P., Chandrasekaran, V.M., Indhira, K.:Queue size dependent service in bulk arrival queueing system with server loss and vacation break-off. International journal of Knowledge Management in Tourism and Hospitality.1(2), 176–207 (2017)CrossRefGoogle Scholar
  6. 6.
    Singh, C.J., Kumar, B.:Bulk queue with Bernoulli vacation and m-optional services under N-policy. International journal of operational research. 30(4), 460–483 (2017)Google Scholar
  7. 7.
    Wu, Wenqing, Tang, Yinghui, Yu, Miaomiao.: Analysis of an M/G/1 queue with N-policy, single vacation, unreliable service station and replaceable repair facility. Operational Research Society of India. 52, 670691 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • S. P. Niranjan
    • 1
    Email author
  • V. M. Chandrasekaran
    • 1
  • K. Indhira
    • 1
  1. 1.Department of Mathematics, School of Advanced SciencesVITVelloreIndia

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