Analysis of multi server Markovian queue with functioning vacation and intolerance of customer

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    In this article, we analyze the operating behavior of two server Markovian queueing model with functioning vacation and infinite population. If the server is halt his service suddenly in a normal busy period and repair work is done immediately and service starts. The server failure and repair rates are follow exponential distribution, when the system become vacation the server takes functioning during this period the customer wait in the queue and server serves the customer with the lower service rate. The steady state behavior is also obtained, the various performance measures are also determined. The numerical example is given to test the feasibility of the model.





  • Keywords

    Vacation, busy period, customer, server, markovian queueing model, distribution.

  • References

      [1] Boxma OJ & de waal PR, “Multiserver queues with impatient customers”, ITC, Vol14, (1994), pp.743-756.

      [2] Choudhury G & deka M, “A batch arrival unreliable server Bernoulli vacation queue with two phases of service and delayed repair”, International Journal of Operations Research, Vol.10, No.3, (2013), pp.134-152.

      [3] Haridass M & Nithya RP, “Analysis of a bulk queuing system with server breakdown and vacation interruption”, International Journal of Operations Research, Vol.12, No.3, (2015), pp.069-090.

      [4] Ibe OC, “Two queues with alternating service and server breakdowns”, Queueing system, Vol.7, No.7, (1990), pp.253-268.

      [5] Kumar BK & Madheswari SP, “An M/M/2 queueing system with heterogeneous servers and multiple vacations”, Mathematical and computer Modelling, Vol.41, (2005), pp.1415-1429.

      [6] Jain M & Jain A, “Working vacations queueing models with multiple types of server breakdowns”, Applied mathematical modelling, Vol.34, No.1, (2010), pp.1-33.

      [7] Jain M & Jain A, “Batch arrival priority queueing model with second optional service and server breakdown”, International Journal of Operations Research, Vol.11, No.4, (2014), pp.112-130.

      [8] Tian NS, Li JH & Zhang ZG, “Matrix analytic method and working vacation queues-a survey”, International Journal of Information and Management Sciences, Vol.20, No.4,(2009), pp.603-633.

      [9] Neuts MF, “Matrix Geometric solutions in stochastic Models”, Johns Hopkins series inthe mathematical sciences, (1981).

      [10] Renisagayaraj M & Chandrasekar B, “Matrix-Geometric method for queueing model with multiple vacation, n-policy, server break down, repair and interruption vacation”, International Journal of Mathematical Archive, Vol.7, No.1, (2016), pp.98-104.

      [11] Renisagayaraj M & Chandrasekar B, “Matrix-Geometric Method for queueing model with state-dependent arrival of an unreliable server and PH-service”, Mathematica Aeterna, Vol.6, No.1, (2016), pp.107-116.

      [12] Aniyeri R & Nadar CR, “A multiphase queueing system with Assorted servers by using Matrix Geometric Method”, International Journal of Applied Engineering Research, Vol.12, No.22, (2017), pp.12052-12059.




Article ID: 12464
DOI: 10.14419/ijet.v7i2.21.12464

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.