\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On the multi-server machine interference with modified Bernoulli vacation

Abstract Related Papers Cited by
  • We study the multi-server machine interference problem with repair pressure coefficient and a modified Bernoulli vacation. The repair rate depends on the number of failed machines waiting in the system. In congestion, the server may increase the repair rate with pressure coefficient $\theta$ to reduce the queue length. At each repair completion of a server, the server may go for a vacation of random length with probability $p$ or may continue to repair the next failed machine, if any, with probability $1-p$. The entire system is modeled as a finite-state Markov chain and its steady state distribution is obtained by a recursive matrix approach. The major performance measures are evaluated based on this distribution. Under a cost structure, we propose to use the Quasi-Newton method and probabilistic global search Lausanne method to search for the global optimal system parameters. Numerical examples are presented to demonstrate the application of our approach.
    Mathematics Subject Classification: Primary: 90B22; Secondary: 60K25.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    F. Benson and D. R. Cox, The productivity of machine requiring attention at random intervals, Journal of the Royal Statistical Society B, 13 (1951), 65-82.

    [2]

    E. K. P. Chong and S. H. Zak, An Introduction of Optimization, 2nd edition, John Wiley and Sons, New Jersey, 2001.doi: 10.1002/9781118033340.

    [3]

    G. Choudhury, A two-stage batch arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and Computer Modeling, 42 (2005), 71-85.doi: 10.1016/j.mcm.2005.04.003.

    [4]

    G. Choudhury and K. Deka, An $M^X/G/1$ unreliable retrial queue with two phases of service and Bernoulli admission mechanism, Applied Mathematics and Comutation, 215 (2009), 936-949.doi: 10.1016/j.amc.2009.06.015.

    [5]

    G. Choudhury and K. C. Madan, A two phase batch arrival queueing system with a vacation time under Bernoulli schedule, Applied Mathematics and Computation, 149 (2004), 337-349.doi: 10.1016/S0096-3003(03)00138-3.

    [6]

    G. Choudhury and L. Tadj, The optimal control of an $M^X/G/1$ unreliable server queue with two phases of service and Bernoulli vacation schedule, Mathematical and Computer Modelling, 54 (2011), 673-688.doi: 10.1016/j.mcm.2011.03.010.

    [7]

    B. T. Doshi, Queueing systems with vacations - a survey, Queueing Systems, 1 (1986), 29-66.doi: 10.1007/BF01149327.

    [8]

    S. M. Gupta, Machine interference problem with warm spares, server vacations and exhaustive service, Performance Evaluation, 29 (1997), 195-211.doi: 10.1016/S0166-5316(96)00046-6.

    [9]

    J. C. Ke, Vacation policies for machine interference problem with an unreliable server and state-dependent service rate, Journal of the Chineses Institute of Industrial Engineers, 23 (2006), 100-114.

    [10]

    J. C. Ke, S. L. Lee and C. H. Liou, Machine repair problem in production systems with spares and server vacations, RAIRO-Operations Research, 43 (2009), 35-54.doi: 10.1051/ro/2009004.

    [11]

    J. C. Ke and C. H. Lin, A Markov repairable system involving an imperfect service station with multiple vacations, Asia-Pacific Journal of Operational Research, 22 (2005), 555-582.doi: 10.1142/S021759590500073X.

    [12]

    J. C. Ke and K. H. Wang, Vacation policies for machine repair problem with two type spares, Applied Mathematical Modelling, 31 (2007), 880-894.doi: 10.1016/j.apm.2006.02.009.

    [13]

    J. C. Ke, C. H. Wu and W. L. Pearn, Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule, Applied Mathematical Modelling, 35 (2011), 2196-2208.doi: 10.1016/j.apm.2010.11.019.

    [14]

    J. C. Ke, C. H. Wu and Z. Zhang, Recent developments in vacation queueing models: A short survey, International Journal of Operations Research, 7 (2010), 3-8.

    [15]

    K. C. Madan, W. Abu-Dayyeh and F. Taiyyan, A two server queue with Bernoulli schedules and a single vacation policy, Applied Mathematics and Computation, 145 (2003), 59-71.doi: 10.1016/S0096-3003(02)00469-1.

    [16]

    R. Oliva, Tradeoffs in responses to work pressure in the service industry, California Management Review, 30 (2001), 26-43.doi: 10.1109/EMR.2002.1022405.

    [17]

    B. Raphael and I. F. C. Smith, A direct stochastic algorithm for global search, Journal of Applied Mathematics and Computation, 146 (2003), 729-758.doi: 10.1016/S0096-3003(02)00629-X.

    [18]

    L. Tadj, G. Choudhury and C. Tadj, A quorum queueing system with a random setup time under N-policy and with Bernoulli vacation schedule, Quality Technology and Quantitative Management, 3 (2006), 145-160.

    [19]

    H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vacation and Priority Systems. part I, vol. 1, North-Holland, Amsterdam, 1991.

    [20]

    N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer-Verlag, New York, 2006.

    [21]

    K. H. Wang, W. L. Chen and D. Y. Yang, Optimal management of the machine repair problem with working vacation: Newton's method, Journal of Computational and Applied Mathematics, 233 (2009), 449-458.doi: 10.1016/j.cam.2009.07.043.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(92) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return