Advanced Search
Article Contents
Article Contents

Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service

Abstract Related Papers Cited by
  • Queues with Markovian service process ($MSP$) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a finite buffer single server batch service ($a, b)$ queue with general input and Markovian service process ($MSP$). The server accesses new arrivals even after service has started on any batch of initial number $a$. This operation continues till the service time of the ongoing batch is completed or the maximum accessible capacity $d ~(a\le d < b)$ of the batch being served is attained whichever occurs first. Using the embedded Markov chain technique and the supplementary variable technique we obtain the steady state queue length distributions at pre-arrival and arbitrary epochs. The primary focus is on the various performance measures of the steady state distribution of the batch service, special cases and also on numerical illustrations.
    Mathematics Subject Classification: Primary: 60K25; Secondary: 90B22, 68M20.


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

    F. J. Albores-Velasco and F. S. Tajonar-Sanabria, Anlysis of the $GI$/$MSP$/$c$/$r$ queueing system, Information Processes, 4 (2004), 46-57.


    Y. Baba, Analysis of $GI$/$M$/$1$ queue with multiple working vacations, Oper. Res. Lett., 33 (2005), 201-209.doi: 10.1016/j.orl.2004.05.006.


    A. D. Banik, U. C. Gupta and M. L. Chaudhry, Finite-buffer bulk service queue under Markovian service process: $GI$/$MSP^(a,b)$/$1$/$N$, Stoch. Anal. Appl., 27 (2009), 500-522.doi: 10.1080/07362990902844157.


    P. P. Bocharov, Stationary distribution of a finite queue with recurrent flow and Markovian service, Automat. Remote Control, 57 (1996), 1274-1283.


    S. Chakravarthy, A finite capacity $GI$/$PH$/$1$ queue with group services, Naval Res. Logist., 39 (1992), 345-357.doi: 10.1002/1520-6750(199204)39:3<345::AID-NAV3220390305>3.0.CO;2-V.


    S. Chakravarthy, Analysis of a finite $MAP$/$G$/$1$ queue with group services, Queueing Systems, 13 (1993), 385-407.doi: 10.1007/BF01149262.


    M. L. Chaudhry and J. G. C. Templeton, "A First Course in Bulk Queues," John Wiley, New York, 1983.


    J. H. Dshalalow, "Frontiers in Queueing: Models and Applications in Sciences and Engineering," CRC press, Boca Raton, FL., 1997.


    H. Gold and P. Tran-Gia, Performance analysis of a batch service queue arising out of manufacturing and system modelling, Queueing Systems, 14 (1993), 413-426.doi: 10.1007/BF01158876.


    V. Goswami, J. R. Mohanty and S. K. Samanta, Discrete-time bulk-service queues with accessible and non-accessible batches, Appl. Math. Comput., 182 (2006), 898-906.doi: 10.1016/j.amc.2006.04.047.


    V. Goswami and K. Sikdar, Discrete-time batch service $GI$/$Geo^(a,b)$/$1$/$N$ queue with accessible and non-accessible batches, Internaional Journal of Mathematics in Operational Research, 2 (2010), 233-257.doi: 10.1504/IJMOR.2010.030818.


    W. K. Grassmann, M. I. Taksar and D. P. Heyman, Regenerative analysis and steady state distributions for Markov chains, Oper. Res., 33 (1985), 1107-1116.doi: 10.1287/opre.33.5.1107.


    D. Gross, J. F. Shortle, J. M. Thompson and C. M. Harris, "Fundamentals of Queueing Theory," 4th Edition, John Wiley & Sons, Inc., New York, 2008.


    U. C. Gupta and A. D. Banik, Complete analysis of finite and infinite buffer $GI$/$MSP$/$1$ queue - A computational approach, Oper. Res. Lett., 35 (2006), 273-280.doi: 10.1016/j.orl.2006.02.003.


    U. C. Gupta and P. V. Laxmi, Analysis of $MAP$/$G^(a,b)$/$1$/$N$ queue, Queueing Systems, 38 (2001), 109-124.doi: 10.1023/A:1010909913320.


    G. Hébuterne and C. Rosenberg, Arrival and departure state distributions in the general bulk-service queue, Naval Res. Logist., 46 (1999), 107-118.doi: 10.1002/(SICI)1520-6750(199902)46:1<107::AID-NAV7>3.0.CO;2-Y.


    L. Kleinrock, "Queueing Systems - Theory," Vol. I, John Wiley & Sons, Inc., New York, 1975.


    D. M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Comm. Statist. Stochastic Models, 7 (1991), 1-7.doi: 10.1080/15326349108807174.


    D. M. Lucantoni and V. Ramaswami, Efficient algorithms for solving non-linear matrix equations arising in phase type queues, Comm. Statist. Stochastic Models, 1 (1985), 29-52.doi: 10.1080/15326348508807003.


    J. Medhi, "Recent Developments in Bulk Queueing Models," Wiley Eastern, 1984.


    M. F. Neuts, A versatile Markovian point process, J. Appl. Probab., 16 (1979), 764-779.doi: 10.2307/3213143.


    M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models," The John Hopkins University Press, Baltimore, 1981.


    M. F. Neuts, "Structured Stochastic Matrices of $M$/$G$/$1$ Type and Their Applications," Marcel Dekker, New York, 1989.


    R. Sivasamy, A bulk service queue with accessible and non-accessible batches, Opsearch, 27 (1990), 46-54.


    R. Sivasamy and N. Pukazhenthi, A discrete time bulk service queue with accessible batch: $(Geo)$/$ NB^{(L,K)}$/$1$, Opsearch, 46 (2009), 321-334.doi: 10.1007/s12597-009-0021-2.

  • 加载中

Article Metrics

HTML views() PDF downloads(130) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint