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2020 | 30 | nr 4 | 5--28
Tytuł artykułu

Impatient Customers in Markovian Queue with Bernoulli Feedback and Waiting Server Under Variant Working Vacation Policy

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with customers' impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using the probability generating function (PGF) technique, we obtain the steady-state solution of the system. Besides, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using a quadratic fit search method (QFSM). Finally, numerical examples are provided to visualise the analytical results. (original abstract)
Rocznik
Tom
30
Numer
Strony
5--28
Opis fizyczny
Twórcy
  • Djillali Liabes University of Sidi Bel Abbes, Algeria
  • The University Moulay Tahar of Saida, Algeria
autor
  • The University Moulay Tahar of Saida, Algeria
autor
  • Government Degree College Mendhar, Poonch, Jammu and Kashmir, India
Bibliografia
  • [1] AMMAR S.I., Transient solution of an vacation queue with a waiting server and impatient customers, J. Egypt. Math. Soc., 2017, 25, 337-342.
  • [2] AZHAGAPPAN A., Transient behavior of a Markovian queue with working vacation variant reneging and a waiting server, TOP, 2019, 27, 351.
  • [3] BOUCHENTOUF A.A., GUENDOUZI A., Cost optimization analysis for an vacation queueing system with waiting servers and impatient customers, SeMA, 2019, 76, 309-341.
  • [4] BOUCHENTOUF A.A., GUENDOUZI A., The Bernoulli feedback queue with variant multiple working vacations and impatient customers: Performance and economic analysis, Arab. J. Math., 2019, DOI: 10.1007/s40065-019-0260-x, 1-19.
  • [5] BOUCHENTOUF A.A., GUENDOUZI A., KANDOUCI A., Performance and economic study of heterogeneous M/M/2/N feedback queue with working vacation and impatient customers, ProbStat Forum, 2019, 12 (1), 15-35.
  • [6] BOUCHENTOUF A.A., CHERFAOUI M., BOUALEM M., Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers, OPSEARCH, 2019, 56 (1), 300-320.
  • [7] BOUCHENTOUF A.A., MESSABIHI A., Heterogeneous two-server queueing system with reverse balking and reneging, OPSEARCH, 2018, 55 (2), 251-267.
  • [8] BOUCHENTOUF A.A., YAHIAOUI L., On feedback queueing system with reneging and retention of reneged customers, multiple working vacations and Bernoulli schedule vacation interruption, Arab. J. Math., 2017, 6 (1), 1-11.
  • [9] CHOUDHURY G., PAUL M., A two phase queueing system with Bernoulli feedback, J. Inf. Manage. Sci., 2005, 16 (1), 35-52.
  • [10] DEEPA B., KALIDASS K., The Markovian vacation queues with a waiting server and geometric abandonments, Int. J. Pure Appl. Math., 2018, 118, 1903-1910.
  • [11] LAXMI V.P., JYOTHSNA K., Analysis of finite buffer renewal input queue with balking and multiple working vacations, OPSEARCH, 2013, 50 (4), 548-565.
  • [12] LAXMI V.P., RAJESH P., Analysis of variant working vacations queue with customer impatience. Int. J. Manage. Sci. Eng. Manage., 2016, 12, 186-195.
  • [13] LAXMI V.P., RAJESH P., Performance measures of variant working vacation on batch arrival queue with reneging, Int. J. Math. Arch., 2017, 8, 85-96.
  • [14] LI J., TIAN N., The M/M/1 queue with working vacations and vacation interruptions, J. Syst. Sci. Syst. Eng., 2007, 16 (1), 121-127.
  • [15] PADMAVATHY R., KALIDASS K., RAMANATH K., Vacation queues with impatient customers and a waiting server, Int. J. Latest Trends Soft. Eng., 2011, 1, 10-19.
  • [16] KALIDASS K., KASTURI R., A two phase service M/G/1 queue with a finite number of immediate Bernoulli feedbacks, OPSEARCH, 2014, 51 (2), 201-218.
  • [17] KALIDASS K., RAMANATH K., Time dependent analysis of queue with server vacations and a waiting server, QTNA 2011, Proc. 6th International Conference on Queueing Theory and Network Applications, Korea University, 2011, 77-83, https://doi.org/10.1145/2021216.2021227
  • [18] KEILSON J., SERVI L.D., A distribution form of Littles law, Oper. Res. Lett., 1988, 7 (5), 223-227.
  • [19] KRISHNA KUMAR B., VIJAYAKUMAR A., ARIVUDAINAMBI D., The M/G/1 retrial queue with Bernoulli schedules and general retrial times, Comp. Math. Appl., 2002, 43, 15-30.
  • [20] SELVARAJU N., GOSWAMI C., Impatient customers in an M/M/1 queue with single and multiple working vacations, Comp. Ind. Eng., 2013, 65, 207-215.
  • [21] SERVI L.D., FINN S.G., M/M/1 queues with working vacations (M/M/1/WV), Perf. Eval., 2002, 50, 41-52.
  • [22] SHAKIR M., MANOHARAN P., Analysis of the M/M/1 queue with single working vacation and vacation interruption (IJMTT), Int. J. Math. Trends Techn., 2017, 47 (1), 32-40.
  • [23] SHAKIR M., MANOHARAN P., Analysis of a M/M/c queue with single and multiple synchronous working vacations, Appl. Appl. Math., 2017, 12 (2), 671-694.
  • [24] SHAKIR M., MANOHARAN P., Impatient customers in an M/M/c queue with single and Multiple Synchronous Working Vacations, Pakistan J. Stat. Oper. Res., 2018, 14 (3), 571-594.
  • [25] SUDHESH R., AZHAGAPPAN A., Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations, OPSEARCH, 2018, 55 (3-4), 787-806.
  • [26] SUDHESH R., RAJ L.F., Computational analysis of stationary and transient distribution of single server queue with working vacation, Global Trends Comp. Comm. Syst. Comm. Comp. Inf. Sci., 2012, 269, 480-489.
  • [27] TIAN N., ZHAO X., WANG K., The M/M/1 queue with single working vacation, Int. J. Inf. Manage. Sci., 2008, 19, 621-634.
  • [28] TAKACS L., A Single Server Queue with Feedback, Bell Syst. Tech. J., 1963, 42, 505-519.
  • [29] YAHIAOUI L., BOUCHENTOUF A.A., KADI M., Optimum cost analysis for an feedback queue under synchronous working vacations and impatient customers, Croatian Operational Research Review, 2019, 10, 211-226.
  • [30] YECHIALI U., On the queue with a waiting server and vacations, Sankhya: Indian J. Stat., 2004, 66 (1), 159-174.
  • [31] YUE D., YUE W., SAFFER Z., Chen X., Analysis of an queueing system with impatient customers and a variant of multiple vacation policy, J. Ind. Manage. Opt., 2014, 10, 89-112.
  • [32] YUE D., YUE W., XU G., Analysis of a queueing system with impatient customers and working vacations, Proc. 6th International Conference on Queueing Theory and Network Applications, Korea University, 2011, 208-211.
  • [33] VARALAKSHMI M., CHANDRASEKARAN V.M., SARAVANARAJAN M.C., A single server queue with immediate feedback, working vacation and server breakdown, Int. J. Eng. Techn., 2018, 7 (4.10), 476-479.
  • [34] VARALAKSHMI M., SARAVANARAJAN M.C., CHANDRASEKARAN V.M., A study on M/G/1 retrial G-queue with two phase of service, immediate feedback and working vacation, IOP Conference Series, Materials Science and Engineering, 2017, 263, 042156.
  • [35] WANG T.Y., KE J.C., CHANG F.M., On the discrete-time queue with randomized vacations and at most vacations, Appl. Math. Model., 2011, 35, 2297-2308.
  • [36] ZHANG Z.G., TIAN N., Discrete time queue with multiple adaptive vacations, Queueing Syst., 2001, 38, 419-429.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171614593

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