126
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Stationary system-length distribution of Markovian bulk service queue with modified bulk service rule and dynamic service rates

ORCID Icon, &
Pages 42-62 | Received 27 Oct 2020, Accepted 24 Oct 2021, Published online: 22 Nov 2021

References

  • G. Ayyappan and T. Deepa, Analysis of an MX/G(a,b)/1 queueing model with multiple vacation controllable arrival during multiple vacation and two phases of repair with delay. Int. J. Indus. Syst. Eng. 34 (2020), pp. 409–431.
  • N.T.J. Bailey, On queueing processes with bulk service, J. R. Stat. Soc. Ser. B 16 (1954), pp. 80–87.
  • B. Bank and S.K. Samanta, Analytical and computational studies of the BMAP/G(a,Y)/1 queue, Commun. Stat. Theory Methods 50 (2020), pp. 3586–3614. Available at https://doi.org/https://doi.org/10.1080/03610926.2019.1708941
  • S.K. Bar-Lev, M. Parlar, D. Perry, W. Stadje, and F.A. Van der Duyn Schouten, Applications of bulk queues to group testing models with incomplete identification, Eur. J. Oper. Res. 183 (2007), pp. 226–237.
  • G. Brière and M.L. Chaudhry, Computational analysis of single-server bulk-service queues, M/GY/1, Adv. Appl. Probab. 27 (1989), pp. 207–225.
  • S.R. Chakravarthy, Shruti and A. Rumyantsev, Analysis of a queueing model with batch Markovian arrival process and general distribution for group clearance, Methodol. Comput. Appl. Probab. 23 (2020), pp. 1551–1579. https://link.springer.com/article/10.1007%2Fs11009-020-09828-4
  • M.L. Chaudhry, G. Singh, and U.C. Gupta, A simple and complete computational analysis of MAP/R/1 queue using roots, Methodol. Comput. Appl. Probab. 15 (2013), pp. 563–582.
  • M.L. Chaudhry and J.G.C. Templeton, A First Course in Bulk Queues, John Wiley and Sons, New York, 1983.
  • A. Chen, X. Wu, and J. Zhang, Markovian bulk-arrival and bulk-service queues with general state-dependent control, Queue. Syst. 95 (2020), pp. 1–48.
  • G.L. Curry and R.M. Feldman, An M/M/1 queue with a general bulk service rule, Naval Res. Log. Quart. 32 (1985), pp. 595–603.
  • 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), pp. 898–906.
  • U.C. Gupta, N. Kumar, S. Pradhan, F.P. Barbhuiya, and M.L. Chaudhry, Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D−MAP/Gn(a,b)/1, Rev d'Orthop. Dento-Faciale 55 (2021).
  • P.E. Hydon, Difference Equations by Differential Equation Methods, Vol. 27, Cambridge University Press, UK, 2014.
  • W.G. Kelley and A.C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, San Diego, USA, 2001.
  • J. Medhi, Recent Developments in Bulk Queueing Models, Wiley Eastern Limited, New Delhi, 1984.
  • J. Medhi, Stochastic Models in Queueing Theory, Elsevier, San Diego, USA, 2002.
  • M.F. Neuts, A general class of bulk queues with Poisson input, Ann. Math. Stat. 38 (1967), pp. 759–770.
  • W.B. Powell, Waiting-time distributions for bulk arrival, bulk service queues with vehicle-holding and cancellation strategies, Naval Res. Log. 34 (1987), pp. 207–227.
  • S. Pradhan and U.C. Gupta, Stationary queue and server content distribution of a batch-size-dependent service queue with batch Markovian arrival process: BMAP/Gn(a,b)/1, Commun. Stat Theory Methods (2020), pp. 1–28. Available at https://doi.org/https://doi.org/10.1080/03610926.2020.1813304.
  • S.K. Samanta and B. Bank, Analysis of stationary queue-length distributions of the BMAP/R(a,b)/1 queue, Int. J. Comput. Math. Comput. Syst. Theory 5 (2020), pp. 198–223.
  • R.F. Serfozo, Little laws for utility processes and waiting times in queues, Queue. Syst. 17 (1994), pp. 137–181.
  • G. Singh, U.C. Gupta, and M.L. Chaudhry, Computational analysis of bulk service queue with Markovian arrival process: MAP/R(a,b)/1 queue, Opsearch 50 (2013), pp. 582–603.
  • G. Singh, U.C. Gupta, and M.L. Chaudhry, Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots, J. Appl. Probab. 53 (2016), pp. 1078–1097.
  • G. Singh, Computational analysis of single-server queues with Markovian arrival processes using roots, Ph.D. diss., Indian Institute of Technology, Kharagpur, India, 2012. Available at http://www.idr.iitkgp.ac.in/xmlui/handle/123456789/1645.
  • R. Sivasamy, A bulk service queue with accessible and non-accessible batches, Opsearch 27 (1990), pp. 46–54.
  • W. Whitt, A review of L=λW and extensions, Queue. Syst. 9 (1991), pp. 235–268.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.