197
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Analytical and computational studies of the BMAP/G(a,Y)/1 queue

& ORCID Icon
Pages 3586-3614 | Received 14 Feb 2019, Accepted 18 Dec 2019, Published online: 07 Jan 2020

References

  • Abolnikov, L., and H. J. Dshalalow. 1992. On a multilevel controlled bulk queueing system MX/Gr,R/1. Journal of Applied Mathematics and Stochastic Analysis 5 (3):237–60.
  • Akar, N., and E. Arikan. 1996. A numerically efficient method for the MAP/D/1/K queue via rational approximations. Queueing Systems 22 (1):97–120.
  • Bagchi, T. P., and J. G. C. Templeton. 1973. A note on the MX/GY/1/K bulk queueing system. Journal of Applied Probability 10 (4):901–6.
  • Banerjee, A., U. C. Gupta, and S. R. Chakravarthy. 2015. Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service. Computers & Operations Research 60:138–49.
  • Banik, A. D. 2009. Queueing analysis and optimal control of BMAP/G(a,b)/1/N and BMAP/MSP(a,b)/1/N systems. Comupters and Industrial Engineering 57 (3):748–61.
  • Banik, A. D. 2015. Single server queues with a batch Markovian arrival process and bulk renewal or non-renewal service. Journal of Systems Science and Systems Engineering 24 (3):337–63. doi:10.1007/s11518-015-5268-y.
  • Bar-Lev, S. K., M. Parlar, D. Perry, W. Stadje, and F. A. Van der Duya Schouten. 2007. Applications of bulk queues to group testing model with incomplete identification. European Journal of Operational Research 83 (1):226–37. doi:10.1016/j.ejor.2006.09.086.
  • Brière, G., and M. L. Chaudhry. 1989. Computational analysis of single-server bulk-service queue. Advances in Applied Probability 21 (1):207–25.
  • Chakravarthy, S. R., A. Maity, and U. C. Gupta. 2017. An (s, S) inventory in a queueing system with batch service facility. Annals of Operations Research 258 (2):263–83.
  • Chang, S. H., D. W. Choi, and T. S. Kim. 2004. Performance analysis of a finite-buffer bulk-arrival and bulk-service queue with variable server capacity. Stochastic Analysis and Applications 22 (5):1151–73. doi:10.1081/SAP-200026427.
  • Chaudhry, M. L., G. Singh, and U. C. Gupta. 2013. A simple and complete computational analysis of MAP/R/1 queue using roots. Methodology and Computing in Applied Probability 15 (3):563–82.
  • Chaudhry, M. L., and J. G. C. Templeton. 1983. A first course in bulk queues. New York, NY: John Wiley & Sons.
  • Chaudhry, M. L., B. K. Yoon, and N. K. Kim. 2010. On the distribution of the number of customers in the D-BMAP/G(a,b)/1/M queue - a simple approach to a complex problem. INFOR 48 (2):121–32.
  • Çinlar, E. 1975. Introduction to stochastic process. Upper Saddle River, NJ: Prentice Hall.
  • Claeys, D., B. Steyaert, J. Walraevens, K. Laevens, and H. Bruneel. 2013. Analysis of a versatile batch-service queueing model with correlation in the arrival process. Performance Evaluation 70 (4):300–16.
  • Gail, H. R., S. L. Hantler, and B. A. Taylor. 1996. Spectral analysis of M/G/1 and G/M/1 type Markov chains. Advances in Applied Probability 28 (1):114–65.
  • Gupta, U. C., G. Singh, and M. L. Chaudhry. 2016. An alternative method for computing system-length distributions of BMAP/R/1 and BMAP/D/1 queues using roots. Performance Evaluation 95:60–79.
  • Gupta, U. C., and S. Pradhan. 2015. A computational approach for determination of system length distribution of a batch arrival and batch service queue. The 6th International Conference on Computational Methods (ICCM2015), Auckland, New Zealand.
  • Kim, N. K., K. C. Chae, and M. L. Chaudhry. 2004. An invariance relation and a unified method to derive stationary queue-length distributions. Operations Research 52 (5):756–64.
  • Lucantoni, D. M. 1991. New results on the single server queue with a batch Markovian arrival process. Stochastic Models 7 (1):1–46. doi:10.1080/15326349108807174.
  • Lucantoni, D. M. 1993. The BMAP/G/1 queue: A tutorial. In Performance evaluation of computer and communications systems, eds. L. Donatiello and R. Nelson, 330–58. Rome, Italy: Springer Verlag.
  • Lucantoni, D. M., and M. F. Neuts. 1994. Some steady-state distributions for the MAP/SM/1 queue. Stochastic Models 10 (3):575–98.
  • Maity, A., and U. C. Gupta. 2015. Analysis and optimal control of a queue with infinite buffer under batch- size dependent versatile bulk-service rule. Opsearch 52 (3):472–89.
  • Medhi, J. 1991. Stochastic models in queueing theory. Boston, MA: Academic Press.
  • Miller, R. G. 1959. A contribution to the theory of bulk queues. Journal of the Royal Statistical Society: Series B (Methodological) 21 (2):320–37.
  • Neuts, M. F. 1989. Structured stochastic matrices of M/G/1 type and their applications. New York, NY: CRC Press, Marcel Dekker.
  • Powell, W. 1985. Analysis of vehicle holding and cancellation strategies in bulk arrival, bulk service queues. Transportation Science 19 (4):352–277. doi:10.1287/trsc.19.4.352.
  • Powell, W., and P. Humblet. 1986. The bulk service queue with a general control strategy: Theoretical analysis and a new computational procedure. Operations Research 34 (2):267–75. doi:10.1287/opre.34.2.267.
  • Pradhan, S., and U. C. Gupta. 2017. Modeling and analysis of an infinite-buffer batch-arrival queue with batch-size-dependent service: MX/Gn(a,b)/1. Performance Evaluation 108:16–31.
  • Pradhan, S., and U. C. Gupta. 2019. Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process. Annals of Operations Research 277 (2):161–96.
  • Ramaswami, V. 1988. A stable recursion for the steady state vector in Markov chain M/G/1 type. Stochastic Models 4 (1):183–8.
  • Samanta, S. K. 2015. Waiting-time analysis of D-BMAP/G/1 queueing system. Annals of Operations Research. doi:10.1007/s10479-015-1974-6.
  • Samanta, S. K., M. L. Chaudhry, and A. Pacheco. 2016. Analysis of BMAP/MSP/1 queue. Methodology and Computing in Applied Probability 18 (2):419–40.
  • Shortle, J. F., P. H. Brill, M. J. Fischer, D. Gross, and D. M. B. Masi. 2004. An algorithm to compute the waiting time distribution for the M/G/1 queue. INFORMS Journal on Computing 16 (2):152–61.
  • Sikdar, K., and U. C. Gupta. 2008. On the batch arrival batch service queue with finite buffer under server’s vacation: MX/GY/1/N queue. Computers & Mathematics with Applications 56 (11):2861–73.
  • Sikdar, K., and S. K. Samanta. 2016. Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation. Opsearch 53 (3):553–83. doi:10.1007/s12597-015-0244-3.
  • Singh, G., U. C. Gupta, and M. L. Chaudhry. 2013. Computational analysis of bulk service queue with Markovian arrival process: MAP/R(a,b)/1 queue. OPSEARCH 50:582–603.
  • Singh, G., U. C. Gupta, and M. L. Chaudhry. 2016. Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots. Journal of Applied Probability 53 (4):1078–97.
  • Yi, X. W., N. K. Kim, B. K. Yoon, and K. C. Chae. 2007. Analysis of the queue-length distribution for the discrete-time batch-service Geo/G(a,Y)/1/K queue. European Journal of Operational Research 181:787–92.

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.