Analysis of an MAP/PH/1 Queue with Flexible Group Service

Atencia, I. (2014). A discrete-time system with service control and repairs, International Journal of Applied Mathematics and Computer Science24(3): 471–484, DOI: 10.2478/amcs-2014-0035.10.2478/amcs-2014-0035Search in Google Scholar

Bailey, N. (1954). On queueing processes with bulk service, Journal of the Royal Statistical Society B16(1): 80–87.10.1111/j.2517-6161.1954.tb00149.xSearch in Google Scholar

Banerjee, A., Gupta, U. and Chakravarthy, S. (2015). Analysis of afinite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service, Computers and Operations Research60: 138–149.10.1016/j.cor.2015.02.012Search in Google Scholar

Casale, G., Zhang, E. and Smirn, E. (2010). Trace data characterization and fitting for Markov modeling, Performance Evaluation67(2): 61–79.10.1016/j.peva.2009.09.003Search in Google Scholar

Chakravarthy, S. (2001). The batch Markovian arrival process: A review and future work, in V.R.E.A. Krishnamoorthy and N. Raju (Eds.), Advances in Probability Theory and Stochastic Processes, Notable Publications Inc., Branchburg, NJ, pp. 21–29.Search in Google Scholar

Chydzinski, A. (2006). Transient analysis of the MMPP/G/1/K queue, Telecommunication Systems32(4): 247–262.10.1007/s11235-006-9001-5Search in Google Scholar

Deb, R. and Serfozo, R. (1973). Optimal control of batch service queues, Advances in Applied Probability5(2): 340–361.10.2307/1426040Search in Google Scholar

Downton, F. (1955). Waiting time in bulk service queues, Journal of the Royal Statistical Society B17(2): 256–261.10.1111/j.2517-6161.1955.tb00199.xSearch in Google Scholar

Dudin, A., Manzo, R. and Piscopo, R. (2015). Single server retrial queue with adaptive group admission of customers, Computers and Operations Research61: 89–99.10.1016/j.cor.2015.03.008Search in Google Scholar

Dudin, A., Lee, M.H. and Dudin, S. (2016). Optimization of the service strategy in a queueing system with energy harvesting and customers’ impatience, International Journal of Applied Mathematics and Computer Science26(2): 367–378, DOI: 10.1515/amcs-2016-0026.10.1515/amcs-2016-0026Search in Google Scholar

Gaidamaka, Y., Pechinkin, A., Razumchik, R., Samouylov, K. and Sopin, E. (2014). Analysis of an M/G/1/R queue with batch arrivals and two hysteretic overload control policies, International Journal of Applied Mathematics and Computer Science24(3): 519–534, DOI: 10.2478/amcs-2014-0038.10.2478/amcs-2014-0038Search in Google Scholar

Heyman, D. and Lucantoni, D. (2003). Modelling multiple IP traffic streams with rate limits, IEEE/ACM Transactions on Networking11(6): 948–958.10.1109/TNET.2003.820252Search in Google Scholar

Kesten, H. and Runnenburg, J. (1956). Priority in Waiting Line Problems, Mathematisch Centrum, Amsterdam.10.1016/S1385-7258(57)50042-5Search in Google Scholar

Kim, C., Dudin, A., Dudin, S. and Dudina, O. (2014). Analysis of an M M AP/P H₁, P H₂/N/∞ queueing system operating in a random environment, International Journal of Applied Mathematics and Computer Science24(3): 485–501, DOI: 10.2478/amcs-2014-0036.10.2478/amcs-2014-0036Search in Google Scholar

Klemm, A., Lindermann, C. and Lohmann, M. (2003). Modelling IP traffic using the batch Markovian arrival process, Performance Evaluation54(2): 149–173.10.1016/S0166-5316(03)00067-1Search in Google Scholar

Lucatoni, D. (1991). New results on the single server queue with a batch Markovian arrival process, Communication in Statistics: Stochastic Models7(1): 1–46.10.1080/15326349108807174Search in Google Scholar