Cost Analysis ofMAP/G(a, b)/1/NQueue with Multiple Vacations and Closedown Times

Study on Infinite Buffer Batch Size Dependent Bulk Service Queue with Queue Length Dependent Vacation

“…Using (32) in ( 53) and (54), and then accumulating the coefficients of z n , we readily obtain the desired result (51) and (52).…”

“…In several queueing systems when no jobs (i.e., primary job) are available for the server, then the server performs some secondary jobs, this type of model is interpreted as the vacation queueing model, and proposed by Levy and Yechiali [ 20 ]. Later many researchers ([ 9 , 11 , 32 , 15 , 16 ] and the references therein) have been attracted to the queueing models with vacation phenomena, and in this connection, an impressive survey is presented in the survey papers by Doshi [ 8 ] and Ke et al [ 17 ]. For the quality literature on vacation theory, readers are requested to see Takagi [ 29 ] and Tian and Zhang [ 31 ].…”

Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance

“…Two major classes of single-server batch service models studied in recent papers are the discrete-time (Claeys et al 2010a;Claeys et al 2010b;Claeys et al 2013;Banerjee et al 2014;Yu and Alfa 2015;Baetens et al 2016;Baetens et al 2017;Baetens et al 2018;Panda and Goswami 2020) and continuous-time models (Saxena et al 2018;D'Arienzo et al 2019;Banerjee and Gupta 2012;Banerjee et al 2015;Yu and Tang 2018;Pradhan and Gupta 2017;Pradhan et al 2016;Pradhan and Gupta 2019;Gupta et al 2020;Gupta and Banerjee 2019;Maity and Gupta 2015;Banik 2015;Vadivu and Arumuganathan 2015;Chaudhry et al 2016;Jeyakumar and Senthilnathan 2017;Zeng and Xia 2017;Niranjan et al 2018;Gupta and Banerjee 2018;Panda et al 2018;Ayyappan and Karpagam 2018;Ayyappan and Nirmala 2018;Bank and Samanta 2020;Xie et al 2020). The variety of techniques used for the analysis includes Kolmogorov equations, Supplementary variable techniques, Roots method, Matrix-Analytic Method, Embedded Markov chain analysis, Spectral methods, Asymptotic Quasi-Toeplitz Markov chain technique and Game theory, to name a few.…”

Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

“…The finite-and infinite-buffer bulk queues with single/multiple vacation(s) rules have been discussed by Gupta et al [22,21], Sikdar et al [42,43], where they have employed SVT to compute the queue length distributions at different epochs. System cost analysis with Markovian arrival process, (a, b) rule, multiple vacations and close-down times has been carried out by Vadivu and Arumuganathan [44]. Chang et al [8] have analyzed a discrete-time finite-buffer Geo X /G Y /1 vacation queue with random serving capacity rule, where they have focused on the steadystate queue length distribution.…”