Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

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.…”

“…Some variations of this classical rule are: the possibility of serving a batch of size less than a with some probability (Saxena et al 2018;Claeys et al 2013), or a single customer service mode for batch smaller than a (Yu and Alfa 2015). A specific version of the GBS rule (when a = b) is the Fixed Bulk Service (FBS) policy (Claeys et al 2010a;Yu and Tang 2018;Gupta and Banerjee 2019;Xie et al 2020). A significant attention is also received by the systems with variable capacity or the so-called versatile Bulk Service rule, where the batch size taken for service is random (Pradhan et al 2016;Maity and Gupta 2015;Jeyakumar and Senthilnathan 2017;Bank and Samanta 2020).…”