Modeling data backups as a batch-service queue with vacations and exhaustive policy

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.…”

“…Batch service type The most widely studied is the classical General Bulk Service (GBS) rule introduced in Neuts (1967): the two finite constant threshold policy states that the server starts service of a batch of size larger or equal to a ≥ 1, and can handle up to b ≥ a customers in a batch, with b finite. 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).…”

“…Aggregation and write caching in modern SSDs is also related to the so-called data deduplication (replacing redundant data writes by pointers to an existing data blocks/pages), that may be performed in advance before the actual write operation is done; thus, improving the lifetime of an SSD by reducing the number of unnecessary writes (see Ivashko et al 2018). Moreover, similar problems are studied at the hard disk drive (HDD) storage, see Xie et al (2020) and Saxena et al (2018) or database level, see O'Mullane et al (2005). We stress that in the context of cloud computing, there is no natural upper bound on the batch size, and thus the batch service can be started for an arbitrary large batch (Saxena et al 2018).…”

“…Moreover, similar problems are studied at the hard disk drive (HDD) storage, see Xie et al (2020) and Saxena et al (2018) or database level, see O'Mullane et al (2005). We stress that in the context of cloud computing, there is no natural upper bound on the batch size, and thus the batch service can be started for an arbitrary large batch (Saxena et al 2018).…”

“…The application examples in cloud storage (see, e.g., Saxena et al (2018)), distributed computing (see, e.g., Ilya et al (2017)) and blood screening (Lohse et al 2020) motivate our interest to study a single-server batch arrival queue with a group clearance in which all those customers present at the time of the beginning of a service are taken into service. We are confident that there are other applications in practice where we can implement the group clearance rule which places no restriction on the size of the batch served.…”