Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control

Xiaohan Wu () and Anyue Chen ()
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Xiaohan Wu: Harbin Institute of Technology
Anyue Chen: Southern University of Science and Technology

Queueing Systems: Theory and Applications, 2023, vol. 104, issue 1, No 3, 19-52

Abstract: Abstract This paper aims to provide several further results for a queueing model recently discussed by Chen et al. (Queueing Syst 95:331–378, 2020), i.e. the Markovian bulk-arrival and bulk-service queue incorporating the general state-dependent control. We use an alternative method which is based on the resolvent decomposition theorem to obtain the important results for this model in this paper, including the important questions regarding equilibrium behaviour, queue length behaviour, hitting time and busy period distributions. Furthermore, a set of interesting examples are also provided in the last section.

Keywords: Bulk-arrival and bulk-service queues; State-dependent control; Resolvent decomposition theorem; Equilibrium distribution; Queue length distributions; Busy period distributions; Primary 60J27; Secondary 60J80 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-022-09870-8

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