Decay parameter for general stopped Markovian bulk-arrival and bulk-service queues

Anyue Chen (), Junping Li (), Xiaohan Wu () and Jing Zhang ()
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Anyue Chen: Southern University of Science and Technology
Junping Li: Central South University
Xiaohan Wu: Harbin Institute of Technology
Jing Zhang: Chinese University of Hong Kong-Shenzhen, and Shenzhen Institute of Artificial Intelligence and Robotics for Society

Queueing Systems: Theory and Applications, 2021, vol. 99, issue 3, No 5, 305-344

Abstract: Abstract We consider the important decay parameter issue for a Markovian bulk-arrival and bulk-service queue which stops at reaching the first m states. The results obtained in this paper are a significant generalization of the ones obtained in Chen et al. (Queueing Syst 66:275–311, 2010). The exact value of the decay parameter is obtained. Based on the results obtained in this paper, we provide a practical method for calculating the decay parameter which is very effective. In some cases, the decay parameter can even be easily expressed explicitly. Some important key lemmas which also have their own interest are provided. The interesting and clear geometric interpretation of the decay parameter is explained. A few examples are provided to illustrate the results obtained in this paper.

Keywords: Continuous time Markov chains; Stopped Markovian bulk-arrival and bulk-service queues; Decay parameter; Primary 60J27; Secondary 60J80 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11134-021-09712-z

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