Stability of a GI/G/1 Queue: A Survey

Yichi Shen and Kan Wu ()
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Yichi Shen: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
Kan Wu: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 03, 1-15

Abstract: Stability of queues is of fundamental importance in the application of queueing models. To establish the stability of a queue, one has to utilize a mathematical model to describe the evolution of the queue and then defines stability on the model. However, the types of stability are various according to their underlying processes. In this study, we survey the different underlying processes of a GI/G/1 queue, classify the various types of stability and study the relations among them. Furthermore, from the viewpoint of sample-path, we propose a new result regarding the growth rate of the queue time when the traffic intensity equals 1.

Keywords: Stability; GI/G/1 queue; underlying process (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S021759591850015X

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