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Shaki, Yair Y.

A Jackson network under general regime. (English) Zbl 1423.62167

Braz. J. Probab. Stat. 33, No. 3, 532-548 (2019).
Summary: We consider a Jackson network in a general heavy traffic diffusion regime with the \(\alpha\)-parametrization. We also assume that each customer may abandon the system while waiting. We show that in this regime the queue-length process converges to a multi-dimensional regulated Ornstein-Uhlenbeck process.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
90B20 Traffic problems in operations research
90B22 Queues and service in operations research
60J60 Diffusion processes

Keywords:

Jackson network; diffusion limits; many-server queue; heavy traffic; conventional diffusion regime; Halfin-Whitt regime; queue-length process; Ornstein-Uhlenbeck process
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