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Limit theorems for queueing systems with different service disciplines

P. 89–89.
Grishunina S.

In this paper we investigate a multi-server queueing system with regenerative input flow and independent service times with finite mean. Queues with several servers are sufficiently complex but considerably interesting. There are many papers devoted to this theme. We consider queueing systems with various rules (disciplines) of the service performance: systems with a common queue and systems with individual queues in front of the servers. In the second case an arrived customer chooses one of the servers in accordance to a certain rule and stays in the chosen queue up to the moment of its departure from the system. We define some classes of disciplines and analyze the asymptotical behavior of a multi-server queueing system in a heavy-traffic situation (traffic rate is more then one). The main result of this work is the weak convergence of scaled processes of waiting time and queue length to the process of the Brownian motion.

Language: English
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Keywords: limit theoremsheavy-trafficqueueing systemservice disciplines

In book

Book of Abstracts of the 17th Applied Stochastic Models and Data Analysis International Conference with Demographics workshop (ASMDA 2017), 6-9 june 2017, London, UK
ISAST: International Society for the Advancement of Science and Technology, 2017.
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