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Z. Saffer, K. Grill, W. Yue:
"Controllable Capacity Queue with Synchronous Constant Service Time and Loss";
Talk: QTNA2018, Tsukuba City, Japan; 2018-07-25 - 2018-07-27; in: "Queueing Theory and Network Applications, Subtitle: 13th International Conference, QTNA 2018, Tsukuba, Japan, July 25-27, 2018, Proceedings", Y. Takahashi, T. Phung-Duc, S. Wittevrongel, W. Yue (ed.); (2018), ISBN: 978-3-319-93735-9; 51 - 63.

In this paper we analyze a queue, in which the number of active servers can be controlled by means of probabilities specifying the dependency of the number of active servers on the actual number of customers and the number of active servers. We call this queue as controllable capacity queue. The service time is constant and the concurrently served customers are served in syncronized manner. The active number of servers can be incremented, decremented or kept unchanged at the ends of service time according to the given probabilities. The system has no buffer for long-term customer waiting, it is a loss system. Such system could be relevant in modeling Machine-To-Machine communication systems, in which the resources are limited.

We provide explicit form results for the joint and marginal distributions of the number of servers and the number of customers on PGF level. We give the condition of the stability and also provide the expressions of the most important system measures including the mean stationary number of servers, the mean stationary number of customers and the blocking probability.

Queueing theory Control of queues State dependent number of servers Variable number of servers

http://dx.doi.org/10.1007/978-3-319-93736-6

https://www.springer.com/de/book/9783319937359