Markovian queues with Poisson control

被引:0
|
作者
Nunez-Queija, R. [1 ]
Prabhu, B. J. [2 ]
Resing, J. A. C. [3 ]
机构
[1] Univ Amsterdam, Amsterdam, Netherlands
[2] Univ Toulouse, LAAS, CNRS, INSA, Toulouse, France
[3] Eindhoven Univ Technol, Eindhoven, Netherlands
来源
INDAGATIONES MATHEMATICAE-NEW SERIES | 2023年 / 34卷 / 05期
关键词
Markovian queues; Variable service speeds; Asymptotics; Time-scale separation; CHAINS;
D O I
10.1016/j.indag.2023.03.002
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate Markovian queues that are examined by a controller at random times determined by a Poisson process. Upon examination, the controller sets the service speed to be equal to the minimum of the current number of customers in the queue and a certain maximum service speed; this service speed prevails until the next examination time. We study the resulting two-dimensional Markov process of queue length and server speed, in particular two regimes with time scale separation, specifically for infinitely frequent and infinitely long examination times. In the intermediate regime the analysis proves to be extremely challenging. To gain further insight into the model dynamics we then analyse two variants of the model in which the controller is just an observer and does not change the speed of the server.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
引用
收藏
页码:990 / 1013
页数:24
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