Diffusion limits for networks of Markov-modulated infinite-server queues

被引:7
|
作者
Jansen, H. M. [1 ]
Mandjes, M. [2 ]
De Turck, K. [3 ]
Wittevrongel, S. [4 ]
机构
[1] Univ Queensland, Ctr Applicat Nat Resource Math CARM, Sch Math & Phys, St Lucia, Qld 4072, Australia
[2] Univ Amsterdam, Korteweg de Vries Inst Math, Sci Pk 904, NL-1098 XH Amsterdam, Netherlands
[3] Cent Supelec, Dept Telecommun, L2S, UMR8506 Plateau Moulon, 3 Rue Joliot Curie, F-91192 Gif Sur Yvette, France
[4] Univ Ghent, TELIN, Sint Pietersnieuwstr 41, B-9000 Ghent, Belgium
基金
澳大利亚研究理事会;
关键词
Queueing networks; Infinite-server queue; Diffusion limit; Markov modulation; M/M/INFINITY QUEUES;
D O I
10.1016/j.peva.2019.102039
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation, meaning that the system's parameters depend on an autonomously evolving Markov chain, called the background process. In previous papers on single-node queues with Markov modulation, two variants were distinguished. In the first variant the arrival rate and the server speed are modulated, whereas in the second variant the arrival rate and the service requirement are modulated. The setup of the present paper, however, is more general: we not only extend single-node systems to a network setting, but also allow both the server speed and the service requirement to depend on the background process. For this model we derive a Functional Central Limit Theorem. In particular, we show that, after accelerating the arrival processes and the background process, a centered and normalized version of the network population vector converges to a multidimensional Ornstein-Uhlenbeck process. The proof of this result relies on weak convergence of stochastic integrals as well as continuous-mapping arguments. (C) 2019 Elsevier B.V. All rights reserved.
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页数:18
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