Ergodic theorems for queuing systems with dependent inter-arrival times

被引：1
|
作者：
Lovas, Attila [1 ,2 ]
Rasonyi, Miklos [1 ]
机构：
[1] Alfred Renyi Inst Math, Realtanoda Utca 13-15, H-1053 Budapest, Hungary
[2] Budapest Univ Technol & Econ, Egry Jozsef Utca 1, H-1111 Budapest, Hungary
来源：
OPERATIONS RESEARCH LETTERS | 2021年 / 49卷 / 05期
关键词：
Queuing; G/GI/1; queue; Dependent random variables; Inter-arrival times; Limit theorem; Law of large numbers; EXPONENTIAL APPROXIMATIONS; TAIL PROBABILITIES; LARGE DEVIATIONS; QUEUES; VOICE;
D O I：
10.1016/j.orl.2021.07.006
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We study a G/GI/1 single-server queuing model with i.i.d. service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to infinity provided that inter-arrival times satisfy a Gartner-Ellis type condition. A convergence rate is given and a law of large numbers established. These results provide tools for the statistical analysis of such systems, transcending the standard case with independent inter-arrival times. (C) 2021 Elsevier B.V. All rights reserved.
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页码：682 / 687
页数：6
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