Variability Analysis for a Two-station Queueing Network in Heavy Traffic with Arrival Processes Driven by Queues  

作　　者：Jian CAO Yong-jiang GUO Kai-ming YANG 

机构地区：[1]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第2期445-466,共22页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11871116 and No.11971074).

摘　　要：The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.

关 键 词：two-station queueing network the law of the iterated logarithm(LIL) strong approximation fluid approximation 

分 类 号：O226[理学—运筹学与控制论]