Asymptotic tail distribution analysis of queueing systems with heavy-tailed input traffic헤비 테일 입력 트래픽을 갖는 대기체계의 꼬리 확률 분포에 대한 점근적 분석

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From recent traffic measurements, it has been shown that the traffic of the Internet has essentially different characteristic from that of the traditional voice networks. The characteristic is referred to as long-range dependence, self-similarity, and heavy-tailedness. The traditional voice networks have usually been modeled by queueing systems with light-tailed input traffic. Thus Markovian model has been applied well in modeling the networks. However, due to heavy-tailed property of the Internet traffic, we should develop a new mathematical model for the Internet. In addition, Markovian models guarantee probabilistic independence between two different time epochs and it made the analysis tractable. Note that heavy-tailed traffic doesn't guarantee such independence. Thus there have been few works for analyzing queueing systems with heavy-tailed input traffic. It is well-known that heavy-tailed traffic significantly degrades the performance of the Internet. So a natural concern is that it is possible to alleviate the heavy-tailedness in users' traffic so that users can experience good quality of service (QoS) as if there were no heavy-tailedness in their traffic. In this dissertation, we use queueing systems with heavy-tailed input traffic, analyze the queueing systems, and then give solutions to alleviate the heavy-tailedness in users' traffic. In Chapter 2, we suggest a distributed server system as a candidate to alleviate the heavy-tailedness in users' traffic. We model the distributed server system by using a fluid queueing system. We tag a server and analyze the tail asymptotic of the stationary amount of traffic in the tagged server. To do so, we first investigate tail asymptotic of a random sum which is needed in analyzing the tail asymptotic of the stationary amount of traffic in the tagged server. We also give sufficient conditions with which the tail asymptotic of the stationary amount of traffic in the tagged server is light-tailed or heavy-tailed, respectively. Numerical results are provided to validate our analysis. In Chapter 3, we investigate how much performance degradation we would have if light-tailed condition which is given in Chapter 2 is not satisfied even though we adopt a distributed server system. To this end, we find the exact tail asymptotic of the stationary amount of traffic in the tagged server when the light-tailed condition is not satisfied. We first generalize the tail aymsptotic of a random sum which is given in Chapter 2 under more general assumption. We also give a simple and efficient traffic assignment policy for all the servers in the distributed server system to satisfy light-tailed condition. Our analytic results are verified through simulation. In Chapter 4, we analyze the impact of channel availability on heavy-tailed traffic in wireless communication systems. To this end, we consider a user with heavy-tailed input traffic in a multichannel wireless communication system and analyze the tail asymptotic of the stationary amount of traffic in the user. As a result of the analysis, we give sufficient conditions of channel availability with which the tail asymptotic of the stationary amount of traffic in the user is light-tailed or heavy-tailed, respectively. We also validate our results by simulation.
Advisors
Hwang, Gangukresearcher황강욱researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2017
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2017.2,[iii, 48 p. :]

Keywords

Distributed Server Systems; Random Sum; Asymptotic Tail Distribution; 대기체계; 헤비 테일; 분산 서버 시스템; 무작위 합; 점근적인 꼬리 분포; Queueing Systems; Heavy-tailedness

URI
http://hdl.handle.net/10203/241901
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=675753&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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