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Kanban에 의해 통제되는 생산/조립 시스템의 분해 근사방법의 개선에 관한 연구
Reports NRF is supported by Research Projects( Kanban에 의해 통제되는 생산/조립 시스템의 분해 근사방법의 개선에 관한 연구 | 2008 Year 신청요강 다운로드 PDF다운로드 | 김선교(아주대학교) ) data is submitted to the NRF Project Results
Researcher who has been awarded a research grant by Humanities and Social Studies Support Program of NRF has to submit an end product within 6 months(* depend on the form of business)
  • Researchers have entered the information directly to the NRF of Korea research support system
Project Number B00032
Year(selected) 2008 Year
the present condition of Project 종료
State of proposition 재단승인
Completion Date 2009년 03월 24일
Year type 결과보고
Year(final report) 2009년
Research Summary
  • Korean
  • 도착과정의 자동 상관관계는 도착과정의 변동성에 영향을 미치며 도착 횟수의 산포 지표 (index of dispersion
    for counts; IDC) 와 도착 간격의 산포 지표 (index of dispersion for intervals; IDI) 에 의해 모형화 할 수 있다
    ( Fendick et al. [4, 5]). 최근 Jagerman et al.[6] 은 일반 혼합 얼랑 재생과정을 이용하여 세 개의 모수로
    자동상관관계가 있는 도착과정을 근사하고 G/G/1 대기행렬 시스템을 분석하는 근사방법을 제안하였다.
    Balcioglu et al. [2] 은 이에 기초하여 자동상관관계가 존재하는 도착과정이 분기/결합 되어 얻어지는 도착과정의
    근사방법을 제안하였다. 본 논문에서는 Balc?Hoglu et al. [2]의 방법이 분기된 과정들의 상관관계를 반영하지 못하여
    심각한 근사오차가 발생할 수 있다는 문제점을 지적하고 이를 보완하여 50% 이상의 근사오차를 설명할 수 있는
    근사방법을 제안한다.
  • English
  • The decomposition approach has been known as an efficient method for queueing network approximation
    since its first appearance about 30 years ago. Kuehn [10], Shanthikumar and Buzacott [12], and Whitt [14]
    provided early theoretical basis on which many researchers improved and refined the functionality and the
    accuracy of the prototype. Bitran and Tirupati [3] modeled the interference between different arrival classes
    under deterministic routing which Whitt [15] and Kim [9] refined later. High variability and burstiness due to
    autocorrelation in an arrival process is modeled based on the index of dispersion for counts (IDC) and the index
    of dispersion for intervals (IDI); Fendick et al. [4, 5]. Whitt [16] proposed the variability function to explain the
    heavy traffic bottleneck phenomenon discussed in Suresh and Whitt [13]. Recently, Jagerman et al.[6]
    proposed the exponential residual (ER) approximation for G/G/1 queueing system which is a three-parameter
    renewal approximation of autocorrelated arrival processes. Balc?Ho?Hglu et al. [2] studied the splitting and
    superposition of arrival processes based on ER approximation.
    The effect of splitting and superposition on the variability of arrival processes was first studied by Albin [1].
    Kim, Muralidharan, and O?HCinneide [8] proposed an approach that accounts for the correlation due to random
    splitting. Kim [7] combined this approach with Whitt?Hs variability function to explain bottleneck phenomenon
    under splitting and superposition.
    In this paper, we propose an analytic approach that can improve the performance of ER approximation based
    on the innovations method proposed in [8]. By this enhancement, application of the ER approximation of
    arrival process can be extended to the approximation of queueing network with random routing.
    The paper is organized as follows. In Section 2, we review basic formulae of ER approximation. Then, we
    present an example in Section 3 as a motivation of our research. In Section 4, we analyze the correlation
    between split streams under random routing and illustrate the efficacy of our approach with numerical examples.
    In Section 5, we propose a streamlined computational procedure that can be used with ER approximation for
    general open queueing networks with random routing. We conclude with discussion of future direction of research
    in Section 6.
Research result report
  • Abstract
  • We propose an extension of the exponential residual (ER) renewal approximation to account for correlation between autocorrelated processes in queueing systems. The ER renewal approximation is an approach to model autocorrelation in interarrival times by 2-stage mixed generalized Erlang distribution with three parameters; residue, decrement, and intensity. First, we show the effect of random splitting on variability of split stream and on mean waiting time. Then, we discuss the effect of correlation created by random routing and propose an ER approximation that properly reflects both correlation between substreams and the autocorrelation. Numerical examples and results show that queueing network approximation can be greatly improved by incorporating correlation into the ER approximation.
  • Research result and Utilization method
  • The exponential residual (ER) approximation provides a theoretical basis for the approximation of G/G/1 queueing systems where arrivals are autocorrelated.
    In this paper, we propose an approach to take into account of correlation between streams with ER approximation. The residue parameter for a superposition of autocorrelated processes can be approximated more accurately. With our approach, the application of the ER approximation can be extended to general open queueing networks with random routing. In order for the ER approximation to be fully applicable in parametric decomposition approximation of more general queueing networks, however, further research needs to be done on the approximation of the decrement parameter under random routing.
  • Index terms
  • Exponential residue; Autocorrelation; Correlation; Index of dispersion for counts; Queueing network
  • List of digital content of this reports
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