Journal of the Korea Society for Simulation (한국시뮬레이션학회논문지)

The Korea Society for Simulation (한국시뮬레이션학회)
권호 표지
DOI QR코드

DOI QR Code

Spreadsheet Model Approach for Buffer-Sharing Fork-Join Production Systems with General Processing Times and Structure

일반 공정시간과 구조를 갖는 버퍼 공유 분기-접합 생산시스템의 스프레드시트 모형 분석

  • Seo, Dong-Won (School of Management and Management Research Institute, Kyung Hee University)
  • Received : 2019.08.29
  • Accepted : 2019.09.27
  • Published : 2019.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

For many years, it has been widely studied on fork-join production systems but there is not much literature focusing on the finite buffer(s) of either individuals or shared, and generally distributed processing times. Usually, it is difficult to handle finite buffer(s) through a standard queueing theoretical approach. In this study, by using the max-plus algebraic approach we studied buffer-shared fork-join production systems with general processing times. However, because it cannot provide proper computational ways for performance measures, we developed simulation models using @RISK software and the expressions derived from max-plus algebra. From the simulation experiments, we compared some properties on waiting time with respect to a buffer capacity under two blocking policies: BBS (Blocking Before Service) and BAS (Blocking After Service).

분기-접합 생산시스템은 오랜 기간 동안 연구되어왔지만, 개별 또는 공유 유한 버퍼를 갖고 일반공정시간 분포를 따르는 시스템에 대한 분석은 제한적이다. 일반적으로 대기행렬 이론적 분석법은 유한 버퍼를 갖는 시스템에 대한 분석에는 어려움이 있다. 본 연구에서는 max-plus 대수적 분석법을 활용하여 일반 공정시간을 갖는 버퍼 공유 분기-접합 생산시스템을 분석하였다. 하지만, 이러한 분석법은 특성치 계산의 관점에서는 적절한 방법을 제공하지 못하기 때문에 max-plus 대수로 도출된 표현식과 @RISK 소프트웨어를 활용하여 스프레드시트 시뮬레이션 모형을 개발하였다. 시뮬레이션 실험을 통해 유한 버퍼와 두 가지 차단규칙인 BBS(통신차단)과 BAS(제조차단) 하에서 시스템 대기시간에 대한 몇몇 특성을 비교 분석하였다.

Keywords

References

  1. @RISK (2019) http://www.palisade.com/risk (Accessed January 21, 2019).
  2. Ayhan, H. and D.-W. Seo (2001) "Laplace transform and moments of waiting times in Poisson driven (Max,+) linear systems", Queueing Systems, Vol. 37, No. 4, pp. 405-438. https://doi.org/10.1023/A:1010845618420
  3. Ayhan, H. and D.-W. Seo (2002) "Tail probability of transient and stationary waiting times in (Max,+) linear systems", IEEE Transaction on Automatic Control, Vol. 47, No. 1, pp. 151-157. https://doi.org/10.1109/9.981736
  4. Baccelli, F., G. Cohen, G. J. Olsder and J-P. Quadrat (1992) Synchronization and Linearity: An Algebra for Discrete Event Systems, John Wiley and Sons.
  5. Baccelli, F., S. Hasenfuss and V. Schmidt (1998) "Expansions for steady state characteristics in (Max,+) linear systems", Stochastic Models, Vol. 14, pp. 1-24. https://doi.org/10.1080/15326349808807458
  6. Chen, R. J. (2011) "An Upper Bound Solution for Homogeneous Fork/Join Queueing Systems", IEEE Transactions on Parallel and Distributed Systems, Vol. 22, No. 5, pp. 874-878. https://doi.org/10.1109/TPDS.2010.168
  7. Flatto, L and S. Hahn (1984) "Two parallel queues created by arrivals with two demands I," SIAM J. Appl. Math., Vol. 44, pp. 1041-1053. https://doi.org/10.1137/0144074
  8. Kim, C., and A. K. Agrawala (1989) "Analysis of the Fork-Join Queue", IEEE Transactions on Computers, Vol. 38, No. 2, pp. 250-255. https://doi.org/10.1109/12.16501
  9. Nelson, R. and A. N. Tantawi (1988) "Approximate Analysis of fork/Join Synchronization in Parallel Queues," IEEE Transactions on Computers, Vol. 37, No. 6, pp. 739-743. https://doi.org/10.1109/12.2213
  10. Seo, D.-W., J. Lee and B.-Y. Chang (2015) "An Approximation Method for Blocking Probabilities in M/D/1/K1${\rightarrow}{\cdot}$/D/1/K2 Queues", Asia-Pacific Journal of Operational Research, Vol. 32, No. 3, 1550017(12 pages). https://doi.org/10.1142/S0217595915500177
  11. Seo, D.-W. (2019) "Spreadsheet Model Approach for Buffer-Sharing Line Production Systems with General Processing Times", Journal of the Korea Society for Simulation, Vol. 28, No. 2, pp. 119-129. https://doi.org/10.9709/JKSS.2019.28.2.119
  12. Shaked, M. and J. G. Shanthikumar (1994) Stochastic Orders and Their Applications, Academic Press.
  13. Takagi, H. (1993) Queueing Analysis, in: Finite Systems, vol. II, North-Holland.
  14. Thomasian, A. (2014) "Analysis of Fork/Join and Related Queueing Systems", ACM Computing Surveys, Vol. 47, No. 2, Article 17, January 2015, Article No. 17.
  15. Yang, D. and D.-W. Seo (2017) "Closed-form formulae for moment, tail probability, and blocking probability of waiting time in a buffer-sharing deterministic system", Operations Research Letters, Vol. 45, pp. 403-408. https://doi.org/10.1016/j.orl.2017.06.004