Journal of the Korea Society for Simulation (한국시뮬레이션학회논문지)

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

DOI QR Code

A Workflow Time Analysis Applying the Queueing Model

대기행렬모형에 의한 워크플로우 시간분석

  • 박진수 (용인대학교 경영정보학과)
  • Received : 2014.06.03
  • Accepted : 2014.09.17
  • Published : 2014.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Traditional workflow time analyses have been performed treating an activity as an independent M/M/1queueing system. Using the general forms of performance measures in the M/M/1 system, various aspects of analyses can be performed. Especially, on the time analysis of an AND structure in a workflow system, the mean system sojourn time can be formalized by applying the performance measures of M/M/1 system. In the real workflow system, the AND structure cannot be described correctly under the assumption of independent M/M/1 systems. To overcome this limitation, this research makes the assumption that the all activities for a task starts simultaneously. In this situation, the theoretical solution can be derived using the performance measures of the M/G/1 system. In addition, the simulation modeling method will be proposed to analyze the AND structure of a real workflow system. Finally, some numerical results from the theoretical solutions and simulation models will be provided for verification. The main performance measures used in this research are mean queueing time and mean sojourn time.

전통적인 워크플로우 시간분석은 단위작업을 독립적인 M/M/1 대기행렬모형에 적용하여 수행해왔다. M/M/1 시스템 성능척도의 일반해들을 활용하면 여러 가지 분석이 가능해진다. 특히 워크플로우 시스템의 AND 구조를 분석함에 있어 M/M/1 시스템 성능척도를 활용하면 그 체재시간에 대한 분석이 가능하다. 그러나 실질적인 AND 구조를 정확히 묘사하기 위해서는 각각의 M/M/1 시스템이 독립이라는 가정이 없어야 한다. 본 연구는 이러한 한계를 극복하기 위해 한 업무에 대한 모든 단위작업이 동시에 시작하는 상황으로 가정한다. 이 가정 하에서는 M/G/1 시스템의 성능척도를 이용하여 이론적 분석이 가능해진다. 또한 시뮬레이션을 이용하여 실질적인 AND 구조를 정확히 묘사할 수 있는 방법론을 소개한다. 마지막으로 가상의 시스템을 구성하여 이론적인 해와 시뮬레이션 결과들을 수록함으로써 제안된 방법론들을 검증한다. 본 연구에서 사용된 주요 시스템 성능척도는 평균대기시간과 평균체재시간이다.

Keywords

References

  1. Lee, H.W., Queueing Theory: Stochastic Process Approach, 3rd Edition, Sigma Press, Seoul, pp. 495-876, 2006.
  2. Burke, P.J., "The output of a queueing system", Operations Research, Vol. 4, No. 6, pp. 699-704, 1956. https://doi.org/10.1287/opre.4.6.699
  3. Chang, D.-H., Son, J.H., Kim, M.H., "Critical path identification in the context of a workflow", Information and Software Technology, Vol. 44, pp. 405-417, 2005.
  4. Jeong, K.-Y., Cho, H., Phillips, D.T., "Integration of queueing network and IDEF3 for business process analysis", Business Process Management Journal, Vol. 14, No. 4, pp. 471-482, 2008. https://doi.org/10.1108/14637150810888028
  5. Kingman, J.F.C., "The single server queue in heavy traffic", Proceedings of the Cambridge Philosophical Society, Vol. 57, pp. 902-904, 1961. https://doi.org/10.1017/S0305004100036094
  6. Li, H., Yang, Y., "Dynamic checking of temporal constraints for concurrent workflows", Electronic Commerce Research and Applications, Vol. 4, pp. 124-142, 2005. https://doi.org/10.1016/j.elerap.2004.09.003
  7. Marshall, K.T., "Some inequalities in queueing", Operations Research, Vol.16, pp. 651-665, 1968. https://doi.org/10.1287/opre.16.3.651
  8. Reijers, H.A., van der Aalst, W.M.P, "The effectiveness of workflow management systems: Predictions and lessons learned", International Journal of Information Management, Vol. 25, pp. 458-472, 2005. https://doi.org/10.1016/j.ijinfomgt.2005.06.008
  9. Son, J.H., Kim, M.H., "Improving the performance of time-constrained workflow processing", The Journal of Systems and Software, Vol. 58, pp. 211-219, 2001. https://doi.org/10.1016/S0164-1212(01)00039-5
  10. Son, J.H., Kim, J.S., Kim, M.H., "Extracting the workflow critical path from the extended well-formed workflow schema", Journal of Computer and Systems Sciences, Vol. 70, pp. 86-106, 2005. https://doi.org/10.1016/j.jcss.2004.07.001
  11. Truong, N.K.V, Choi, Y., Kim, I., Shin, S., Hwang, W.J., "A Probabilistic Approach to Workflow Time Analysis for Business Process Mangement", International Journal of Human and Social Sciences, Vol. 5, No. 12, pp. 811-815, 2010.
  12. Zhuge, H., Cheung, T., Pung, H., "A timed workflow process model", The Journal of Systems and Software, Vol. 55, pp. 231-243, 2001. https://doi.org/10.1016/S0164-1212(00)00073-X