Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지

Decomposition of the Most Generalized Triadic Operating Policy Using its Corresponding Expected Busy Period

Busy Period 기대값을 사용하여 가장 일반화된 삼변수 운용방침의 분석

  • Rhee, Hahn-Kyou (Department of Industrial and Management Engineering Hannam University)
  • 이한교 (한남대학교 산업경영공학과)
  • Received : 2011.10.25
  • Accepted : 2011.12.17
  • Published : 2011.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

The most generalized form of the triadic operating policy for a controllable M/G/I queueing model is analyzed to obtain fundamental relations among the other forms of operating policies based on its corresponding expected busy period. Since it consists of three decision variables N, T and D, it could be possible to decompose into the simple, the dyadic and other forms of the triadic operating policies. The procedures to decompose the most generalized triadic policy into other forms of operating policies could provide a general methodology to identify each element associated with it.

Keywords

References

  1. Balachandran, K. R. and Tijms, H.; "On the D-policy for the M/G/1 Queue," Management Science, 9 : 1073-1076, 1975.
  2. Conolly, B.; Lecture Notes on Queueing Systems, Halsted, NY, 1975.
  3. Gakis, K. G., Rhee, H. K., and Sivazlian, B. D.; "Distributions and First Moments of the Busy and Idle Periods in Controllable M/G/1 Queueing Models with Simple and Dyadic Policies," Stochastic Analysis and Applications, 13(1) : 47-81, 1995. https://doi.org/10.1080/07362999508809382
  4. Heyman, D.; "The T-policy for the M/G/1 Queue," Management Science, 23(7) : 775-778, 1977. https://doi.org/10.1287/mnsc.23.7.775
  5. Kella, O.; "The Threshold Policy in the M/G/1 Queue with Server Vacations," Naval Research Logistics, 36 : 111-123, 1989. https://doi.org/10.1002/1520-6750(198902)36:1<111::AID-NAV3220360109>3.0.CO;2-3
  6. Kleinrock, L.; Queueing Systems, 1 : Theory, John Wiley and Sons, New York, NY, 1975.
  7. Rhee, H. K. and Oh, H. S.; "가상확률밀도함수를 사용하여 Max(N, T, D) 운용방침이 적용되는 조정가능한 M/G/1 대기모형의 busy period의 기대값 유도", 한국산업경영시스템학회지, 31(4) : 86-92, 2008.
  8. Rhee, H. K. and Oh, H. S.; "삼변수 운용방침이 적용되는 M/G/1 대기모형에서 가상확률밀도함수를 이용한 busy period의 기대값 유도", 한국산업경영시스템학회지, 30(2) : 51-57, 2007.
  9. Rhee, H. K. and Sivazlian, B. D.; "Distribution of the Busy Period in a Controllable M/M/2 Queue Operating under the Triadic (0, K, N, M) Policy," Journal of Applied Probability, 27 : 425-432, 1990. https://doi.org/10.2307/3214662
  10. Rhee, H. K.; "가장 일반화된 삼변수 운용방침 개발과 그에 따른 busy period 기대값 유도", 한국산업경영시스템학회지, 32(4) : 161-168, 2009.
  11. Rhee, H. K.; "Busy Period 기대값을 사용하여 삼변수 Min(N, T, D) 와 Max(N, T, D) 운용방침사이의 관계식 설정", 한국산업경영시스템학회지, 33(3) : 63-70, 2010.
  12. Rhee, H. K.; "Development of a New Methodology to find the Expected Busy Period for Controllable M/G/1 Queueing Models Operating under the Multi-variable Operating Policies : Concepts and Application to the Dyadic Policies," 대한산업공학회지, 23(4) : 729-739, 1997.
  13. Teghem, J.; "Control of the Service Process in a Queueing System," European Journal of Operational Research, 23 : 141-158, 1986. https://doi.org/10.1016/0377-2217(86)90234-1
  14. Yadin, M. and Naor, P.; "Queueing System with Removable Service Station," Operational Research Quarterly, 14, 393-405, 1963. https://doi.org/10.1057/jors.1963.63