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

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

Development of the Most Generalized Form of the Triadic Operating Policy and Derivation of its Corresponding Expected Busy Period

가장 일반화된 형태의 삼변수 운용방침 개발과 그에 따른 Busy Period 기대값 유도

  • Rhee, Hahn-Kyou (Department of Industrial & Management Engineering, Hannam University) ;
  • Oh, Hyun-Seung (Department of Industrial & Management Engineering, Hannam University)
  • 이한교 (한남대학교 산업경영공학과) ;
  • 오현승 (한남대학교 산업경영공학과)
  • Published : 2009.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

The most generalized form of the triadic operating policy for an M/G/1 queueing model is developed. It consists of three simple N, T and D operating policies and has a peculiar structure possessing concepts of dyadic policies. Using the concept of the pseudo probability density function of the busy period, its expected busy period for the controllable M/G/1 queueing model is derived. Since the obtained result is the most generalized form the triadic polity, the expected busy periods for all known dyadic policies are recovered as special cases from it.

Keywords

References

  1. K. R. Balachandran and H. Tijms; “On the D-policy for the M/G/1 Queue,” Management Science, 9：1073-1076, 1975
  2. P. H. Brill and C. M. Harris; “Waiting Timrs for M/G/1 Queues with Service Time or Delay-Dependent Server Vacations,” Naval Research Logistics, 39：775-787, 1992 https://doi.org/10.1002/1520-6750(199210)39:6<775::AID-NAV3220390604>3.0.CO;2-K
  3. B. Conolly; Lecture Notes on Queueing Systems, Halsted, NY, 1975
  4. K. G. Gakis, H. K. Rhee and B. D. Sivazlian; “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
  5. D. Heyman; “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
  6. O. Kella and U. Yechiali; “Priorities in M/G/1 Queue with Server Vacations,” Naval Research Logistics, 35：23-34, 1998
  7. O. Kella; “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
  8. L. Kleinrock; Queueing Systems, Theory, John Wiley and Sons, New York, NY, 1：1975
  9. H. K. Rhee; “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
  10. H. K. Rhee; “조정가능한 대기모형에 이변수 운용방침(Dyadic Policy)이 적용될 때 busy period의 기대값의 수리적 분석”, 한남대학교 논문집, 32：141-153, 2002
  11. H. K Rhee and H. S. Oh; “삼변수 운용방침이 적용되는 M/G/1 대기모형에서 가상확률밀도함수를 이용한 busy period의 기대값 유도”, 한국산업경영시스템학회지, 30(2)：51-57, 2007
  12. H. K. Rhee and H. S. Oh; “가상확률밀도함수를 사용하여 Max(N, T, D) 운용방침이 적용되는 조정가능한 M/G/1 대기모형의 busy period의 기대값 유도”, 한국산업경영시스템학회지, 31(4)：86-92, 2008
  13. H. K. Rhee and B. D. Sivazlian; "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
  14. B. D. Sivazlian and S. N. Iyer; “A Dyadic Age-Replacement Policy for a Periodically Inspected Equipment Items Subject to Random Deterioration,” European Journal of Operational Research, 6：315-320, 1981 https://doi.org/10.1016/0377-2217(81)90236-8
  15. J. Teghem; “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
  16. M. Yadin and P. Naor; "Queueing System with Removable Service Station," Operational Research Quarterly, 14：393-405, 1963 https://doi.org/10.1057/jors.1963.63