변동 운용방침이 적용되는 조정가능한 대기모형 분석
Analysis of a Controllable Queueing Model Operating under the Alternating Operating Policies
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Different from general operating policies to be applied for controllable queueing models, two of three well-known simple N, T and D operating policies are applied alternatingly to the single server controllable queueing models, so called alternating (NT), (ND) and (TD) policies. For example, the alternating (ND) operating policy is defined as the busy period is initiated by the simple N operating policy first, then the next busy period is initiated by the simple D operating policy and repeats the same sequence after that continuously. Because of newly designed operating policies, important system characteristic such as the expected busy and idle periods, the expected busy cycle, the expected number of customers in the system and so on should be redefined. That is, the expected busy and idle periods are redefined as the sum of the corresponding expected busy periods and idle periods initiated by both one of the two simple operating policies and the remaining simple operating policy, respectively. The expected number of customers in the system is represented by the weighted or pooled average of both expected number of customers in the system when the predetermined two simple operating policies are applied in sequence repeatedly. In particular, the expected number of customers in the system could be used to derive the expected waiting time in the queue or system by applying the famous Little’s formulas. Most of such system characteristics derived would play important roles to construct the total cost functions per unit time for determination of the optimal operating policies by defining appropriate cost elements to operate the desired queueing systems.
Abstract
Different from general operating policies to be applied for controllable queueing models, two of three well-known simple N, T and D operating policies are applied alternatingly to the single server controllable queueing models, so called alternating (NT), (ND) and (TD) policies. For example, the alternating (ND) operating policy is defined as the busy period is initiated by the simple N operating policy first, then the next busy period is initiated by the simple D operating policy and repeats the same sequence after that continuously. Because of newly designed operating policies, important system characteristic such as the expected busy and idle periods, the expected busy cycle, the expected number of customers in the system and so on should be redefined. That is, the expected busy and idle periods are redefined as the sum of the corresponding expected busy periods and idle periods initiated by both one of the two simple operating policies and the remaining simple operating policy, respectively. The expected number of customers in the system is represented by the weighted or pooled average of both expected number of customers in the system when the predetermined two simple operating policies are applied in sequence repeatedly. In particular, the expected number of customers in the system could be used to derive the expected waiting time in the queue or system by applying the famous Little’s formulas. Most of such system characteristics derived would play important roles to construct the total cost functions per unit time for determination of the optimal operating policies by defining appropriate cost elements to operate the desired queueing systems.
참고문헌 (19)
- Artalejo, J. R., "On the M", G, Applied Mathematical Modelling, pp.2001, 25(12)[DOI]
- Balachandran, K. R., "On the D-policy for the M", G, Management Science, pp.1975, 9[DOI]
- Conolly, B., "Lecture Notes on Queueing Systems" (1975), Halsted
- Gakis, K. G., "Distributions and First Moments of the Busy and Idle Periods in Controllable M", G, Stochastic Analysis and Applications, pp.1995, 13(1)[DOI]
- Ham T. J., "Structural Analysis for an Optimum Maintenance Policy", Journal of the Korean Institute of Plant Engineering, 6(4), pp.31~43 (2001)
- Heyman, D., "The T-policy for the M", G, Management Science, pp.1977, 23(7)[DOI]
- Kleinrock, L., "Queueing Systems, Vol. 1 : Theory" (1975), John Wiley and Sons
- Li, Jingwen, "The waiting-time Distribution for GI", G, Probability in the Engineering and Information Science, pp.1992, 6[DOI]
- 문기주, "제한된 조건하에서의 배송설비 운영 최적화 연구", 대한설비관리학회지, 10(1), pp.5~17 (2005), 대한설비관리학회
- 이한교, "조정가능한 M", G, 산업경영시스템학회지, pp.2009, 32(3)[DOI]
- 이한교, "가장 일반화된 형태의 삼변수 운용방침 개발과그에 따른 Busy Period 기대값 유도", 산업경영시스템학회지, 32(4), pp.161~168 (2009), 한국산업경영시스템학회
- Rhee, H. K., "Distribution of the Busy Period in a Controllable M", M, Journal of Applied Probability, pp.1990, 27[DOI]
- 이한교, "Busy period 기대값을 사용하여 삼변수 Min(N, T, D)와 Max(N, T, D) 운용방침사이의 관계식 설정", 산업경영시스템학회지, 33(3), pp.63~70 (2010), 한국산업경영시스템학회
- 이한교, "Busy Period 기대값을 사용하여 가장 일반화된 삼변수 운용방침의 분석", 산업경영시스템학회지, 34(4), pp.162~168 (2011), 한국산업경영시스템학회
- 이한교, "삼변수 Max(N, T, D) 운용방침이 적용되는 조정가능한 M", G, 산업경영시스템학회지, pp.2011, 34(1)[DOI]
- Rhee, H. K., "Development of a New Methodology to find the Expected Busy Period for Controllable M", G, Journal of the Korean Institute of Industrial Engineers, pp.1997, 23(4)[DOI]
- 이한교, "조정가능한 대기모형에 {T:Min(T,N)} 운용방침이 적용되었을 때의 시스템분석", 산업경영시스템학회지, 38(1), pp.21~29 (2015), 한국산업경영시스템학회
- Teghem, J., "Control of the Service Process in a Queueing System", European Journal of Operational Research, 23, pp.141~158 (1986)
- Yadin, M., "Queueing System with Removable Service Station", Operational Research Quarterly, 14, pp.393~405 (1963)