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가상확률밀도함수를 사용하여 Max(N, T, D) 운5방침이 적용되는 조정가능한 M/G/1 대기모형의 busy period의 기대값 유도
이한교,오현승,Rhee, Hahn-Kyou,Oh, Hyun-Seung 한국산업경영시스템학회 2008 한국산업경영시스템학회지 Vol.31 No.4
The expected busy period for the controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy is derived by using a new concept so called "the pseudo probability density function." In order to justify the proposed approaches for the triadic policy, well-known expected busy periods for the dyadic policies are recovered from the obtained result as special cases.
Development of a Stochastic Group Replacement Model for Two Independent Equipments
이한교,Rhee, Hahn-Kyou 대한산업공학회 1999 산업공학 Vol.12 No.1
A system consisting of two continuously and independently operating equipment subject to breakdown and repair, is considered. It is assumed that both equipment age only when in operation, and a group replacement policy is in effect, that is, both equipment are replaced simultaneously by new identical ones as soon as either of them reaches a specified replacement age. First, a system of partial differential equations based on enumerating the various probabilistic events, is derived. Then, solutions of such system of equations for a model considered in the steady-state are obtained. Finally, an economic analysis is performed to determine the optimal replacement ages of both equipment.
Busy Period 기대값을 사용하여 가장 일반화된 삼변수 운용방침의 분석
이한교(Hahn-Kyou Rhee) 한국산업경영시스템학회 2011 한국산업경영시스템학회지 Vol.34 No.4
The most generalized form of the triadic operating policy for a controllable M/G/1 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.
삼변수 Med(N, T, D) 운용방침에 따른 Busy Period 기대값의 상한과 하한 유도
이한교(Hahn-Kyou Rhee) 한국산업경영시스템학회 2013 한국산업경영시스템학회지 Vol.36 No.1
Using the known result of the expected busy period for the triadic Med (N, T, D) operating policies applied to a controllable M/G/l queueing model, its upper and lower bounds are derived to approximate its corresponding actual values. Both bounds are represented in terms of the expected busy periods for the dyadic Min (N, T), Min (N, D) and Min (T, D) or Max (N, T), Max (N, D) and Max (T, D) with the simple N, T and D operating policies without using any other types of triadic operating policies such as Min (N, T, D) and Max (N, T, D) policies. All three input variables N, T and D are equally contributed to construct such bounds for estimation of the expected busy period.
삼변수 Max(N, T, D) 운용방침이 적용되는 조정가능한 M/G/1 대기모형의 busy period 기대값의 상한과 하한 유도
이한교(Hahn-Kyou Rhee) 한국산업경영시스템학회 2011 한국산업경영시스템학회지 Vol.34 No.1
Using the known result of the expected busy period for a controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy, its upper and lower bounds are derived to approximate its corresponding actual value. Both bounds are represented in terms of the expected busy periods for the dyadic Min (N, T), Min (N, D) and Min (T, D) and simple N, T and D operating policies. All three input variables N, T and D are equally contributed to construct such bounds for better estimation.
삼변수운용방침이 적용되는 M/G/1 대기모형에서 가상확률밀도함수를 이용한 busy period의 기대값 유도
이한교(Hahn-Kyou Rhee),오현승(Hyun-Seung Oh) 한국산업경영시스템학회 2007 한국산업경영시스템학회지 Vol.30 No.2
The expected busy period for the controllable M/G/1 queueing model operating under the triadic policy is derived by using the pseudo probability density function which is totally different from the actual probability density function. In order to justify the approach using the pseudo probability density function to derive the expected busy period for the triadic policy, well-known expected busy periods for the dyadic policies are derived from the obtained result as special cases.
이한교(Hahn Kyou Rhee) 한국산업경영시스템학회 2016 한국산업경영시스템학회지 Vol.39 No.1
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.
상호보완적인 이변수 운영정책이 교대로 적용되는 정비서비스센터 모형분석
이한교(Hahn-Kyou Rhee) 한국신뢰성학회 2017 신뢰성응용연구 Vol.17 No.1
Different from general operating policies applied for various waiting line situations, two complementary dyadic operating policies are applied alternatingly to a single server maintenance service center model. That is, either of the two dyadic Min (N, T) or Max (N, T) policy is applied to operate such center first and the other operating policy should be applied later, and then the same sequence of both operating policies is followed repeatedly. This operating policy is denoted by the Minimax (N, T) policy. Purpose: Because of the newly introduced operating policy, important system characteristics of the considered service center model such as the expected busy and idle periods, the expected number of customers in the service center and so on should be derived to provide necessary information for determination of the optimal operating policy. Methods: Based on concepts of the newly introduced Minimax (N, T) policy, all necessary system characteristics should be redefined and then derived by constructing appropriate relations between complementary two dyadic operating policies. Results: Desired system characteristics are obtained successfully using simple procedures developed by utilizing peculiar structure of the Minimax (N, T) policy. Conclusion: Applying Minimax (N, T) operating policy is equivalent to applying the simple N and T operating policies alternatingly.
조정가능한 대기모형에 {T:Min(T,N)} 운용방침이 적용되었을 때의 시스템분석
이한교(Hahn Kyou Rhee) 한국산업경영시스템학회 2015 한국산업경영시스템학회지 Vol.38 No.1
A steady-state controllable M/G/1 queueing model operating under the {T:Min(T,N)} policy is considered where the {T:Min(T,N)} policy is defined as the next busy period will be initiated either after T time units elapsed from the end of the previous busy period if at least one customer arrives at the system during that time period, or after T time units elapsed without a customer' arrival, the time instant when Nth customer arrives at the system or T time units elapsed with at least one customer arrives at the system whichever comes first. After deriving the necessary system characteristics including the expected number of customers in the system, the expected length of busy period and so on, the total expected cost function per unit time for the system operation is constructed to determine the optimal operating policy. To do so, the cost elements associated with such system characteristics including the customers' waiting cost in the system and the server's removal and activating cost are defined. Then, procedures to determine the optimal values of the decision variables included in the operating policy are provided based on minimizing the total expected cost function per unit time to operate the queueing system under considerations.
가상확률밀도함수를 사용하여 Max(N, T, D) 운용방침이 적용되는 조정가능한 M/G/1 대기모형의 busy period의 기대값 유도
이한교(Hahn-kyou Rhee)ㆍ오현승(Hyun-seung Oh) 한국산업경영시스템학회 2008 한국산업경영시스템학회지 Vol.31 No.4
The expected busy period for the controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy is derived by using a new concept so called “the pseudo probability density function.” In order to justify the proposed approaches for the triadic policy, well-known expected busy periods for the dyadic policies are recovered from the obtained result as special cases.