• 산업경영시스템학회지
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• 제38권1호
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• pp.21-29
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• 2015

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.

• 산업경영시스템학회지
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• 제14권24호
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• pp.149-154
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• 1991

The one of the important problems in the design of queueing systems is the decision of the order of service stations. The object of this problem is the decision of the order that minimizes the expected sojourn time per customer in the given arrival process and service time distributions. In this paper, the tandem queueing system in series is studied with the emphasis on the optimal order of the tandem queueing system which has three stations with single servers. In one system, customers arrive at the first station with Poisson process. This system is composed of service stations with a constant, a general distribution and a Exponential distribution is studied. To select the optimal order after the orders of each pair of two stations is decided, it is compared the two orders of system. With this results, total expected delay of the systems which has three stations is compared. The result is the best that service station with constant time is on the first place, then the service station with general distribution and the service station with Exponential distribution is followed. And the other system is consist of service stations with a constant and two probabilistic distributions. In this case, two probabilistic distributions has a non-overlapping feature. It is the optimal order that the service station with constant time is on the first place then the service station with longer service time and the service station with shorter service time is followed.

• 한국통신학회논문지
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• 제27권10C호
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• pp.945-950
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• 2002

본 논문에서는 유선 및 무선환경에 상관없이 ATM(Asynchronous Transfer Mode) 접속망의 주요구성 요소인 ATM 접속노드의 셀 손실율, 버퍼용량 및 지연시간간의 상관관계를 제시함으로서 ATM접속망 설계를 위한 기본적인 기술적 사항을 분석하였다. 이를위해 ATM 접속노드의 트래픽 성능평가를 위한 트래픽 모델을 ATM cell-scale queueing, burst-scale queueing 레벨로 구분하여 설명하였고 CBR(Constant Bit Rate), 랜덤 및 VBR(Variable Bit Rate) 트래픽 형태별 모델적용을 검토하였다. 결국 유선 또는 무선방식으로 ATM 서비스를 제공하기 위한 ATM접속노드 설계시 서비스별 QoS(Quality of Service)를 만족시키기 위한 셀 손실율, 버퍼용량 및 지연시간간의 상관관계를 정량적으로 분석하였다.

• 한국통신학회논문지
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• 제30권2A호
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• pp.98-106
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• 2005

본 논문에서는 MAC 계층 이하에 존재하는 링크 계층 재전송 기법과 잘 부합할 수 있는 새로운 무선 패킷 스케줄링 알고리즘인 WFQ-R (Wireless Fair Queueing with Retransmission) 알고리즘을 제안한다. WFQ-R 알고리즘에서 링크 계층 재전송에 의해 사용된 자원은 재전송을 수행한 플로우(flow)가 다른 플로우들에게 미리 차용한 자원으로 취급한다. 즉 MAC 계층 이하의 재전송 과정에서 패킷 스케줄러의 허락 없이 사용되어진 자원을 재전송을 수행한 플로우에게 책임 지움으로써 WFQ-R 알고리즘은 무선 공평성(fairness)을 획득할 수 있게 된다. 본 논문에서는 실험을 통하여 WFQ-R 알고리즘기 공평성을 유지함과 동시에 시스템 성능을 최대화 함을 보인다. 또 플로우 구분성(seperation)과 보상성(compensation)도 획득할 수 있음도 보인다.

• 한국통신학회논문지
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• 제28권3B호
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• pp.171-182
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• 2003

본 논문에서는 Minimum Possible Packet Fair Queueing (MPSFQ)로 명명되는 효율적이면서 구현의 관점에서 용이한 패킷 스케줄링 알고리즘을 제안한다. MPSFQ 알고리즘은 O(1) 의 가상 시간 계산의 복잡도를 가지며 WFQ (Weighted Fair Queueing)알고리즘과 동일한 지연 특성 및 우수한 fairness 특성을 가지고 있다. MPSFQ의 중요한 특징은 시스템 가상 시간은 패킷의 종료 시간에 현재 전송될 패킷이 있는 세션의 최 선두에 있는 패킷들의 가능한 가상 시간의 값 중 최소의 값으로 시스템 가상 시간의 재조정이 이루어지며 시스템 가상 시간의 재조정 시간의 중간에 도착한 패킷의 시스템 가상 시간은 이전 시스템 가상 시간에 두 시간 사이의 실시간을 더함으로써 계산된다. 제안하는 알고리즘이 위와 같은 간단한 알고리즘을 이용하면서도 우수한 지연 특성 및 fairness 특성을 가짐을 수학적인 분석을 통해 증명하고 시뮬레이션을 통하여 그 결과를 확인한다.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.601-616
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• 2021

Retrial queueing models have been studied extensively in the literature. These have many practical applications, especially in service sectors. However, retrial queueing models have their own limitations. Typically, analyzing such models involve level-dependent quasi-birth-and-death processes, and hence some form of a truncation or an approximate method or simulation approach is needed to study in steady-state. Secondly, in general, the customers are not served on a first-come-first-served basis. The latter is the case when a new arrival may find a free server while prior arrivals are waiting in the retrial orbit due to the servers being busy during their arrivals. In this paper, we take a different approach to the study of multi-server retrial queues in which the signals are generated in such a way to provide a reasonably fair treatment to all the customers seeking service. Further, this approach makes the study to be level-independent quasi-birth-and-death process. This approach is different from any considered in the literature. Using matrix-analytic methods we analyze MAP/M/c-type retrial queueing models along with Poisson signals in steady-state. Illustrative numerical examples including a comparison with previously published retrial queues are presented and they show marked improvements in providing a quality of service to the customers.

• 산업경영시스템학회지
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• 제39권1호
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• pp.81-90
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• 2016

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.

• 산업경영시스템학회지
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• 제39권2호
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• pp.1-10
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• 2016

In this paper, we present a new way to derive the mean cycle time of the G/G/m failure prone queue when the loading of the system approaches to zero. The loading is the relative ratio of the arrival rate to the service rate multiplied by the number of servers. The system with low loading means the busy fraction of the system is low. The queueing system with low loading can be found in the semiconductor manufacturing process. Cluster tools in semiconductor manufacturing need a setup whenever the types of two successive lots are different. To setup a cluster tool, all wafers of preceding lot should be removed. Then, the waiting time of the next lot is zero excluding the setup time. This kind of situation can be regarded as the system with low loading. By employing absorbing Markov chain model and renewal theory, we propose a new way to derive the exact mean cycle time. In addition, using the proposed method, we present the cycle times of other types of queueing systems. For a queueing model with phase type service time distribution, we can obtain a two dimensional Markov chain model, which leads us to calculate the exact cycle time. The results also can be applied to a queueing model with batch arrivals. Our results can be employed to test the accuracy of existing or newly developed approximation methods. Furthermore, we provide intuitive interpretations to the results regarding the expected waiting time. The intuitive interpretations can be used to understand logically the characteristics of systems with low loading.

• 산업경영시스템학회지
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• 제40권3호
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• pp.66-75
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• 2017

Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.

• 한국건설관리학회논문집
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• 제23권6호
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• pp.3-14
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• 2022

현장에서 발생하는 정량적인 공사 인원과 기간의 분석은 새로운 적정 인원의 기준을 제시할 수 있다. 본 연구는 업무효율 지표들 중 가장 중요한 요소인 업무절차의 수행시간을 예측하는 대기행렬 모형을 제시한다. 아파트 골조공사 작업 사이클은 같은 공정이 반복되는 특성을 가진다. 본 연구는 이러한 특성을 바탕으로 지연된 골조공사 기준층 사이클을 대기행렬 모형을 활용하고 그것을 분석하였다. 그리고 인원수와 공사 기간을 조정한 후 모형의 성능을 분석하였다. 본 연구는 대기행렬의 성능 분석을 실시하여 공정의 물량에 따른 인적자원관리 의사결정을 지원하고자 한다.