• Journal of the Korean Statistical Society
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• 제31권4호
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• pp.491-507
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• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.

• 대한산업공학회지
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• 제12권1호
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• pp.63-71
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• 1986

In the organization with a hierarchical network queue structure a production function is derived whose input factors are the numbers of servers at nodes and output is the number of served customers. Its useful properties are investigated. Using this production function, the contributions of servers to the number of served customers are studied. Also given an expected waiting time in the system for each customer, the optimal numbers of servers at nodes are obtained minimizing a cost function.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2000년도 추계학술대회 및 정기총회
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• pp.59-62
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• 2000

Many of the previous researchers have been studied for the performance estimation of an AS/RS with a static model or computer simulation. Especially, they assumes that the storage/retrieval (S/R) machine performs either only single command (SC) or dual command (DC) and their requests are known in advance. However, the S/R machine performs a SC or a DC. or both or becomes idle according to the operating policy and the status of system at an arbitrary point of time. In this paper, we propose a stochastic model for the performance estimation of a unit-load AS/RS by using a M/G/1 queueing model with a single-server and two queues. Expected numbers of waiting storage and retrieval commands, and the waiting time in queues for the storage and retrieval commands are found

• 한국융합학회논문지
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• 제12권4호
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• pp.217-228
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• 2021

버스카드를 활용한 통합 요금제 시행 이 후 대중교통 통행량 및 환승 통행량은 증가하였다. 이에 따라 버스운영에 있어서 환승객을 고려하는 것은 보다 중요해졌다. 기존 연구들에서는 환승객을 고려할 때 결정적 수리모델을 제안하여 승객과 버스의 확률적인 움직임을 반영하지 못하는 한계가 있었으나 본 연구에서는 미시 시뮬레이션 모델을 바탕으로 하여 보다 실제적인 버스 정류장 모델을 제안하였다. 제안한 시뮬레이션 모델을 기반으로 버스 도착 간격과 승객 대기 시간의 관계를 회귀 모델로 표현하였으며 환승객을 고려할 때와 고려하지 않을 때의 차이를 실증적으로 검증하였다. 또한 승객 대기 시간을 비용으로 변환하는 방법을 제안하고 이를 바탕으로 하여 최적 버스 도착 간격을 제안하였다. 연구에서 제안한 방법을 활용하면 버스 운영에 있어서 보다 현실을 반영한 상향식 의사결정을 가능하게 해줄 것으로 기대된다.

• 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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• 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.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2022년도 춘계학술대회
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• pp.275-276
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• 2022

해상교통관제사는 항로폭이 협소한 항만에서 선박 충돌사고 예방을 위해 one-way로 항해하도록 선박의 입·출항 대기 지시를 한다. 현재 해상교통관제사의 입·출항대기 지시는 과학적이고 통계적인 데이터를 기반으로 하지 않고 해상교통관제사의 개인 역량에 따라 편차가 크다. 이에 따라 본 연구에서는 항만에서의 선박 입·출항 대기 지시를 위한 정확한 이동 시간을 예측하기 위해 선박 및 기상 데이터를 수집하여 1d-합성곱신경망 모델을 구축하였다. 제안한 모델이 다른 앙상블 기계학습 모델보다 4.5% 이상 개선된 것을 확인하였다. 본 연구를 통해 다양한 상황에서도 선박 입·출항 소요시간 예측이 가능하여 해상교통관제사는 선박에게 정확한 정보 제공 및 대기지시 판단에 도움이 될 것으로 기대된다.

• 대한교통학회지
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• 제13권4호
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• pp.105-115
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• 1995

This paper deals with an operation concept of "time-transfer of buses", in which buses arrive a transfer center at the same time and allow passengers to transfer to other bus lines, so that passengerscan go anywhere all the timed-transfere buses operate with only one transfer. This timed-transfer bus system is known as an efficient operating technique which can be adopted in an area with sparsely distrubuted bus demand. A model of timed-transfer is estabilished in terms of vaious factors such as the expected(or average) arrival time, distribution of arrival time, timed-transfer cycle, shceduled departure time, etc. It is assumed that the objective of timed-transfer bus system is to minimize the total transfer waiting time. The optimal schedualed arrival time or buffer time(time required to arrive ealy in consideration of delay) is analyzed for a general case and various speicial cases. It was found that the optiaml buffer time is an inverse funcion of the timed-transfer cycl and increases with the cycle time, assumin g that there is a fixed scheduled departure time at the transfer cetner regardless of whether one or more buses fail to arrive before the scheduled departure time. If buses are to wait uhtil all the buses arrive at the transfer center, that is, the transfer departure time is vairable, the optimal scheduled arrival times can be obtained by a mathmatical programming.

• Management Science and Financial Engineering
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• 제20권2호
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• pp.27-31
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• 2014

This paper studies the assortment optimization problem in online retailing by using a multinomial logit model in order to take consumer choice behavior into account. We focus on two unique features of online purchase behavior: first, there exists increased amount of uncertainty (e.g., size and color of merchandize) in online shopping as customers cannot experience merchandize directly. This uncertainty is captured by the scale parameter of a Gumbel distribution; second, online shopping entails unique shopping-related disutility (e.g., waiting time for delivery and security concerns) compared to offline shopping. This disutility is controlled by the changes in the observed part of utility function in our model. The impact of changes in uncertainty and disutility on the expected profit does not exhibit obvious structure: the expected profit may increase or decrease depending on the assortment. However, by analyzing the structure of the optimal assortment based on convexity property of the profit function, we show that the cardinality of the optimal assortment decreases and the maximum expected profit increases as uncertainty or disutility decreases. Therefore, our study suggests that it is important for managers of online retailing to reduce uncertainty and disutility involved in online purchase process.

• 대한토목학회논문집
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• 제34권5호
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• pp.1525-1534
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• 2014

최근, 환승시스템 구축 및 통합 교통체계, 스마트폰 보급 등으로 인한 실시간 대중교통 정보제공이 가능해 지면서 이용자들의 대중교통 경로선택이 유연해지고 있어 미리 수단을 정하고 통행하는 것이 아니라 상황에 맞춰 경로를 선택하는 특성으로 변해가고 있다. 우리나라의 경우 2004년부터 시행된 대중교통 요금통합에 따라 이용자가 경로를 선택함에 있어 저항을 느끼지 않는 특징을 보이고 있으며, 이용자들의 경로선택은 대중교통 용량에 따른 혼잡으로 인해 대기시간이 증가 될 경우 달라진다. 이러한 이용자의 노선경로 선택이 대중교통 시스템에서의 혼잡에 따른 대기시간에 영향을 받지만 기존 전통적인 모형으로 묘사하기에는 한계점이 존재하며 이와 관련된 기초연구 역시 부족한 상황이다. 용량과 상관없이 주어진 모형에 의해서 수요를 추정하는 기존 모형의 문제를 해결하기 위해 본 논문에서는 승용차 통행배정에서 사용되는 링크 통행비용함수의 개념을 도입하였으며, 실질운행횟수의 이원화된 변수를 설정하여 용량을 초과하지 않도록 수리모형상의 제약식을 완성하였다. 모형의 검증으로 신규직결노선 도입과 돌발상황에 따른 각각의 시나리오 예제 네트워크를 구축하여 적용하고 그에 대한 유의성을 검증한 결과 용량초과에대한 통행량은 배정되지 않았으며, 대중교통시스템 용량이 초과할 경우에도 초과된 수요의 경로전환으로 통행량이 안정적으로 배정되는 결과가 나타났다. 따라서 본 논문이 대중교통 시스템에서 혼잡 등으로 인해 변동되는 대기시간에 따라 이용자의 경로선택이 유연해지는 현실을 반영 할 수 있는 선행연구가 될 것으로 기대한다.