• 대한수학회논문집
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• 제28권2호
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• pp.383-396
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• 2013

We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.489-497
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• 2000

The M/M/1 queue with impatient customers is studied. Impatient customers wait for service only for limited time K/0 and leave the system if their services do not start during that time. Notice that in the analysis of virtual waiting time, the impatient customer can be considered as the customer who enters the system only when his/her waiting time does not exceed K. In this paper, we apply martingale methods to the virtual waiting time and obtain the expected period from origin to the point where the virtual waiting time crosses over K or reaches 0, and the variance of this period. With this results, we obtain the expected busy period of the queue, the distribution, expectation and variance of the number of times the virtual waiting time exceeding level K during a busy period, and the probability of there being no impatient customers in a busy period.

• 대한산업공학회지
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• 제14권2호
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• pp.1-10
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• 1988

We consider a vacation system in which the server takes two different types of vacations alternately. We obtain the server idle probability and derive the system size distribution and the waiting time distribution by defining supplementary variables. We show that the decomposition property works for these mixed-vacation queues. We also propose a method directly to obtain the waiting time distribution without resorting to the system equations. The T-policy is revisited and is shown that the cost is minimized when the length of vacations are the same.

• 한국산업정보학회논문지
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• 제23권1호
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• pp.53-63
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• 2018

본 논문에서는 D-정책을 갖는 이산시간 BMAP/G/1 대기행렬시스템의 대기시간을 분석한다. 고객(또는 패킷)들은 마코비안 도착과정을 따라 집단으로 시스템에 도착하며, 유휴한 서버는 시스템에 도착한 고객집단의 서비스시간의 총합이 이미 정해놓은 임계값 D를 초과하면 시스템에 더 이상 서비스할 고객이 없을 때까지 서비스를 제공한다. 시스템의 안정상태 대기시간 분포를 변환 형태로 구하고 성능척도로서 평균값을 유도하였다. 시뮬레이션을 통하여 이론값들의 타당성을 검증하고 간단한 수치예제를 보였다.

• 대한수학회지
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• 제38권4호
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• pp.807-842
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• 2001

This paper summarizes recent development of analytical and algorithmical results for stationary FIFO queues with multiple Markovian arrival streams, where service time distributions are general and they may differ for different arrival streams. While this kind of queues naturally arises in considering queues with a superposition of independent phase-type arrivals, the conventional approach based on the queue length dynamics (i.e., M/G/1 pradigm) is not applicable to this kind of queues. On the contrary, the workload process has a Markovian property, so that it is analytically tractable. This paper first reviews the results for the stationary distributions of the amount of work-in-system, actual waiting time and sojourn time, all of which were obtained in the last six years by the author. Further this paper shows an alternative approach, recently developed by the author, to analyze the joint queue length distribution based on the waiting time distribution. An emphasis is placed on how to construct a numerically feasible recursion to compute the stationary queue length mass function.

• 한국경영과학회지
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• 제17권2호
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• pp.107-115
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• 1992

Many manufacturing processes involved in the fabrication and assembly of hightech components have highly variable yields that tend to complicate the production control. Under this random yield situation we develop a model to determine optimal input quantity, mean waiting time in the system and variance of waiting time in the system. An example which considers beta distribution as a yield distribution is given.

• 산업공학
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• 제25권3호
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• pp.283-289
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• 2012

M/G/1 queue with server vacations period depending on the previous vacation and customer's arrival is considered. Most existing studies on M/G/1 queue with server vacations assume that server vacations are independent of customers' arrival. However, some vacations are terminated by some class of customers' arrival in certain queueing systems. In this paper, therefore, we investigate M/G/1 queue with server vacations where each vacation period has different distribution and vacation length is influenced by customers' arrival. Laplace-Stieltjes transform of the waiting time distribution and the distribution of number of customers waiting for each class of customers are respectively derived. As performance measures, mean waiting time and average number of customers waiting for each class of customers are also derived.

• 한국항만경제학회지
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• 제34권2호
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• pp.69-82
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• 2018

컨테이너 터미널의 선박대기율에 관한 정부의 공식적 발표가 없는 상황에서 부산항 컨테이너 터미널의 선박 입항척수는 연 2.9%이상 증가하고 있다. 컨테이너 터미널의 선석 혼잡이 발생하고 있지만 실제 선박대기율 및 평균 대기시간은 측정되지 않고 있어 터미널 운영 정책 결정에 어려움이 예상된다. 본 연구는 항만시설사용실적자료와 터미널운영데이터자료를 통해 컨테이너 터미널의 대기율을 공인된 대기시간으로 산정하고자 한다. 이를 통해 컨테이너터미널의 선박대기율 측정 방식을 제안하고 터미널의 실제 대기율과 대기행렬이론상의 대기율을 비교하여 차이가 어떻게 발생하는지를 밝혀내고자 한다. 분석결과, 부산항 A터미널의 최근 3년간(2014~2016) 발생한 대기 척수는 총 587척이며, 월평균 16.3척의 대기선박이 발생하는 것으로 나타났으며 대기율은 123.9%를 보이고 있다. 반면, 행렬이론상의 대기율과 실제 터미널의 대기율을 비교하였으며, 점유율 70%일 때 대기행렬이론상 대기율은 31.1%이 도출되었다. 이러한 차이가 나는 이유로는 항만의 특성상 입항선박이 많은 피크요일로 인한 것이라 추정된다. 피크요일 시 대기척수를 조사한 결과, 일요일 197척, 화요일 89척, 수요일 89척의 선박이 대기한 것으로 나타났다.

• 산업경영시스템학회지
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• 제21권48호
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• pp.223-232
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• 1998

In order to improve the hospital service quality, some hospitals try to reduce the outpatients' waiting time in the hospital. One of the dissatisfied service items at the hospital is the long waiting time to take the prescribed medicine. In most cases, the smaller the number of pharmacists, the longer could be the waiting time. The suggestion of criteria for optimal allocation of appropriate number of pharmacists must be very important to manage the hospital pharmacy. In this paper, we suggest the method to figure out appropriate number of pharmacists through the real situation study at the Sampling Medical Center Pharmacy. We present the simulation study results using the simulation package ARENA and the analysis of statistical distribution of the arriving prescriptions. The result of this research could be applied to the other service business to figure out the optimal allocation of available human resources and to do the job analysis for better service quality.

• KEPCO Journal on Electric Power and Energy
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• 제6권1호
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• pp.59-64
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• 2020

Scheduling of electric vehicles and optimizing for charging waiting time have been critical. Meanwhile, it is challengeable to exploit the fluctuating data from electric vehicles in real-time. We introduce an optimal routing algorithm and a simulator with electric vehicles obeying the Poisson distribution of the observed information about time, space and energy-demand. Electric vehicle routing is updated in every cycle even it is already set. Also, we suggest an electric vehicle routing algorithm for minimizing total trip time, considering a threshold of the waiting time. Total trip time and charging waiting time are decreased 34.3% and 86.4% respectively, compared to the previous algorithm. It can be applied to the information service of charging stations and utilized as a reservation service.