• Communications of the Korean Mathematical Society
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• v.28 no.2
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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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• v.7 no.2
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.14 no.2
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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.

• Journal of Korea Society of Industrial Information Systems
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• v.23 no.1
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• pp.53-63
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• 2018

In this paper, we analyze the waiting time of a queueing system with D-BMAP (discrete-time batch Markovian arrival process) and D-policy. Customer group or packets arrives at the system according to discrete-time Markovian arrival process, and an idle single server becomes busy when the total service time of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state waiting time distribution is derived in the form of a generating function. Mean waiting time is derived as a performance measure. Simulation is also performed for the purpose of verification and validation. Two simple numerical examples are shown.

• Journal of the Korean Mathematical Society
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• v.38 no.4
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.2
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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.

• IE interfaces
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• v.25 no.3
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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.

• Journal of Korea Port Economic Association
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• v.34 no.2
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• pp.69-82
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• 2018

The number of ships serviced at the container terminals in Busan is increasing by 2.9% per year. In spite of the increase in calling ships, there are no official records of waiting rate by the port authority. This study attempts to compare the theoretical ship waiting ratio and actual ship waiting ratio. The actual ship waiting ratio of container terminals is acquired from the 2014 to 2016 data of PORT-MIS and Terminal Operating System (TOS). Furthermore, methods and procedures to measure the actual ship's waiting rate of container terminal are proposed for ongoing measurement. In drawing the theoretical ship waiting ratio, the queuing theory is applied after deploying the ship arrival probability distribution and ship service probability distribution by the Chi Square method. As a result, the total number of ships waiting in a terminal for three years was 587, the average monthly service time and the average waiting time was 13.8 hours and 17.1 hours, respectively, and the monthly number of waiting ships was 16.3. Meanwhile, according to the queuing theory with multi servers, the ship waiting ratio is 31.1% on a 70% berth occupancy ratio. The reason behind the huge gap is the congested sailing in the peak days of the week, such as Sunday, Tuesday, and Wednesday. In addition, the number of waiting ships recorded on Sundays was twice as much as the average number of waiting ships.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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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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• v.6 no.1
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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.