• Journal of Korean Society of Industrial and Systems Engineering
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• v.47 no.3
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• pp.1-7
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• 2024

In an influential paper, Choi and Kim (2010) derived waiting times in an M/M/1 queuing model under net neurality and under prioritization. In this short paper, we argue that the waiting times of content transmission that Choi and Kim (2010) derived by using the M/M/1 gueuing model under the non-preemptive priority rule are miscalculated. We provide corrected waiting times in the M/M/1 queuing model in the prioritization case. We also show that this correction does not affect their main results on the delay time and the incentive to invest in the network capacity qualitatively.

• Journal of the Korea Safety Management & Science
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• v.12 no.2
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• pp.225-230
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• 2010

The purpose of the study was to apply and to expand the six sigma to reduce waiting times for computed tomography (CT) examination which manipulated by the department of radiology. It was preceded by DMAIC (Define, Measure, Analyze, Improve, and Control). In the stage of definition, it wereselected for total 5 critical to quality (CTQ), which were the kindness, the waiting time, the examination explanation, the waiting day and the waiting stand environment, that increased the reserved time of CT examination. In the stage of measurement, the number of examinations and of reservation waiting days performed and resulted in final CTQ(Y) which measured each 1.68 and 1.85 sigma. In the stage of analysis, the examination concentrated on morning time, non-scheduled examination of the day, the delayed time of booking, frequent telephone contacting and equipment malfunction were determined as variable key causes. In the stage of improvement, it were performed with expansion of the examination in the morning time, integration of laboratories that used to in each steps, developing the ability of simultaneous booking schedule for the multiple examinations, developing program of examination request, and the customer management team operations. For the control, the number of examinations and reserved waiting days were measured each 3.14 and 1.13 sigma.

• 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 the Korea Society for Simulation
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• v.24 no.2
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• pp.11-17
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• 2015

Although systems with finite capacities have been the topic of much study, there are as of yet no analytic expressions for (higher) moment and tail probability of stationary waiting times in systems with even constant processing times. The normal queueing theory cannot properly handle such systems due to the difficulties caused by finite capacity. In this study, for a DBR (Drum-Buffer-Rope) line production system with constant processing times, we introduce analytic expressions by using previous results obtained using a max-plus algebraic approach.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.749-757
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• 2012

We consider the M/PH,G/1 queue with two classes of customers in which class-1 customers have deterministic impatience time and have preemptive priority over class-2 customers who are assumed to be infinitely patient. The service times of class-1 and class-2 customers have a phase-type distribution and a general distribution, respectively. We obtain performance measures of class-2 customers such as the queue length distribution, the waiting time distribution and the sojourn time distribution, by analyzing the busy period of class-1 customers. We also compute the moments of the queue length and the waiting and sojourn times.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.881-892
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• 1999

In this paper we consider a polling system with two classes of stations; high priority and low priority. High priority stations are polled more frequently than low priority stations. We derive an exact and explicit formula for computing the mean waiting times for a message when the arrival processes are batch Poisson. In general the formula requires to solve two sets of simultaneous equations By specializing them to the case of two priority classes we greatly reduce the number equations and provide a simple formula for mean waiting times. We apply the results to a data communication processing system and show that the overall mean waiting time can be reduced by using priority polling.

• Journal of the Korea Society for Simulation
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• v.28 no.2
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• pp.119-129
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• 2019

Although line production systems with finite buffers have been studied over several decades, except for some special cases there are no explicit expressions for system performances such as waiting times(or response time) and blocking probability. Recently, a max-plus algebraic approach for buffer-sharing systems with constant processing times was introduced and it can lead to analytic expressions for (higher) moment and tail probability of stationary waiting. Theoretically this approach can be applied to general processing times, but it cannot give a proper way for computing performance measures. To this end, in this study we developed simulation models using @RISK software and the expressions derived from max-plus algebra, and computed and compared blocking probability, waiting time (or response time) with respect to two blocking policies: communication(BBS: Blocking Before Service) and production(BAS: Blocking After Service). Moreover, an optimization problem which determines the minimum shared-buffer capacity satisfying a predetermined QoS(quality of service) is also considered.

• Industrial Engineering and Management Systems
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• v.15 no.1
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• pp.19-31
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• 2016

A design method of the network for automated transporters mounted on rails is addressed for automated container terminals. In the network design, the flow directions of some path segments as well as routes of transporters for each flow requirement must be determined, while the total transportation and waiting times are minimized. This study considers, for the design of the network, the waiting times of the transporters during the travel on path segments, intersections, transfer points below the quay crane (QC), and transfer points at the storage yard. An algorithm, which is the combination of a modified Dijkstra's algorithm for finding the shortest time path and a queuing theory for calculating the waiting times during the travel, is proposed. The proposed algorithm can solve the problem in a short time, which can be used in practice. Numerical experiments showed that the proposed algorithm gives solutions better than several simple rules. It was also shown that the proposed algorithm provides satisfactory solutions in a reasonable time with only average 7.22% gap in its travel time from those by a genetic algorithm which needs too long computational time. The performance of the algorithm is tested and analyzed for various parameters.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• Korean Journal of Digital Imaging in Medicine
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• v.15 no.1
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• pp.39-45
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• 2013

PACS Import external image of the thread of the tasks and duties of hospital revenue and business efficiency falls over time. 500 beds or more medical imaging import work outside of the hospital, most hospitals use a PC, KIOSK, and was used in 15 hospitals where, CD Autoloader where use was the only one. Working hours compared to CD and DVD media to test the results of the Import target PC, KIOSK, CD Autoloader Import spent less time in the order, and also the greater capacity of CD Autoloader four times the PC, KIOSK 2 times Import could be implemented quickly. In addition, the waiting time of the patients was measured using the PC's time to Import, 2011 14.5 minutes and the average patient waiting time, KIOSK and later use CD Autoloader 2012 average patient wait time of 8.25 minutes, 43% of the existing average waiting time was 5.25 minutes to reduce. However, KIOSK case of a patient in a way that directly Import latency time was soon. Import of three ways: in terms of efficiency and excellent CD Autoloader way, the patient waiting time in terms of ease of use and KIOSK was excellent. In addition, with the introduction of CD Autoloader with KIOSK Joint of the items waiting time of patients and patient satisfaction rating is considered to be a major contribution.