• ETRI Journal
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• v.36 no.4
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• pp.609-616
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• 2014

Even though many computational methods (recursive formulae) for blocking probabilities in finite-capacity M/D/1 queues have already been produced, these are forms of transforms or are limited to single-node queues. Using a distinctly different approach from the usual queueing theory, this study introduces explicit (transform-free) formulae for a blocking probability, a stationary probability, and mean sojourn time under either production or communication blocking policy. Additionally, the smallest buffer capacity subject to a given blocking probability can be determined numerically from these formulae. With proper selection of the overall offered load ${\rho}$, the approach described herein can be applicable to more general queues from a computational point of view if the explicit expressions of random vector $D_n$ are available.

• Industrial Engineering and Management Systems
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• v.12 no.3
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• pp.281-287
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• 2013

In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.186-189
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• 1998

In this paper, we provide a mathematical formulation to describe the random mobility of users in cellular radio systems. With this, we can also study tile cell sojourn time (CST) distribution as well as the channel holding time (CHT) distribution. The study on user mobility enables to improve the resource management in cellular radio systems. We provide a versatile analysis tool that improves the limit of simplified analyses.

• Journal of Preventive Medicine and Public Health
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• v.47 no.4
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• pp.201-205
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• 2014

Objectives: This retrospective cohort study aimed to estimate the mean sojourn time (MST) of preclinical gastric cancer in Korean men. Methods: The subjects consisted of voluntary male screenees aged 40 to 69 years who underwent subsequent screening gastroscopies after testing negative at a baseline screening performed between January 2007 and December 2011. A new case was defined if gastric cancer cells were present in the biopsy specimens obtained from gastroscopy. The follow-up period was calculated as the number of person-years between the date of baseline screening gastroscopy and positive findings at a subsequent screening. The MST was calculated using transition rates of gastric cancer to determine the best screening interval. Results: Of the 171 979 voluntary male screenees, 61 688 (36%) underwent subsequent screening gastroscopies between January 2007 and December 2011. A total of 91 incident cases were found during 19 598 598 person-years of follow-up. The MST of gastric cancer was 2.37 years (95% confidence intervals, 1.92 to 2.96), and those aged 40 to 49 years had a shorter MST than those 50 to 69 years did. Conclusions: These findings support the 2-year interval of screening recommended by the nationwide gastric cancer screening program in Korea. Further studies for the age-specific MST among women are needed.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.2
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• pp.1-12
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• 1997

We consider an M/M/2 queue with two servers placed in series. System performance measures that we present in closed expressions are the first and the second moments for the system size, the queue walting time and the sojourn time. We also present an algorithm for computing the queue waiting time distribution function based on the randomization method. As an application, we analyze the double tollbooth system and compare its performance with the conventional single tollbooth system's.

• Journal of Korea Society of Industrial Information Systems
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• v.22 no.1
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• pp.23-32
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• 2017

In this paper, We suggest a unified approach for the analysis of discrete-time MAP/G/1 queueing system. Many researches on the D-MAP/G/1 queue have been used different approach to analyze system queue length and waiting time for the same system. Therefore, a unified framework for analyzing a system is necessary from a viewpoint of system design and management. We first derived steady-state workload distribution, and then waiting time and sojourn time are derived by the result of workload analysis. Finally, system queue length distribution is derived with generating function from the sojourn time distribution.

• Journal of Korea Society of Industrial Information Systems
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• v.29 no.2
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• pp.69-80
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• 2024

In this paper, we studied a discrete-time queuing system that operates under a mixed situation of D-policy and T-policy, one of the representative server control policies in queuing theory. A single server serves customers arriving by Bernoulli arrival process on a first-in, first-out basis(FIFO). If there are no customers to serve in the system, the server goes on vacation and returns, until the total service time (i.e., total amount of workload) of waiting customers exceeds predetermined workload threshold D. The operation of the system covered in this study can be used to model the efficient resource utilization of mobile devices using secondary batteries. In addition, it is significant in that the steady state waiting time and system sojourn time of the queuing system under a flexible mixed control policy were derived within a unified framework.

• Journal of the Korea Society for Simulation
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• v.23 no.3
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• pp.1-9
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• 2014

Traditional workflow time analyses have been performed treating an activity as an independent M/M/1queueing system. Using the general forms of performance measures in the M/M/1 system, various aspects of analyses can be performed. Especially, on the time analysis of an AND structure in a workflow system, the mean system sojourn time can be formalized by applying the performance measures of M/M/1 system. In the real workflow system, the AND structure cannot be described correctly under the assumption of independent M/M/1 systems. To overcome this limitation, this research makes the assumption that the all activities for a task starts simultaneously. In this situation, the theoretical solution can be derived using the performance measures of the M/G/1 system. In addition, the simulation modeling method will be proposed to analyze the AND structure of a real workflow system. Finally, some numerical results from the theoretical solutions and simulation models will be provided for verification. The main performance measures used in this research are mean queueing time and mean sojourn time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.26
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• pp.151-157
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• 1992

This paper presents a method for analyzing the transfer lines with finite storage buffers. Each machine spends a random amount of time processing each material. This transfer line can be modeled by the tandem queueing system with finite buffers. The great dimensionality of the state space renders the analysis of such system a formidable task. We propose an efficient algorithm to obtain the marginal state probabilities based on the exact algorithm for the two-machine system. Other performance measures, such as the utilization, the blocking probability, the average sojourn time, and the average queue length, can be easily calculated.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.137-146
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• 1993

We consider single server feedback queueing systems with priorities. In the model, there are J stations and job classes. Jobs of class i arrive at station i according to a Poisson process, and have a general service time distribution. We derive the generating functions of the number of jobs at each station just after a busy period and the formula for the mean sojourn time that a specific tagged job spends at station j from its arrival to departure from the system.