• Journal of the Korea Society for Simulation
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• v.13 no.1
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• pp.1-9
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• 2004

In this paper some models for obtaining the distribution of a sojourn time in CDMA cellular systems are proposed. Knowledge on this is essential for reliable modeling of the soft handoff and for solving other related problems in the analysis of cellular system. The proposed model is based on random walk and can be adopted to different conditions. Analytical results can be obtained that lead to a quite complicated numerical scheme so simulation models are used for Monte Carlo experiments. Main assumptions include different kinds of mobile carriers (pedestrians and transport passengers) and round shape of a cell. The scheme for simulation experiments is presented along with the discussion of simulation results.

• 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 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 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 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.

• 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.

• The Journal of the Korea Contents Association
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• v.16 no.7
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• pp.146-153
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• 2016

This work studies the equilibrium behavior of customers and optimal pricing strategies of the sever in a continuous-time M/M/1 queueing system. In this work, we consider two pricing models. The first one is called the ex-ante payment scheme where the server charges a flat price for all services, and the second one is called the ex-post payment scheme where the server charges a price that is proportional to the time a customer spends in the system. In each pricing model, the departing customer receives the reward that is inversely proportional to his/her sojourn time. The server should make the optimal pricing decisions in order to maximize its expected profit per unit time in each payment scheme. This work also investigates customer's equilibrium joining or balking behaviors under server's optimal pricing strategies. Numerical experiments are conducted to help the server best select one between two pricing models.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.923-929
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• 2002

We discuss scheduling analysis for a discrete event system with time windows of which firing or holding time delays are subject to random variation within some finite range. To do this, we propose a modified p-lime Petri net, named p+-time Petri net. We develop a condition for which a synchronized transition does not have a dead token, that is, the firing epochs do not violate the time window constraints. We propose a method of computing the feasible range of the token sojourn time at each place based on a time difference graph. We also discuss an application for analyzing wafer residency times within the process chambers for a dual-armed cluster tool for chemical vapor deposition.