• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.985-1004
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• 2016

We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.35.3-35
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• 2002

Reinforcement Learning (RL) is one of machine learning methods and an RL agent autonomously learns the action selection policy by interactions with its environment. At the beginning of RL research, it was limited to problems in environments assumed to be Markovian Decision Process (MDP). However in practical problems, the agent suffers from the incomplete perception, i.e., the agent observes the state of the environments, but these observations include incomplete information of the state. This problem is formally modeled by Partially Observable MDP (POMDP). One of the possible approaches to POMDPS is to use historical nformation to estimate states. The problem of these approaches is how t..

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1101-1103
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• 2006

For a broad class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process) arrivals, we present a distributional Little's law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue for example, we illustrate how to utilize this relation to get the desired distribution of the number of customers.

• Journal of Korea Society of Industrial Information Systems
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• v.11 no.1
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• pp.1-6
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• 2006

Queueing models are good models for fragments of communication systems and networks, so their investigation is interesting for theory and applications. Theses queues may play an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, in this paper we illustrate that the batch size distribution affects the loss probability, which is the main performance measure of a finite buffer queues.

• Journal of the Korea Society for Simulation
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• v.2 no.1
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• pp.46-54
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• 1993

Analytic and simulation models for prioritized token ring are presented in this paper. Its protocol is based on prioritized token ring with reservation (R-PTR). Since the protocol of the R-PTR is simple and the performance of the R-PTR is not inferior to that of the IEEE-PTR under almost all traffic load environments, we use the R-PTR as our token ring model. By using the properties of Markovian process, the expressions for average throughput and average packet transmission delay are derived. The results obtained from the analytic model are compared with that of the discrete event simulation model.

• Journal of Korean Society for Quality Management
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• v.21 no.1
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• pp.65-77
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• 1993

Often in a production process, the quality of items is serially dependent. We assume that the quality of items is an attribute which can be classified as good or bad with a Markovian dependence structure. In order to determine sampling inspection plan characteristics such as total inspection cost and average outgoing quality, we design an economic model and illustrate an efficient procedure for design of best inspection plan using graphs based on numerical calculations.

• Proceedings of the Korean Biophysical Society Conference
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• 1998.06a
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• pp.15-15
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• 1998

Pores can form and grow in biomembranes because of factors such as thermal fluctuation, transmembrane electrical potential, and cellular environment. We propose a new statistical physics model of the pore growth treated as a non-Markovian stochastic process, with a free energy barrier and memory friction from the membrane matrix treated as a quasi-two-dimensional viscoelastic and dielectric fluid continuum.(omitted)

• 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.1
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• pp.63-76
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• 2024

In this study, we analyzed queue length and sojourn time of discrete-time BMAP/G/1 queues under the workload control. Group customers (packets) with correlations arrive at the system following a discrete-time Markovian arrival process. The server starts busy period when the total service time of the arrived customers exceeds a predetermined workload threshold D and serves customers until the system is empty. From the analysis of workload and waiting time, distributions of queue length at the departure epoch and arbitrary time epoch and system sojourn time are derived. We also derived the mean value as a performance measure. Through numerical examples, we confirmed that we can obtain results represented by complex forms of equations, and we verified the validity of the theoretical values by comparing them with simulation results. From the results, we can obtain key performance measures of complex systems that operate similarly in various industrial fields and to analyze various optimization problems.

• 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.