• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.159-163
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• 1991

For a continuous-time absorvation Markov chain, we apply and simplify the general method of finding the transition rates given the transition probabilities obtained from discrete observation of the continuous system. An example is given.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.4
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• pp.290-297
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• 2013

The increasing level of operation in high-tech industry is likely to require ever more complex structure in reliability problem. Furthermore, system failures are more significant on society as a whole than ever before. Reliability redundancy optimization problem (RROP) plays a important role in the designing and analyzing the complex system. RROP involves selection of components with multiple choices and redundancy levels for maximizing system reliability with constraints such as cost, weight, etc. Meanwhile, previous works on RROP dealt with system with perfect failure detection, which gave at most a good solution. However, we studied RROP with imperfect failure detection and switching. Using absorbing Markov Chain, we present not a good solution but the optimal one. In this study, the optimal system configuration is designed with warm and cold-standby redundancy for k-out-of-n system in terms of MTTF that is one of the performance measures of reliability.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.231-231
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• 1993

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.657-676
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• 2011

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.537-556
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• 2021

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

• Journal of Communications and Networks
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• v.13 no.4
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• pp.393-399
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• 2011

We evaluate the link-level performance of cooperative multi-hop relaying networks with an maximum distance separable (MDS) code. The effect of the code on the link-level performance at the destination is investigated in terms of the outage probability and the spectral efficiency. Assuming a simple topology, we construct an absorbing Markov chain. Numerical results indicate that significant improvement can be achieved by incorporating an MDS code. MDS codes successfully facilitate recovery of the message block at a relaying node due to powerful error-correcting capability, so that it can reduce the outage probability. Furthermore, we evaluate the average number of hops where the message block can be delivered.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2499-2522
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• 2017

Multi-hop networks are a low-setup-cost solution for enlarging an area of network coverage through multi-hop routing. Carrier sense multiple access with collision avoidance (CSMA/CA) is frequently used in multi-hop networks. Multi-hop networks face multiple problems, such as a rise in contention for the medium, and packet loss under heavy-load, saturated conditions, which consumes more bandwidth due to re-transmissions. The number of re-transmissions carried out in a multi-hop network plays a major role in the achievable quality of service (QoS). This paper presents a statistical, analytical model for the end-to-end delay of contention-based medium access control (MAC) strategies. These strategies schedule a packet before performing the back-off contention for both differentiated heterogeneous data and homogeneous data under saturation conditions. The analytical model is an application of Markov chain theory and queuing theory. The M/M/1 model is used to derive access queue waiting times, and an absorbing Markov chain is used to determine the expected number of re-transmissions in a multi-hop scenario. This is then used to calculate the expected end-to-end delay. The prediction by the proposed model is compared to the simulation results, and shows close correlation for the different test cases with different arrival rates.

• Journal of the Korea Institute of Military Science and Technology
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• v.17 no.6
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• pp.733-743
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• 2014

Since the technology of anti-ship missiles has advanced rapidly, defending battleships from the threat of anti-ship missiles is a crucial factor for the survival of warships. In this paper, we analyze the performance of an anti-ship missile defense system whose name is Close-In-Weapon-System. We show the survival probability of a warship equipped with the Close-In-Weapon-System as the number of anti-ship missiles attacking the warship varies. Because of the complex and dynamic operational characteristics surrounding the Close-In-Weapon-System such as speed of missiles, different range of an individual weapon in the weapon system, and the continuous change of the kill probability of the missiles corresponding to the distance of missiles from ships, few work has been done for the performance of Close-In-Weapon-System. We present a model to incorporate all the dynamic characteristics of the system using absorbing Markov Chain. With our results, we expect commanders of warships equipped with Close-In-Weapon-System to be provided with more helpful information on how to deal with the anti-ship missiles.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.2
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• pp.1-10
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• 2016

In this paper, we present a new way to derive the mean cycle time of the G/G/m failure prone queue when the loading of the system approaches to zero. The loading is the relative ratio of the arrival rate to the service rate multiplied by the number of servers. The system with low loading means the busy fraction of the system is low. The queueing system with low loading can be found in the semiconductor manufacturing process. Cluster tools in semiconductor manufacturing need a setup whenever the types of two successive lots are different. To setup a cluster tool, all wafers of preceding lot should be removed. Then, the waiting time of the next lot is zero excluding the setup time. This kind of situation can be regarded as the system with low loading. By employing absorbing Markov chain model and renewal theory, we propose a new way to derive the exact mean cycle time. In addition, using the proposed method, we present the cycle times of other types of queueing systems. For a queueing model with phase type service time distribution, we can obtain a two dimensional Markov chain model, which leads us to calculate the exact cycle time. The results also can be applied to a queueing model with batch arrivals. Our results can be employed to test the accuracy of existing or newly developed approximation methods. Furthermore, we provide intuitive interpretations to the results regarding the expected waiting time. The intuitive interpretations can be used to understand logically the characteristics of systems with low loading.

• ETRI Journal
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• v.34 no.6
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• pp.816-826
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• 2012

Self-healing Ethernet rings show promise for realizing the SONET/SDH-grade resilience in Carrier Ethernet infrastructures. However, when a ring is faulty, high-priority protection messages are processed in less time than low-priority data frames are processed. In this situation, any delayed data frames either being queued or traveling through long ring spans will cause the ring nodes to generate incorrect forwarding information. As a result, the data frames spread in the wrong direction, causing the ring to become unstable. To solve this problem, we propose four schemes, that is, dual flush, flush delay timer setting, purge triggering, and priority setting, and evaluate their protection performance under various traffic conditions on a ring based on the Ethernet ring protection (ERP) method. In addition, we develop an absorbing Markov chain model of the ERP protocol to observe how traffic congestion can impact the protection performance of the proposed priority setting scheme. Based on our observations, we propose a more reliable priority setting scheme, which guarantees faultless protection, even in a congested ring.