• Journal of Information Processing Systems
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• 제7권4호
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• pp.653-678
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• 2011

WiMAX is intended for fourth generation wireless mobile communications where a group of users are provided with a connection and a fixed length queue. In present literature traffic of such network is analyzed based on the generator matrix of the Markov Arrival Process (MAP). In this paper a simple analytical technique of the two dimensional Markov chain is used to obtain the trajectory of the congestion of the network as a function of a traffic parameter. Finally, a two state phase dependent arrival process is considered to evaluate probability states. The entire analysis is kept independent of modulation and coding schemes.

• Journal of Communications and Networks
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• 제16권2호
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• pp.217-226
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• 2014

In this research, we study the problem of opportunistic spectrum access (OSA) in a time-varying environment with fading channels, where the channel state is characterized by both channel quality and the occupancy of primary users (PUs). First, a finite-state Markov channel model is introduced to represent a fading channel. Second, by probing channel quality and exploring the activities of PUs jointly, a two-dimensional partially observable Markov decision process framework is proposed for OSA. In addition, a greedy strategy is designed, where a secondary user selects a channel that has the best-expected data transmission rate to maximize the instantaneous reward in the current slot. Compared with the optimal strategy that considers future reward, the greedy strategy brings low complexity and relatively ideal performance. Meanwhile, the spectrum sensing error that causes the collision between a PU and a secondary user (SU) is also discussed. Furthermore, we analyze the multiuser situation in which the proposed single-user strategy is adopted by every SU compared with the previous one. By observing the simulation results, the proposed strategy attains a larger throughput than the previous works under various parameter configurations.

• 충청수학회지
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• 제27권2호
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• pp.237-242
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• 2014

In this paper we provide a valuation method for multi-asset derivatives with single jump regime-switching volatilities. We suppse that volatilities of assets are affected by an n-dimensional independent Markov regime-switching process.

• 대한수학회논문집
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• 제12권2호
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• pp.419-425
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• 1997

Consider a d-dimensional domain D that has finite Lebesque measure and a Dirichlet form which has discontinuous coefficient. Then the stationary Markov process corresponding to the given Dirichlet form is a semimartingale under suitable condition for D and the coefficient.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권9호
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• pp.3110-3125
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• 2014

Network coding improves TCP's performance in lossy wireless networks. However, the complex congestion window evolution of network coded TCP (TCP-NC) makes the analysis of end-to-end throughput challenging. This paper analyzes the evolutionary process of TCP-NC against lossy links. An analytic model is established by applying a two-dimensional Markov chain. With maximum window size, end-to-end erasure rate and redundancy parameter as input parameters, the analytic model can reflect window evolution and calculate end-to-end throughput of TCP-NC precisely. The key point of our model is that by the novel definition of the states of Markov chain, both the number of related states and the computation complexity are substantially reduced. Our work helps to understand the factors that affect TCP-NC's performance and lay the foundation of its optimization. Extensive simulations on NS2 show that the analytic model features fairly high accuracy.

• 한국통신학회논문지
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• 제11권3호
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• pp.179-196
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• 1986

본 논문에서는 통계적 패킷 음성/데이터 다중화기의 성능을 연구하였다. 성능해석은 음성과 데이터가 서로 분리된 한정된 queue를 사용하고, 전송에 있어서 음성이 데이터보다 우선권을 갖는 것을 가정하고, 다중화기의 출력 link를 시간 slot단위로 나누고 음성은 (M+1)-state의 Markov Process로, 데이터는 Poisson process로 modeling 하여 수행하였다. 전송시 음성신호가 데이터 신호보다 우선권을 가지므로 음성의 queueing behavior는 data에 거의 영향을 받지 않는다. 다라서 본 연구에서는 음성의 queueing behavior를 먼저 해석한 다음 data의 queueing behavior를 해석하였다. 패킷 음성 다중화기의 성능 해석은 입력상태와 buffer의 점유를 2차원의 Markov chain을 가지고 formulation하였고, 집적된 음성/data의 다중화기는 data를 추가한 3차원 Markov chain으로 하였다. 이러한 model을 사용하여 Gauss-Seidel방법으로 결과를 얻고 simulation으로 입증하였다. 이들 결과로 부터 음성 가입자의 수, 출력 link용량, 음성의 queue크기, 음성의 overflow확률에서는 서로 trade-off가 있고 data에서도 비슷한 tradeoff가 있음을 알았다. 또한 입력 traffic량과 link의 용량에 따라서 음성과 데이타간의 성능에서 서로 tradeoff가 있고, TASI의 이득이 2이상이고 음성가입자의 수가 적을 경우 데이타의 평균 지연시간은 buffer의 최대길이 보다 길음을 알아내었다.

• 전자공학회논문지CI
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• 제45권5호
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• pp.125-133
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• 2008

본 논문은 다양한 서비스 클래스가 제공되는 BcN (Broadband convergence Network) 환경에서 상위 우선순위 서비스의 품질을 보장하기 위한 능동 큐 관리 메커니즘 (Active-WRED)을 제안한다. 네트워크 혼잡 상황에서 제안된 메커니즘은 상대적으로 낮은 우선순위를 갖는 서비스의 drop 확률을 증가시키고 이에 따라 상위 우선순위 서비스의 drop 확률을 감소시킴으로써 상위 우선순위 서비스에 대해 패킷 손실로부터 품질을 보장할 수 있다. 제안된 능동 큐 관리 메커니즘의 성능을 분석하기 위해 이산 시간 큐잉 시스템의 통계적 분석 방법을 도입하였다. 두 서비스 클래스 (GS: Guaranteed Service, BS: Best Effort Service)만을 고려하여 제안 방안의 성능 분석을 위해 MMBP-2 (two-state Markov-Modulated Bernoulli arrival Process) 트래픽 소스 모델과 2차 이산시간 Markov 체인을 도입하였다.

• 한국군사과학기술학회지
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• 제15권4호
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• pp.442-449
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• 2012

Cognitive Radio(CR) is the technology that allocates the frequency by using dynamic spectrum access. We proposed a model to calculate the optimal level of the cognitive radiotelegraph, where secondary users opportunistically share the spectrum with primary users through the spectrum sensing. When secondary user with cognitive radio detects the arrival of a primary user in its current channel, the secondary user moves to the idle channel or be placed in the virtual queue. We assume that the primary users have finite buffers and the population of secondary users is finite. Using a two-dimensional Makov model with preemptive priority queueing, we could derive the blocking and waiting probability as well as the optimal level of cognitive radiotelegraph under a various range of parameter circumstances.

• 산업경영시스템학회지
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• 제39권2호
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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.

• 대한수학회지
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• 제59권2호
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• pp.311-335
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• 2022

This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.