• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권6호
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• pp.2450-2469
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• 2018

In this paper, we develop a spatiotemporal model to analysis of cellular user in underlay D2D communication by using stochastic geometry and queuing theory. Firstly, by exploring stochastic geometry to model the user locations, we derive the probability that the SINR of cellular user in a predefined interval, which constrains the corresponding transmission rate of cellular user. Secondly, in contrast to the previous studies with full traffic models, we employ queueing theory to evaluate the performance parameters of dynamic traffic model and formulate the cellular user transmission mechanism as a M/G/1 queuing model. In the derivation, Embedded Markov chain is introduced to depict the stationary distribution of cellular user queue status. Thirdly, the expressions of performance metrics in terms of mean queue length, mean throughput, mean delay and mean dropping probability are obtained, respectively. Simulation results show the validity and rationality of the theoretical analysis under different channel conditions.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.943-952
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• 1999

Models of single-server queues with vacation have been widely used to study the performance of many computer communica-tion and production system. In this paper we use the formula for a wide class of vacation policies and multiple types of vacations based on the M/G/1 queue with generalized vacations and exhaustive service. furthermore we derive the waiting times for many complex vacation policies which would otherwise be to analyze. These new results are also applicable to other related queueing models. if they conform with the basic model considered in this paper.

• 산업경영시스템학회지
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• 제44권4호
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• pp.154-168
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• 2021

COVID-19 has been spreading all around the world, and threatening global health. In this situation, identifying and isolating infected individuals rapidly has been one of the most important measures to contain the epidemic. However, the standard diagnosis procedure with RT-PCR (Reverse Transcriptase Polymerase Chain Reaction) is costly and time-consuming. For this reason, pooled testing for COVID-19 has been proposed from the early stage of the COVID-19 pandemic to reduce the cost and time of identifying the COVID-19 infection. For pooled testing, how many samples are tested in group is the most significant factor to the performance of the test system. When the arrivals of test requirements and the test time are stochastic, batch-service queueing models have been utilized for the analysis of pooled-testing systems. However, most of them do not consider the false-negative test results of pooled testing in their performance analysis. For the COVID-19 RT-PCR test, there is a small but certain possibility of false-negative test results, and the group-test size affects not only the time and cost of pooled testing, but also the false-negative rate of pooled testing, which is a significant concern to public health authorities. In this study, we analyze the performance of COVID-19 pooled-testing systems with false-negative test results. To do this, we first formulate the COVID-19 pooled-testing systems with false negatives as a batch-service queuing model, and then obtain the performance measures such as the expected number of test requirements in the system, the expected number of RP-PCR tests for a test sample, the false-negative group-test rate, and the total cost per unit time, using the queueing analysis. We also present a numerical example to demonstrate the applicability of our analysis, and draw a couple of implications for COVID-19 pooled testing.

• Interdisciplinary Bio Central
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• 제3권2호
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• pp.8.1-8.6
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• 2011

Background: Thanks to the development of the mathematical/statistical reverse engineering and the high-throughput measuring biotechnology, lots of biologically meaningful genegene interaction networks have been revealed. Steady-state analysis of these systems provides an important clue to understand and to predict the systematic behaviours of the biological system. However, modeling such a complex and large-scale system is one of the challenging difficulties in systems biology. Results: We introduce a new stochastic modeling approach that can describe gene regulatory mechanisms by dividing two (DNA and protein) layers. Simple queuing system is employed to explain the DNA layer and the protein layer is modeled using G-networks which enable us to account for the post-translational protein interactions. Our method is applied to a transcription repression system and an active protein degradation system. The steady-state results suggest that the active protein degradation system is more sensitive but the transcription repression system might be more reliable than the transcription repression system. Conclusions: Our two layer stochastic model successfully describes the long-run behaviour of gene regulatory networks which consist of various mRNA/protein processes. The analytic solution of the G-networks enables us to extend our model to a large-scale system. A more reliable modeling approach could be achieved by cooperating with a real experimental study in synthetic biology.

• 대한산업공학회지
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• 제21권2호
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• pp.167-181
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• 1995

We develop an analytical model to estimate the time a workpiece spends in both input and output queues in trip-based material handling systems. The waiting times in the input queues are approximated by M/G/1 queueing system and the waiting times in the output queues are estimated using the method discussed in Bozer, Cho, and Srinivasan [2]. The analytical results are tested via simulation experiment. The result indicates that the analytical model estimates the expected waiting times in both the input and output queues fairly accurately. Furthermore, we observe that a workpiece spends more time waiting for a processor than waiting for a device even if the processors and the devices are equally utilized. It is also noted that the expected waiting time in the output queue with fewer faster devices is shorter than that obtained with multiple slower devices.

• 한국통신학회논문지
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• 제32권12A호
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• pp.1320-1328
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• 2007

최근 무선 LAN의 인기로 IEEE 802.11 프로토콜의 성능 분석과 개선에 많은 관심이 생겨났다. 본 논문에서는 도착하는 패킷의 크기가 일반 확률분포를 가질 때 MAC 계층 패킷 서비스 시간을 조사하여 IEEE 802.11 프로토콜의 두 가지 매체 접속 방식을 분석한다. 무선 LAN에서 IEEE 802.11 프로토콜의 수율 및 지연 성능을 분석하기 위해 M/G/1/K 큐잉 모델을 사용한다. 두 가지 접속 방법, 기본 접속과 RTS/CTS 접속 방식의 성능을 비교한다. 그리고 시스템의 수율 및 평균 패킷 지연과 패킷 블록킹 확률을 포함하여 큐의 동작 상태를 보기 위한 여러가지 수치예를 보여준다.

• 대한산업공학회지
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• 제25권1호
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• pp.125-129
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• 1999

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.

• 전자공학회논문지S
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• 제34S권4호
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• pp.1-11
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• 1997

In this paper, modeling of the communication channel occupancy characteristics at the base station in the wide area radio trunking syste has been performed. Using the results, mathematical analysis for the switching capacity at the network switch has also been done. Specificatlly, we propose a G/M/m queueing model for the single service area modeling, and analyze changes in call blockingprobabilities accoridng to changes in the burstness characteristics of group paging calls. As a result, we have observe dthat the channel occupancy variations become larger as the burstness characteristics become more apparent, to make the call blocking probability higher. Next, based on the single service area analysis, we have anayzed mathematically the average switching capacity required to serve mobile subscribers for a wide area radio trunking sytem, where multiple switching port assignments are required when the people in the same group are distributed over several base stations. Accordingly, we have observed that the average and the variance of switching channel occupancy are closely related to the mobility characteristics of subscribers, and that we need a netowrk switch having bigger capacity as subscribers show wider distribution. Especially, with the call dropping probability within 0.2%, a switch having about 5 to 6 times bigger can be required, compared with the one when the mobility of subscribers is mostly restricte dto a single service area.

• 한국항만학회지
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• 제9권1호
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• pp.33-43
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• 1995

Korean economic and industrial structure has been seperated into some areas with the trend of the change to the bloc system of international economy: the Gyeongin including the capital area, the Middle-West, the South-West, the South-East, and the Eastern sea areas. Mokpo port has played a major role as the central one of the South-West area and the entrance of Yeong-san river of Jeonnam province gate. Some studies has been done on the Mokpo port, but there is no research of the analytical approach about it. In this paper, we analyze the data of 1994's on the domestic and oceangoing piers in the Mokpo port and simulate the transportation process of it through a queueing model. The results of the simulation are summarized as follows: The average arrival interval of the domestic vessel is 6.034 hours. The average service time and the berth utility rate are 24.056 hours and over 100%, respectively. The average arrival interval of the oceangoing vessel is 34.48 hours. The average service time and the berth utility rate are 120.04 hours and the 34.91%, respectively. The proposal to improving of the Mokpo port as follows: It is desirable to extend the capacity of domestic pier to about 50% for the optimal utility rate of 70% and in the case of oceangoing pier to be increase 65% of the vessel capacity for the optimal utility rate of 70%.

• 한국통신학회논문지
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• 제17권11호
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• pp.1206-1218
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• 1992

토큰으로 매체 이용 자격을 부여하는 토큰링 시스템은 링 혹은 버스 구조의 LAN에서 매체 이용방법으로 흔히 이용되어 왔으며 이러한 시스템으로 모델링 될 수 있다. 이 시스템은 단순히 프레임을 저장하고 전송 조건에 해당되면 전송을 진행하는 브리지를 이용함으로써 단일 링들이 상호 연결된 멀티 토큰링 시스템으로 시스템 규모를 확장할 수 있다. 본 논문에서는 상호 연결된 토큰링 시스템의 전송성능을 분석하기 위하여 스테이션 큐에 도착하는 프레임들이 Poisson과정이고 각 도착 프레임의 길이가 서로 독립이며 동등한 일반 분포를 갖는 M/G/1 큐잉 시스템을 가정하여, 임의의 프레임이 목적지까지 전달에 영향을 미치는 해석적으로 조사하였다. 프레임 전송 지연시간에 영향을 미치는 요소는 임의의 시간으로 부터 토큰이 전송하는 스테이션까지 오는데 걸리는 시간, 전송 스테이션의 전송 시간부터 스테이션 내의 대상 프레임이 전송되기까지 소요되는 대기시간, 대상 프레임의 길이와 목적지까지 소요되는 시간의 합으로 주어지며, 외부링으로부터 내부링 브리지 큐까지. 그리고 외부링 브리지 큐로부터 목적 스테이션 까지의 시간에 대한 합으로 주어진다. 또한 전송지연시간에 미치는 파라미터들을 변화시킬때 전체 지연시간에 미치는 영향을 조사하였다. 그 결과 프레임 전송 지연시간에 상대적으로 큰 영향을 미치는 요소는 프레임의 평균 도착율이 크고 수신 스테이션이 타 외부링일 비율이 커질때이며, 이는 우선순위 서비스 방식의 이용 여부에 관계없이 지연 시간이 지수적 증가를 나타낸다. 이를 감소시키려면 외부링 스테이션의 수를 줄여 상대적으로 중추링의 스테이션 수를 증가시킴으로써 전체 지연시간을 줄일 수 있다.