• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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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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• v.6 no.3
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.4
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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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• v.3 no.2
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.2
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.12A
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• pp.1320-1328
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• 2007

In recent year, the popularity of WLAN has generated much interests on improvement and performance analysis of the IEEE 802.11 protocol. In this paper, we analyze two medium access methods of the IEEE 802.11 MAC protocol by investigating the MAC layer packet service times when arrival packet sizes have a general probability distribution. We use the M/G/1/K queueing model to analyze the throughput and the delay performance of IEEE 802.11 MAC protocol in a wireless LAN. We compare the performances of Basic access method and RTS/CTS access method. We take some numerical examples for the system throughput and the queue dynamics including the mean packet delay and packet blocking probability.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.1
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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.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.4
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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.

• Journal of Korean Port Research
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• v.9 no.1
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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%.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.11
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• pp.1206-1218
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• 1992

Token ring systems which control to switch the data stream of networks by passing the token have been widely used to medium access controls in many ring or bus topology LANs. The system could be modeled for analysis as single-server-multi-queue system of the cyclic service method. These concepts could be expanded to multi-token ring systems interconnected with single ring consisting of bridges implemented simply to be stored and transmitted. In the proposal for the performance analysis of the interconnected token ring system, in has been assumed M/G/1 queueing model that frame arrivals are the Poisson process at each station queue and frame sizes are independently and identically distributed. And the average time delays were analyzed mathematically for arbitrary frame transferred from source station to destination area. The time delay of the frame transmission could be explained as the sum of the average time which the token passed from arbitrary position to source station, such as the waiting time in the source station transferring the previous arrival frames, and the propagation time from source station to interdestinated point. These delays were given as the sum of the duration from inner and outer bridge queues, the time delays from inner and outer bridge queues, and the time from outer bridge queue to destination station. These results were investigated by varing parameters effected to total time delays. In the results, those factors to be effected to dominant the total time delays were increased were in the cases of the high arrival rates and the high ration of destination of the other outerring. The system were shown the time delays increased exponentially in spite of the priority service policy. In order to decreasing the number of outerrings and increasing the number of nodes in backbone relatively, so the systems could be decreased the total delay in the interconnected token ring system.