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(N, n)-Preemptive Repeat-Different Priority Queues
Kilhwan Kim(김길환) 한국산업경영시스템학회 2017 한국산업경영시스템학회지 Vol.40 No.3
Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.
도착 시점 접근 방법을 이용한 M/G/1 재시도 대기행렬 분석
김길환(Kilhwan Kim),채경철(Kyung C. Chae) 대한산업공학회 2008 대한산업공학회 추계학술대회논문집 Vol.2008 No.11
Chae et al. (2001) proposed a simple approach, called the arrival time approach, of finding the queue length distribution for M/G/1-type queues with generalized server vacations. The proposed approach serves as a useful alternative to understanding complicated queueing processes. Recently, there have been several studies on some M/G/1 retrial queues with general retrial times, in which the retrial time has a general distribution and only the first customer in the retrial queue is allowed to try to enter the service area. Most of the studies employ the supplementary variable technique to obtain the queue length distributions. In this paper, we present that the arrival time approach is a simple and straightforward alternative to obtain the queue length distribution for M/G/1 retrial queues with general retrial times.
대기행렬을 이용한 위음성률이 있는 코로나 취합검사 시스템의 분석
김길환(Kilhwan Kim) 한국산업경영시스템학회 2021 한국산업경영시스템학회지 Vol.44 No.4
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-neg-ative 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.
유한 및 무한 용량 대기열을 가지는 선점 우선순위 M/G/1 대기행렬
김길환(Kilhwan Kim) 한국산업경영시스템학회 2020 한국산업경영시스템학회지 Vol.43 No.4
Recently, M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers have applied to the analysis of communication systems with two heterogeneous traffics : delay-sensitive traffic and loss-sensitive traffic. However, these studies are limited to M/G/1 priority queues with finite and infinite buffers under a work-conserving priority discipline such as the nonpreemptive or preemptive resume priority discipline. In many situations, if a service is preempted, then the preempted service should be completely repeated when the server is available for it. This study extends the previous studies to M/G/1 priority queues with finite and infinite buffers under the preemptive repeat-different and preemptive repeat-identical priority disciplines. We derive the loss probability of high-priority customers and the waiting time distributions of high- and low-priority customers. In order to do this, we utilize the delay cycle analysis of finite-buffer M/G/1/K queues, which has been recently developed for the analysis of M/G/1 priority queues with finite and infinite buffers, and combine it with the analysis of the service time structure of a low-priority customer for the preemptive-repeat and preemptive-identical priority disciplines. We also present numerical examples to explore the impact of the size of the finite buffer and the arrival rates and service distributions of both classes on the system performance for various preemptive priority disciplines.
엄격한 T‐축출 우선순위 대기행렬을 이용한 기회 주파수 접근 방식의 성능 분석
김길환(Kilhwan Kim) 한국산업경영시스템학회 2012 한국산업경영시스템학회지 Vol.35 No.4
We propose a new priority discipline called the strict T-preemptive priority discipline, and derive the waiting time distributions of each class in the strict T-preemptive priority M/G/1 queue. Using this queueing analysis, we evaluate the performance of an opportunistic spectrum access in cognitive radio networks, where a communication channel is divided into time slots, a licensed primary user is assigned to one channel, and multiple unlicensed secondary users may opportunistically exploit time slots unused by the primary user. We also present a numerical example of the analysis of the opportunistic spectrum access where the arrival rates and service times distributions of each users are identical.
Exact ML Criterion Based on Semidefinite Relaxation for MIMO Systems
Minjoon Kim,Jangyong Park,Kilhwan Kim,Jaeseok Kim IEEE Signal Processing Society 2014 IEEE signal processing letters Vol. No.
<P>In this letter, we propose an exact maximum likelihood (ML) criterion based on semidefinite relaxation (SDR) in multiple-input multiple-output systems. Although a conventional SDR criterion for determining whether a symbol is the ML solution exists, its results cannot be guaranteed when noise is present. In place of the conventional criterion's positive semidefinite (PSD) discriminant, we propose a new, exact ML criterion based on the condition that all diagonal values are positive (PDV), a simple characteristic and necessary condition of PSD. The proposed criterion has a lower calculation complexity for testing than does a PSD and can ensure that the ML solution is always satisfactory.</P>