• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.1-12
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• 1998

We consider G/M/1 queues with multiple vacation disci-pline where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vaca-tion time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

• 대한수학회논문집
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• 제10권2호
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• pp.443-460
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• 1995

We consider a G/M/1 vacation model where the vacation time has k-stages generalized Erlang distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the limiting probabilities of the queue length at arrival time points and arbitrary time points simultaneously. Operational calculus technique is used for solving non-homogeneous difference equations.

• 대한교통학회지
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• 제9권1호
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• pp.47-56
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• 1991

With respect to stochastic delays at linked signals the solid quantitative information has not been available as yet. On the basis of field data the values of "I" (variance-mean ration of flow) were related with the rate of flow. The stochastic delays with specific "I" values were obtained from the distribution of overflow queue, which were calculated by the use of Markov chains. This examination of the results led to the derivation of a simple method for calculating stochastic dclays through the introduction of "I" into Miller's model. The good agreement was shown between the model and the field. The relationships between the cycle lengths and delays were examinated in a large number of conditions with regard to degree of saturation. signal split and link length. Within the practical range of cycle length uniform delays were dominant and no critical point was found in terms of minimum, delay. In highly saturated conditions however the weight of stochastic delay is noticeable.

• 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.

• Industrial Engineering and Management Systems
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• 제12권3호
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• pp.281-287
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• 2013

In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

• 한국정보처리학회논문지
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• 제6권4호
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• pp.1058-1070
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• 1999

이 논문은 이동통신 시스템의 제어국에 순간적으로 가해지는 다량의 입력 메시지에 대하여 효율적이고 신뢰성 있는 제어를 위하여 입력 메시지를 메시지 특성에 따라 분리한 다음 다중 프로세서를 사용하여 제어하는 모델을 제안한다. 제안 모델의 성능 개선에 필요한 요소들의 특성을 사전에 파악하기 위하여 M/M/c/K 큐잉 모델을 이용한다. 이 결과를 토대로 SLAM II를 이용한 시뮬레이션에 의해 입력 메시지에 대한 손실확률, 큐의 평균점유 길이의 분포, 프로세서 관리기(서버)의 점유율, 큐에서의 평균 대기 시간에 대하여 제안 모델과 기존 모델의 성능을 비교한다. 또한 과도한 입력 메시지로 인하여 과부하가 발생할 경우 두 입력 메시지에 대한 부하 제어 기능을 추가한 모델을 제안하고, 시뮬레이션에 의해 성능을 분석한다.

• 한국통신학회논문지
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• 제34권5A호
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• pp.355-362
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• 2009

In real-time communication services, delay constraints are among the most important QoS (Quality of Service) factors. In particular, it is difficult to guarantee the delay requirement over wireless channels, since they exhibit dynamic time-varying behavior and even severe burst-errors during periods of deep fading. Channel throughput may be increased, but at the cost of the additional delays when ARQ (Automatic Repeat Request) schemes are used. For real-time communication services, it is very essential to predict data deliverability. This paper derives the delay distribution and the successful delivery probability within a given delay budget using a priori channel model and a posteriori information from the perspective of queueing theory. The Gilbert-Elliot burst-noise channel is employed as an a Priori channel model, where a two-state Markov-modulated Bernoulli process $(MMBP_2)$ is used. for a posteriori information, the channel parameters, the queue-length and the initial channel state are assumed to be given. The numerical derivation is verified and analyzed via Monte Carlo simulations. This numerical derivation is then applied to a rate control scheme for real-time video transmission, where an optimal encoding rate is determined based on the future channel capacity and the distortion of the reconstructed pictures.

• 전자공학회논문지A
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• 제32A권8호
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• pp.31-38
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• 1995

In this paper, we consider the leaky bucket parameter dimensioning problem in the presence of the cell delay variation(CDV) which arises at the customer premises network dud to the multiplexing with other traffic streams. We consider an ATM multiplexer in which a single CBR stream and several heterogeneous VBR traffic streams are multiplexed. Choosing an MMPP model for the bursty traffic streams, we derive an (MMPP+DD)/D/1/K queueing model for the evaluation of the CDV experienced by the CBR stream. We first evaluate the equilibrium queue length distribution embedded at tagged-cell arrival-time instants, based on whcih we calcuate the inter-cell time distribution and the distribution kof the number of tagged-cell departures in an arbitrary interval. Then we apply the analysis to the dimensionging problem of the leaky bucket parameters, examining how the employed traffic model affects the determination of the bucket size. Through numerical examples, we confirm that the Poisson traffic model can underestimate the bucket size, thus causing a considerable blocking probability for compliant use cells while the MMPP model can optimally design the bucket size which keeps the blocking probability under the target value.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1995년도 추계학술대회발표논문집; 서울대학교, 서울; 30 Sep. 1995
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• pp.113-118
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• 1995

본 연구는 폐쇄형 대기행렬망(CQN:Closed Network of Queue)으로 표시되는 FMS 시스템의 최적 성능을 산정하는 방법과 각 작업장의 작업 부하 (Workload)를 최적화하기 위한 방법에 관한 연구이다. FMS 생산 시스템의 성능 (Performance)을 기존의 생산률(Production Rate)외에 기대생산률 (Expected Production Rate), 평균 대기작업량(Mean Queueue Length), 및 기대 투자이용률(Expected Investment Utilization Rate)과 이들 각각의 분산 (Variance)들을 고려하였다. 이러한 성과측정 문제를 수리 모델링하고 이를 이용하여 각 작업장에서의 가공 장비의 그룹(Machine Group)별 최적 작업배 분(Workload) 조건을 보였다. 또한 위의 과정을 최근의 FMS 전용 Simulator인 FACTOR/AIM을 이용한 분석 결과와 비교하여 보였다.

• Journal of Communications and Networks
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• 제7권4호
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• pp.408-416
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• 2005

Quality of service (QoS) provision is an important and indispensable function for multi-service wireless networks. In this paper, we present a new scheduling/admission control frame­work, including an efficient rate-guaranteed opportunistic scheduling (ROS) scheme and a coordinated admission control (ROS­CAC) policy to support statistic QoS guarantee in multi-service wireless networks. Based on our proposed mathematical model, we derive the probability distribution function (PDF) of queue length under ROS and deduce the packet loss rate (PLR) for individual flows. The new admission control policy makes admission decision for a new incoming flow to ensure that the PLR requirements of all flows (including the new flow) are satisfied. The numerical results based on ns-2 simulations demonstrate the effectiveness of the new joint packet scheduling/admission control framework.