• Journal of the Korean Statistical Society
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• 제34권1호
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• pp.39-47
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• 2005

We adopt the P/sub λ, T//sup M/ policy of dam to introduce a service policy with alternating service rates for a Poisson arrival queue, in which the service rate alternates depending on the number of customers in the system. The stationary distribution of the number of customers in the system is derived and, after operating costs being assigned to the system, the optimization of the policy is studied.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.355-363
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• 1997

In queueing theory, polling systems have been widely studied as a way of serving several stations in cyclic order. In this paper we consider Markov-modulated Poisson process which is useful for approximating a superposition of heterogeneous arrivals. We derive the mean waiting time of each station in a polling system where the arrival process is modeled by a Markov-modulated Poisson process.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.469-474
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• 2011

In a M/G/I queue where the server alternates between busy and idle periods, we assume that firstly customers arrive at the system according to a Poisson process and the arrival process and customer service times are mutually independent, secondly the system has infinite waiting room, thirdly the server utilization is less than 1 and the system has reached a steady state. With these assumptions, we analyze waiting times on the systems where some vacation policies are considered.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.125-133
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• 1999

We consider a FIFO single-server queueing model in which both the arrival and service processes are modulated by the amount of work in the system. The arrival process is a non-homogeneous Poisson process(NHPP) modulated by work, that is, with an intensity that depends on the work in the system. Each customer brings a job consisting of an exponentially distributed amount of work to be processed. The server processes the work at various service rates which also depend on the work in the system. Under the stability conditions obtained by Browne and Sigman(1992) we derive the exact stationary distribution of the work W(t) and the first exit probability that the work level b is exceeded before the work level a is reached, starting from x$\in$[a, b].

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.455-464
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• 2005

In this paper, we analyze a queueing system with overload control by arrival rates. This paper is motivated by overload control to prevent congestion in telecommunication networks. The arrivals occur dependent upon queue length. In other words, if the queue length increases, the arrivals may be reduced. By considering the burstiness of traffics in telecommunication networks, we assume the arrival to be a Markov-modulated Poisson process. The analysis by the embedded Markov chain method gives to us the performance measures such as loss and delay. The effect of performance measures on system parameters also is given throughout the numerical examples.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.879-890
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• 2002

In this paper we consider open queueing system with a Poisson arrival process which have a finite upper bound on the arrival rate for which the system is stable. Interpolation approximations for quantities of interest, such as moments of the sojourn time distribution, have previously been developed for such systems, utilizing exact light and heavy traffic limits. These limits cannot always be easily computed for complex systems. Thus we consider an interpolation approximation where all of the relevant information is estimated via simulation. We show that all the relevant information can in fact be simultaneously estimated in a single regenerative simulation at any arrival rate. In addition to light and heavy traffic limits, both the quantity of interest and its derivative (with respect to the arrival rate) are estimated at the arrival rate of the simulation. All of the estimates are then combined, using a least squares procedure, to provide an interpolation approximation.

• 경영과학
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• 제32권2호
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• pp.69-78
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• 2015

This paper considers a Bayesian Poisson model for multivariate count data using multiplicative rates. More specifically we compose the parameter for overall arrival rates by the product of two parameters, a common effect and an individual effect. The common effect is composed of autoregressive evolution of the parameter, which allows for analysis on seasonal effects on all multivariate time series. In addition, analysis on individual effects allows the researcher to differentiate the time series by whatevercharacterization of their choice. This type of model allows the researcher to specifically analyze two different forms of effects separately and produce a more robust result. We illustrate a simple MCMC generation combined with a Gibbs sampler step in estimating the posterior joint distribution of all parameters in the model. On the whole, the model presented in this study is an intuitive model which may handle complicated problems, and we highlight the properties and possible applications of the model with an example, analyzing real time series data involving customer arrivals to a large retail store.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.601-616
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• 2021

Retrial queueing models have been studied extensively in the literature. These have many practical applications, especially in service sectors. However, retrial queueing models have their own limitations. Typically, analyzing such models involve level-dependent quasi-birth-and-death processes, and hence some form of a truncation or an approximate method or simulation approach is needed to study in steady-state. Secondly, in general, the customers are not served on a first-come-first-served basis. The latter is the case when a new arrival may find a free server while prior arrivals are waiting in the retrial orbit due to the servers being busy during their arrivals. In this paper, we take a different approach to the study of multi-server retrial queues in which the signals are generated in such a way to provide a reasonably fair treatment to all the customers seeking service. Further, this approach makes the study to be level-independent quasi-birth-and-death process. This approach is different from any considered in the literature. Using matrix-analytic methods we analyze MAP/M/c-type retrial queueing models along with Poisson signals in steady-state. Illustrative numerical examples including a comparison with previously published retrial queues are presented and they show marked improvements in providing a quality of service to the customers.

• 한국정보과학회논문지:정보통신
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• 제30권3호
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• pp.416-423
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• 2003

본 논문에서는 버퍼를 공유하는 패킷 교환기의 연속 시간 큐잉 모델을 제시하고 큐 길이 확률 분포를 구하는 근사 계산 알고리즘을 제안한다. N 개의 입력 프로세스는 상호 이질적인 버스트 특성을 갖는다. 입력 프로세스는 계차-2 콕시안 분포로서 모형화하며 서버의 서비스 시간은 계차-r 얼랑 분포로서 모형화한다. 근사 알고리즘은 통합된 상태 변수를 사용하여 큐잉 시스템을 표현한다. 먼저 N개의 입력프로세스는 하나의 통합된 상태 변수로 나타내며 큐잉 시스템은 서브 시스템으로 분해하고 이것을 통합된 상태 변수로 나타낸다. 그리고 이러한 통합된 상태 변수를 사용하여 반복적인 방법에 의해서 상태 방정식의 해를 유도한다. 근사 알고리즘의 타당성은 시뮬레이션을 통해서 검증한다.

• 한국정보통신설비학회:학술대회논문집
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• 한국정보통신설비학회 2005년도 하계학술대회
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• pp.109-112
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• 2005

In this thesis, we recommend the method for VOD service traffic modeling. By the analysis of service traffic, we verify that the process of VOD service is the POISSON process. So it is important to determine the probability of the user's existence in the system. But, because it is difficult to measure, we recommend proper using of arrival rate and service rate.