• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.147-154
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• 2013

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

• 한국경영과학회지
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• 제30권2호
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• pp.131-142
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• 2005

This paper proposes queueing models for a Web server system which is composed of an infinite-buffer main server and finite-buffer auxiliary server(s). The system is modeled by the level-dependent quasi-birth- death (QBD) process. Utilizing the special structure of the QBD, we convert the infinite level-dependent QBD into a finite level-independent QBD and compute the state probabilities. We then explore the operational characteristics of the proposed web-server models and draw some useful conclusions.

• Communications for Statistical Applications and Methods
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• 제4권2호
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• pp.497-505
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• 1997

We attempt to get a probabilistic model of a queueing system in the maximum entropy condition. Applying the maximum entropy principle to the queueing system, we obtain the most uncertain probability model compatible with the available information expressed by moments.

• 한국경영과학회지
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• 제19권3호
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• pp.93-109
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• 1994

Even though sojourn time distributions are essential information in analyzing queueing networks, there are few methods to compute them accurately in non-product form queueing networks. In this study, we model the location process of a typical customer as a GMPH semi-Markov chain and develop computationally useful formula for the transition function and the first-passage time distribution in the GMPH semi-Markov chain. We use the formula to develop an effcient method for approximating sojourn time distributions in the non-product form queueing networks under quite general situation. We demonstrate its validity through numerical examples.

• East Asian mathematical journal
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• 제31권5호
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• pp.707-716
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• 2015

We consider a queueing system with N-limited nonstop forwarding. In this queueing system, when the server breaks down, up to N customers can be serviced during the repair time. It can be used to model an assembly line consisting of several automatic stations and a manual backup station. Within the framework of $Geo^X/D/1$ queue, the matrix analytic approach is used to obtain the performance of the system. Some numerical examples are provided.

• International Journal of Internet, Broadcasting and Communication
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• 제15권3호
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• pp.43-51
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• 2023

Slotted ALOHA (S-ALOHA) is a classical medium access control protocol widely used in multiple access communication networks, supporting distributed random access without the need for a central controller. Although stability and delay have been extensively studied in existing works, most of these studies have assumed ideal channel conditions or independent fading, and the impact of time-correlated wireless channels has been less addressed. In this paper, we investigate the queueing delay performance in S-ALOHA networks under time-correlated channel conditions by utilizing a Gilbert-Elliott model. Through simulation studies, we demonstrate how temporal correlation in the wireless channel affects the queueing delay performance. We find that stronger temporal correlation leads to increased variability in queue length, a larger probability of having queue overflows, and higher congestion levels in the S-ALOHA network. Consequently, there is an increase in the average queueing delay, even under a light traffic load. With these findings, we provide valuable insights into the queueing delay performance of S-ALOHA networks, supplementing the existing understanding of delay in S-ALOHA networks.

• 경영과학
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• 제28권1호
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• pp.117-127
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• 2011

In the Multi-Echelon maintenance environment, METRIC(Multi-Echelon Technique for Repairable Item Control) has been used in several different inventory level selection models, such as MOD-METRIC, Vari-METRIC, and Dyna- ETRIC. While this model's logic is easy to be implemented, a critical assumption of infinite maintenance capacity would deteriorate actual values, especially Expected Back Order(EBO)s for each item. To improve the accuracy of EBO, we develop two models using simulation and queueing theory that calculates EBO considering finite capacity. The result of our numerical example shows that the expected backorder from our model is much closer to the true value than the one from Vari-METRIC. The queueing model is preferable to the simulation model regarding the computational time.

• 한국건설관리학회논문집
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• 제23권6호
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• pp.3-14
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• 2022

현장에서 발생하는 정량적인 공사 인원과 기간의 분석은 새로운 적정 인원의 기준을 제시할 수 있다. 본 연구는 업무효율 지표들 중 가장 중요한 요소인 업무절차의 수행시간을 예측하는 대기행렬 모형을 제시한다. 아파트 골조공사 작업 사이클은 같은 공정이 반복되는 특성을 가진다. 본 연구는 이러한 특성을 바탕으로 지연된 골조공사 기준층 사이클을 대기행렬 모형을 활용하고 그것을 분석하였다. 그리고 인원수와 공사 기간을 조정한 후 모형의 성능을 분석하였다. 본 연구는 대기행렬의 성능 분석을 실시하여 공정의 물량에 따른 인적자원관리 의사결정을 지원하고자 한다.

• 한국경영과학회지
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• 제36권3호
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• pp.45-59
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• 2011

OFDMA systems have been expected to be widely used to provide multimedia services over wireless channels. To evaluate performance of the OFDMA system, power should be considered as system resource as well as subcarriers. This study propose a queueing traffic model incorporating two kinds of resources (power and subcarriers), and an extended model giving a priority to handoff calls over new calls. Some extensive experiments are conducted to illustrate the usefulness of the proposed traffic model.

• 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.