• Journal of applied mathematics & informatics
• /
• 제38권3_4호
• /
• pp.351-373
• /
• 2020

There is an extensive literature on retrial queueing models. While a majority of the literature on retrial queueing models focuses on the retrial times to be exponentially distributed (so as to keep the state space to be of a reasonable size), a few papers deal with nonexponential retrial times but with some additional restrictions such as constant retrial rate, only the customer at the head of the retrial queue will attempt to capture a free server, 2-state phase type distribution, and finite retrial orbit. Generally, the retrial queueing models are analyzed as level-dependent queues and hence one has to use some type of a truncation method in performing the analysis of the model. In this paper we study a retrial queueing model with threshold-type policy for orbiting customers in the context of nonexponential retrial times. Using matrix-analytic methods we analyze the model and compare with the classical retrial queueing model through a few illustrative numerical examples. We also compare numerically our threshold retrial queueing model with a previously published retrial queueing model that uses a truncation method.

• Journal of Communications and Networks
• /
• 제6권1호
• /
• pp.78-87
• /
• 2004

This paper presents deterministic, worst-case analysis of a queueing system whose multiple homogeneous input streams are regulated by the associated leaky buckets and the queueing system that has a single stream regulated by the jumping-window. Queueing delay averaged over all items is used for performance measure, and the worst-case input traffic and the worst-case performance are identified for both queueing systems. For the former queueing system, the analysis explores different phase relations among leaky-bucket token generations. This paper observes how the phase differences among the leaky buckets affect the worst-case queueing performance. Then, this paper relates the worst-case performance of the former queueing system with that of the latter (the single stream case, as in the aggregate streams from many users, whose item arrivals are regulated by one jumping-window). It is shown that the worst-case performance of the latter is identical to that of the former in which all leaky buckets have the same phase and have particular leaky bucket parameters.

• 한국경영과학회지
• /
• 제24권4호
• /
• pp.111-122
• /
• 1999

In this paper, we consider a queueing network model. where the population constraint within each subnetwork is controlled by a semaphore queue. The total number of customers that may be present in the subnetwork can not exceed a given value. Each node has a constant service time and the arrival process to the queueing network is an arbitrary distribution. A major characteristics of this model is that the lower layer flow is halted by the state of higher layer. We present some properties that the inter-change of nodes does not make any difference to customer's waiting time in the queueing network under a certain condition. The queueing network can be transformed into a simplified queueing network. A dramatic simplification of the queueing network is shown. It is interesting to see how the simplification developed for sliding window flow control, can be applied to multi-layered queueing network.

• 한국통신학회논문지
• /
• 제27권9C호
• /
• pp.836-841
• /
• 2002

패킷에 대한 스케줄링(Scheduling)은 현재 Best-effort 방식으로 운용되는 인터넷에서 서비스를 차별화하여 전송 품질보장(QoS: Quality of Service)을 제공하기 위해 필수적인 기능이다. 지금까지 제안된 많은 스케줄링 알고리즘들은 간단한 구현에 의한 고속의 처리를 장점으로 하는 Round-Robin 방식과 정확한 서비스를 장점으로 하는 Fair Queueing 방식으로 나눌수 있다. 특히, 기존의 Fair Queueing 알고리즘들은 모든 플로우(Flow)에 대한 상태를 스케줄러가 관리하기 때문에 계산량 및 구현상의 복잡성에 따른 문제를 안고 있다. 본 논문에서는 패킷의 서비스 순서 결정을 위한 계산을 각 플로우가 분산처리 하는 방식을 제안하여 스케줄러의 계산량을 대폭 줄이는 동시에 기존 Fair Queueing 알고리즘 수준의 정확성을 제공한다. 또한, 제안된 방식은 입력 큐에서의 스케줄링이 필요한 대형 라우터의 설계에 응용될 수 있다.

• Industrial Engineering and Management Systems
• /
• 제7권2호
• /
• pp.143-149
• /
• 2008

There have been some approximation analysis methods for a GI/G/1 queueing system. As one of them, an approximation technique for the steady-state probability in the GI/G/1 queueing system based on the iteration numerical calculation has been proposed. As another one, an approximation formula of the average queue length in the GI/G/1 queueing system by using the diffusion approximation or the heuristics extended diffusion approximation has been developed. In this article, an approximation technique in order to analyze the GI/G/1 queueing system is considered and then the formulae of both the steady-state probability and the average queue length in the GI/G/1 queueing system are proposed. Through some numerical examples by the proposed technique, the existing approximation methods, and the Monte Carlo simulation, the effectiveness of the proposed approximation technique is verified.

• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.349-357
• /
• 2002

In this paper, we analyze queueing behaviors and investigate the possibilities of reducing and controlling shortages and oversupplies in the bidirectional queueing system which forms a negative queue by demand and a positive queue by supply. Interarrival times of units in the bidirectional queueing system investigated are exponetially distributed. Instant pairing off implies that queue can be either positive or negative, but not both at the same time. The results include a proof that sum of queue lengths is minimized if rates of demand and supply in each system are equal and optimum solutions for rates of supply which minimize the sum of queue lengths when rates of demand and sum of rates of supply are given. In addition, the relationship between the ordinary queueing system and the bidirectional queueing system is investigated.

• 한국통신학회논문지
• /
• 제41권10호
• /
• pp.1240-1243
• /
• 2016

In this paper, we analyze the queueing performance of cumulative distribution function (CDF)-based opportunistic scheduling over Nakagami-m Markov fading channels. We derive the formula for the average queueing delay and the queue length distribution by constructing a two-dimensional Markov chain. Using our formula, we investigate the queueing performance for various fading parameters.

• 한국시뮬레이션학회논문지
• /
• 제17권2호
• /
• pp.75-82
• /
• 2008

기존의 대기행렬시스템 추론에 관한 연구들은 서비스시작시점과 서비스종료시점을 이용하여 수행되었다. 그러나 서비스시작시점은 시스템 내부 관측치로서 실제로 관측하기 어려울 때가 많다. 본 논문에서는 서비스시작시점 대신 외부 관측치인 도착시점을 이용하여 대기행렬시스템을 추론한다. 도착 및 이탈시점에 근거한 대기행렬 모형의 분석은 서비스시작시점의 결정이 관건이다. 본 연구의 선행연구로서 선입선출 및 후입선출 시스템에 대한 서비스시작시점의 결정방법은 이미 개발되었다. 본 논문에서는 임의순서규칙 대기행렬시스템으로 추론 범위를 확장한다. 구하고자 하는 성능척도는 평균대기시간과 평균서비스시간이며 이들의 분산을 구함으로써 통계적 분석기법의 사용이 가능하도록 하였다. 마지막으로 시뮬레이션 결과로부터 얻은 데이터를 이용하여 본 연구의 추론방법을 적용함으로써 그 타당성을 검증하였다.

• 한국경영과학회지
• /
• 제34권4호
• /
• pp.113-121
• /
• 2009

In this paper, we consider the departure process from the open and nested tandem Queueing network with population constraint and constant service times. It is known that the Queueing network can be transformed into a simple Queueing network which can be easy to analyze. Using this simple Queueing network, upper and lower bounds on the interdeparture time are obtained. We prove that the variance of the interdeparture time is bounded within these two bounds. Validation against simulation data is shown that how it works the variance of the interdeparture time within two bounds. These bounds can be applied to obtain the better variance of the interdeparture time using a suitable method.

• 한국정보통신학회논문지
• /
• 제7권5호
• /
• pp.916-924
• /
• 2003

공정큐잉은 자원이 노드들 간에 공유되는 유선 및 무선 멀티미디어망에서 주요한 주제중의 하나이다. 대부분의 공정큐잉 알고리즘은 GPS 알고리즘에 근거하고 있으며 공정성을 강조하는 반면 망에서 멀티미디어를 서비스를 지원하기 위해서는 필수적인 제한된 지연시간 보장 측면은 간과하고 있다. 이 논문에서는 새로운 공정큐잉 방안인 지연 보장 공정큐잉 (DGFQ, Delay Guaranteed Fair Queueing)을 제안한다. 이 방식은 무선 패킷망에서 멀티미디어 서비스를 제공하기 위하여 각 flow 별 지연시간 요구에 맞추어 제한된 지연시간을 보장한다.