• 대한산업공학회지
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• 제20권3호
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• pp.139-149
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• 1994

For general open queueing network models, the relationship between weak limits of queue lengths and waiting times at stations is investigated under heavy traffic situations. It is shown that under suitable normalization, weak convergence of queue lengths and arrival processes is a sufficient condition for that of waiting times, and is also necessary condition when the network is of feedforward type. Moreover, these weak limits for queue lengths and waiting times are shown to be simply related.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.19-29
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• 1995

In this paper, we investigate the asymptotic distributions of maximum queue length for M/G/1 and GI/M/1 systems which are positive recurrent. It is well knwon that for any positive recurrent queueing systems, the distributions of their maxima linearly normalized do not have non-degenerate limits. We show, however, that by concerning an array of queueing processes limiting behaviors of these maximum queue lengths can be established under certain conditions.

• 한국ITS학회 논문지
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• 제2권2호
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• pp.13-22
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• 2003

기존의 신신호 시스템에서 문제점으로 지적되고 있는 과포화 상태에서의 신호제어전략을 개선할 수 있는 방안으로서, 기존의 포화도를 기준으로 한 방식이 아닌 대기행렬의 길이를 균형화 하는 방식을 개발하였다. 이 방식은 대기행렬의 길이를 각 방향별로 동일하게 유지하면서 전체적인 대기행렬의 길이를 감소시킬 수 있는 것으로 나타났다. 또한 이 방식을 신호주기 산출 및 현시분할에도 적용하는 방법을 개발하였다. 이 방식은 기존의 방식과 비교하여 거시적으로는 대기행렬의 길이를 감소시킴과 동시에 미시적으로는 차량의 평균지체를 감소시키는 효과를 나타내었다.

• 대한수학회보
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• 제46권4호
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• pp.673-689
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• 2009

We analyze $MAP_1,\;MAP_2$/G/1 finite queues with service scheduling function dependent upon queue lengths. The customers are classified into two types. The arrivals of customers are assumed to be the Markovian Arrival Processes (MAPs). The service order of customers in each buffer is determined by a service scheduling function dependent upon queue lengths. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, the performance measures such as loss probability and mean waiting time are derived. Some numerical examples also are given with applications in telecommunication networks.

• 응용통계연구
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• 제22권3호
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• pp.541-551
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• 2009

Generalized processor sharing(GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. In a queueing system with single-class traffic, the stationary queue length becomes larger stochastically when the bandwidth (i.e. the service rate) of the system decreases. For a given GPS server, we consider the similar problem to this. We define the monotonicity for the head of the line processor sharing(HLPS) servers in which the units in the heads of the queues are served simultaneously and the bandwidth allocated to each queue are determined by the numbers of units in the queues. GPS is a type of monotonic HLPS. We obtain the HLPS server whose queue length of a class stochastically bounds upper that of corresponding class in the given monotonic HLPS server for all classes. The queue lengths process of all classes in the obtained HLPS server has the stationary distribution of product form. When the given monotonic HLPS server is GPS server, we obtain the explicit form of the stationary queue lengths distribution of the bounding HLPS server. Numerical result shows how tight the stochastic bound is.

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

• 대한교통학회지
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• 제18권2호
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• pp.73-89
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• 2000

본 연구에서는 평균차량통행량 대신 매주기마다 입력되는 대기차량, 차량도착율을 기초로 대기차량을 최소화하는 동적신호시간 결정모형을 개발하였다. 본 모형은 각 진입로에서의 대기차량예측모델을 기초로 하여 다음 주기에서의 대기차량을 예측한 후 유전자 알고리즘을 적용하여 신호시간을 산출하였다. 본 모형에서 산출된 신호주기와 녹색시간은 대기차량길이를 최소화하는 신호시간으로서 교차로간의 연동효과를 고려하여 실시간 교통 상황에 따라 주기별로 변화한다. 본 모형은 3개의 교차로로 구성되어 있는 간선도로를 대상으로 적용하였다. 이 모형은 MATLAB으로 구현하였으며, 동일한 조건 하에서 정주기식으로 신호시간을 주었을 때의 통과차량, 주기, 현시, 대기차량 등을 구하여 본 모형의 결과와 비교 및 평가를 실시하였다. 실험결과 포화상태나 포화상태의 경우 모두 정주기식보다는 동적으로 신호를 계산하는 본 모형이 더 좋은 결과를 나타내었다. 또한. 적합도 함수를 변형하여 Inbound, Balanced, Outbound 연동상황을 설정하여 수행한 경우 주방향의 대기차량이 상대적으로 다른 방향에 비해 감소하였으며, 주방향에 대한 연동효과를 나타내었다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.469-481
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• 2004

In this paper, we investigate the mean queue length and the mean packet delay of a dynamic bandwidth allocation(DBA) scheme in an Ethernet passive optical network(EPON). We focus on the interleaved polling system with a gated service discipline. We assume that input packets arrive at an optical network unit(ONU) according to Poisson process. We use a continuous time queueing model in order to find the queue length distribution of the gated interleaved polling system with the first stage input queue and the second stage transmission queue. We give some numerical results to investigate the mean queue lengths and mean packet delays for the symmetric polling system with statistically identical stations.

• 대한교통학회:학술대회논문집
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• 대한교통학회 1999년도 제36회 학술발표회논문집
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• pp.235-240
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• 1999

• 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.