• Journal of Korean Institute of Industrial Engineers
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• v.20 no.3
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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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• v.24 no.1
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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.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.2 no.2 s.3
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• pp.13-22
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• 2003

It is recognized that one of the problems for the current 'Traffic Adaptive Control System in Seoul' is the performance at the oversaturated condition. Instead of 'Degree of Saturation' adopted in the current system, the methodology of balancing the queue length was developed and evaluated in this study. This method keeps the balance of queue lengths on the intersections and reduces the overall queue lengths. In addition a traffic signal control model was developed based on the method. This model can reduce not only the queue lengths but also the average delay of vehicles according to the macroscopic and microscopic evaluations.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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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.

• The Korean Journal of Applied Statistics
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• v.22 no.3
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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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• v.9 no.1
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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.

• Journal of Korean Society of Transportation
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• v.18 no.2
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• pp.73-89
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• 2000

This Paper documents the development of a cycle free based, coordinated dynamic signal timing model for minimizing queue lengths using Genetic A1gorithm. The model was embodied using MAT-LAB, the language of technical computing. A special feature of this model is its ability to manage queue lengths of turning movements at the start of green times. The model produces a cycle-free based signal timing(cycles and green times) for each intersection to minimize queue lengths of turning movements on the cycle basis. Concurrently, appropriate offsets could be accomplished by applying cycle-free based signal timings for respective intersections. The model was applied to an example network which consists of three intersections. The result shows that the model produces superior signal timings to the existing signal timing model in terms of managing queue lengths of turning movements.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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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.

• Proceedings of the KOR-KST Conference
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• 1999.10a
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• pp.235-240
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• 1999

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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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.