• Journal of Korean Institute of Industrial Engineers
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• v.22 no.1
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• pp.95-104
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• 1996

We consider a two-phase queueing system with generalized vacation. Poisson arrivals receive a batch type service in the first phase and individual services in the second phase. The server takes generalized vacation when the system becomes empty. Generalized vacation includes single vacation, multiple vacation, and other types. We consider both gated batch service and exhaustive batch service. This is an extension of the model presented by Selvam and Sivasankaran [6].

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.107-116
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• 2009

We consider a single server multi-class queueing model with Poisson arrivals and relative priorities. For this queue, we derive a system of equations for the transform of the queue length distribution. Using this system of equations we find the moments of the queue length distribution as a solution of linear equations.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.881-892
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• 1999

In this paper we consider a polling system with two classes of stations; high priority and low priority. High priority stations are polled more frequently than low priority stations. We derive an exact and explicit formula for computing the mean waiting times for a message when the arrival processes are batch Poisson. In general the formula requires to solve two sets of simultaneous equations By specializing them to the case of two priority classes we greatly reduce the number equations and provide a simple formula for mean waiting times. We apply the results to a data communication processing system and show that the overall mean waiting time can be reduced by using priority polling.

• Journal of the Korean Institute of Navigation
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• v.7 no.1
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• pp.1-32
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• 1983

The delay due to congestion has recently attracted widespread attention with the analysis of over-all operation at the port. But, the complexity of the situation is evident in view of the large number of factors which impinge on the considerable end. Queueing theory is applicable to a large scale transportation system which is associated with arrivals of vessels in a large port. The attempt of this paper is to make an extensive analysis of the port transport system and its economic implications from the viewpoint that port is one of the physical distribution facilities and a kind of queueing system which includes ships and cargoes as port customer. By analyzing the real data on the Port of Pusan, it is known that this port can be represented as a set of multi-channel with identical setof Poisson arrival and Erlang service time, and also it is confirmed that the following formula is suitable to calculate the mean delay in this port, namely, $W_4={\frac{\rho}{\lambda(1-\rho)} {\frac{e_N(\rho{\cdot}N)}{D_{N-1}(\rho{\cdot}N)}$ where, ${\lambda}$: mean arrival rate $\mu$: mean servicing rate; N: number of servicing channel; ${\rho}$: utillization rate (${\lambda}/N{\mu}$) $e_N$: the Poisson function Coming to grips with the essentials of the cost of delay due to congestion, a simple ship journey cost model is adopted and the operating profit sensitivity to variation in port time is examined, and for purpose of a future development for port princing service the marginal cost is approximately calculated on the basis of queueing theory.

• Industrial Engineering and Management Systems
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• v.8 no.4
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• pp.221-227
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• 2009

There are customer services jointly provided by two facilities so that each customer will complete the course made up of both facilities' sub-services. The two facilities are assumed invested respectively by an infrastructure owner and one subordinate facility owner, whose partnership is built on their capital investments. This paper presents a mathematical model of Stackelberg competition between the two facility owners to derive their optimal Nash equilibrium. In this study, each facility owner's profit is consisted of fixed revenue fractions of sold services, operating costs (including depreciation cost) and maintenance costs of her facility. The maintenance costs of one facility are incurred both by failures and deterioration due to usage. Moreover, for both facilities, failures are rectified immediately by minimal repairs and preventive maintenance is carried out at a fixed time epoch. Additional assumptions are also employed to develop the model such as customer arrivals are manipulated to follow a Poisson process, and each facility's lifetime is independently Weibull-distributed. The Stackelberg game proceeds as follows. At the first stage of decision making process, the infrastructure owner (acting as a leader) decides the allocation of revenue shares based on her self-interest. After observing the allocation of revenue shares, the subordinate facility owner determines her own optimal price of services. This paper investigates actions and reactions of the two partners in the system. Then analytical conditions are proposed to achieve a unique optimal Nash equilibrium. Finally, some suggestions for further research are discussed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.3
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• pp.61-68
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• 1983

In this paper various aspects of statistical maltiplexing of data signs have been investigated. A queueing model with finite waiting room and batch poisson arrivals is studied assuming that data signals are transmitted at a constant rate. Using traffic intensity and average burst length as parameters, overflow probabilities and expected queueing delay due to buffering are obtained. Also, a real system model of a statistical multiplexer that can be directly used in micro-programmed hardware realization is proposed. To examine the performance of the system, computer simulation has been done at various conditions. The results obtained can be used in designing a buffer efficiently.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.2A
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• pp.26-33
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• 2005

Exact prediction of resource demands for future calls enhances the efficiency of the limited resource utilization in resource reservation methods for potential calls in wireless IP networks. In this paper, we propose a LMS-Wiener resource(bandwidth) prediction for future handoff calls, and then an the proposed method is compared with an existing Wiener-based method in terms of prediction error through our simulations. In our simulations, we assume that handoff call arrivals follow a non-Poisson process and each handoff call has an non-exponentially distributed channel holdingtime in the cell, considering that handoff call arrival pattern is not Poisson distribution but non-Poisson for long periods of time in wireless picocellular IP networks. Simulation results show that the prediction error in the proposed method converges to the lower value while in an existing method increase as time is passed. Therefore we may conclude that the proposed method improves the efficiency of resource utilization by more exactly predicting resource demands for future handoff calls than an existing method.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.5
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• pp.52-59
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• 1996

The boroadband ISDN will transprot the traffics for a wide range of applications with different quality-of-service (QOS) requirements and the priorit control mechanism is an effective method to support multiple classes of services. This paper proposes a new mechanism to satisfy simultaneously the different levels of cell loss performance for the two classes of heterogeneous nonreal-time ATM traffics as well as the delay and loss requirements of real-time traffics. Its performance is analyzed using the stochastic integral approach with the cell arrivals of input streams modeled as markov modulated poisson processes.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.2
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• pp.31-39
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• 1999

A new approximation method for finding the steady-state probabilities of the number of customers present in queueing systems with Poisson arrivals and two servers with different deterministic service times with infinite waiting room capacity is developed. The major assumption made for the approximation is that the residual service times of the servers have mutually independent uniform distributions with densities equal to the reciprocals of the respective service times. The method reflects the heterogeneity of the servers only through the ratio of their service times, irrespective of the actual magnitudes and difference. The transition probability matrix is established and the steady-state probabilities are found for a variety of traffic intensities and ratios of the two service times; also the mean number of customers present in the system and in the queue, and server utilizations are found and tabulated. The method was validated by simulation and turned out to be very sharp.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.481-493
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• 1996

We consider a retrial queue with two classes of customers where arrivals of class 1(resp. class 2) customers are MMPP and Poisson process, respectively. In the case taht arriving customers are blocked due to the channel being busy, the class 1 customers are queued in priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrial group in order to try service again after a random amount of time. We consider the following retrial rate control policy, which reduces their retrial rate as more customers join the retrial group; their retrial times are inversely proportional to the number of customers in the retrial group. We find the joint generating function of the numbers of custormers in the two groups by the supplementary variable method.