• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 한국산업경영시스템학회 2002년도 춘계학술대회
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• pp.133-138
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• 2002

In this paper, we model a two-server queueing system with priority, to which we put a restriction of the number of servers for each customer class. A group of customers is divided into two different classes. The class 1 customers has non -preemptive priority over class 2 customers. We use the method of PGF depending on the state of server We find the PGF of the number of customers in queue, server utilization, mean queue length and mean waiting time for each class of customers.

• Proceedings of the Korean Statistical Society Conference
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• 한국통계학회 2004년도 학술발표논문집
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• pp.295-300
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• 2004

We consider a G/M/1 queue with two-stage service policy. The server starts to serve with rate of ${\mu}1$ customers per unit time until the number of customers in the system reaches A. At this moment, the service rate is changed to that of ${\mu}2$ customers per unit time and this rate continues until the system is empty. We obtain the stationary distribution of the number of customers in the system.

• Journal of Korean Institute of Industrial Engineers
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• 제32권2호
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• pp.120-125
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• 2006

Since Korean government has implemented the "Number Portability System" in the domestic mobile communications market, mobile communication companies have been striving to hold onto existing customers and at the same time to attract new customers. This paper presents a competing risk model that considers the characteristics of a customer in order to predict the customer's life under the "Number Portability System." Three competing risks considered are pricing policy, quality of communication, and usefulness of service. It was observed that the customers who pay more are less sensitive on pricing policy younger people are less sensitive than older people to the quality of communication and women are more sensitive than men to the degree of usefulness of service. We expect that the result of this study can be used as a guideline for effective management of mobile phone customers under the Number Portability System.

• Journal of Korean Society of Industrial and Systems Engineering
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• 제25권5호
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• pp.31-38
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• 2002

In this paper, we model a two-server queueing system with priority, to which we put a restriction on the number of servers for each customer class. customers are divided into two different classes. Class 1 customers have non-preemptive priority over class 2 customers. They are served by both servers when available but class 2 customers are served only by a designated server. We use a method of generating function depending on the state of servers. We find the generating function of the number of customers in queue, server utilization, mean queue length and mean waiting time for each class of customers.

• Journal of Korean Institute of Industrial Engineers
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• 제25권1호
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• pp.130-140
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• 1999

This paper deals with a priority queueing model in an ATM system. Two types of customers are considered. Type-1 customers have push-put priority over type-2 customers. Type-1 customers can enter the service only when the number of type-2 customers is less than a threshold T. We derive the joint probability of the number of customers in the buffer, the mean waiting time, and the loss probabilities of each type. We also propose an optimal control policy that satisfies a given quality of service.

• Journal of Korean Institute of Industrial Engineers
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• 제7권1호
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• pp.5-11
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• 1981

In the case of numerical implementation, the exact solution method for the M/M/s system where customers demand multiple server use [2] reveals limitations, if a system has large number of servers or types of customers. This is due to the huge matrices involved in the course of the calculations. This paper offers an approximation scheme for such cases. Capitalizing the characteristics of the service rate curve of the system, this method approximates the service rate as a piecewise linear function. With the service rates obtained from the linear function for each number of customers n (n=0. 1. 2,$\cdots$), ${\mu}(n)$, steady-state probabilities and measures of performance are found treating this system as an ordinary M/M/s system. This scheme performs well when the traffic intensity of a system is below about 0.8. Some numerical examples are presented.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.287-299
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• 2007

We consider a multiclass queue where queued customers are served in their order of arrival at a rate which depends on the customer type. By using the asymptotic results obtained by Dabrowski et al. (2006) we calculate the sharp asymptotics of the stationary distribution of the number of customers of each class in the system and the distribution of the number of customers of each class when the total number of customers reaches a high level before emptying. We also obtain a fast simulation algorithm to estimate the overflow probability and compare it with the general simulation and asymptotic results.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.217-228
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• 2009

In this paper, we consider a multi-class queueing system in which different classes of customers have different arrival rates, service rates and class-transition probabilities. We use the fast simulation method to estimate the overflow probability and the expected number of customers of each class at the first time the total number of customers hits a high level. We also discuss the overflow probabilities and the expected number of customers at different loads, respectively.

• Journal of the Korean Operations Research and Management Science Society
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• 제22권4호
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• pp.167-172
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• 1997

We present a procedure which finds the probability distribution of number of customers accumulated when the server ends a vacation in the Geo/G/1 gated queueing system, where the service for a customer and the vacation, respectively, takes one slot time. The pp. g. f. for the number of customers accumulated at the gate closing epoch is obtained as a recursive form. The full probabilities, then, are derived using an iterative procedure. This system finds an application in a packet transmitting telecommunications system where the server transmits(serves) packets(customers) accumulated at a gate closing epoch, and takes one slot time vacation thereafter.

• Industrial Engineering and Management Systems
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• 제15권2호
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• pp.131-142
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• 2016

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.