• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.489-497
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• 2000

The M/M/1 queue with impatient customers is studied. Impatient customers wait for service only for limited time K/0 and leave the system if their services do not start during that time. Notice that in the analysis of virtual waiting time, the impatient customer can be considered as the customer who enters the system only when his/her waiting time does not exceed K. In this paper, we apply martingale methods to the virtual waiting time and obtain the expected period from origin to the point where the virtual waiting time crosses over K or reaches 0, and the variance of this period. With this results, we obtain the expected busy period of the queue, the distribution, expectation and variance of the number of times the virtual waiting time exceeding level K during a busy period, and the probability of there being no impatient customers in a busy period.

• International Journal of Reliability and Applications
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• v.3 no.4
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• pp.165-171
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• 2002

An optimization of the M/M/1 queue with impatient customers is studied. The impatient customer does not enter the system if his or her virtual waiting time exceeds the threshold K ＞ 0. After assigning three costs to the system, a cost proportional to the virtual waiting time, a penalty to each impatient customer, and also a penalty to each unit of the idle period of the server, we show that there exists a threshold K which minimizes the long-run average cost per unit time.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.623-649
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• 2017

Retrial queues have been widely used to model the many practical situations arising from telephone systems, telecommunication networks and call centers. An approximation method for a simple Markovian retrial queue by reducing the two dimensional problem to one dimensional problem was presented by Fredericks and Reisner in 1979. The method seems to be a promising approach to approximate the retrial queues with complex structure, but the method has not been attracted a lot of attention for about thirty years. In this paper, we exposit the method in detail and show the usefulness of the method by presenting the recent results for approximating the retrial queues with complex structure such as multi-server retrial queues with phase type distribution of retrial time, impatient customers with general persistent function and/or multiclass customers, etc.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.289-294
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• 2004

We consider M/G/1 queue in which the customers are classified into n+1 classes by their impatience time. First, we analyze the model of two types of customers; one is the customer with constant impatience duration k and the other is patient customer. The expected busy period of the server and the limiting distribution of the virtual waiting time process are obtained. Then, the model is generalized to the one in which there are classes of customers according to their impatience duration.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.89-94
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• 2001

There are many queueing systems where customers wait for service up to a certain amount of time and leave the system if they are not served during that time. This paper considers a finite capacity multi-server queueing system with Poisson input and Erlang service time, where a customer becomes a lost customer when his service has not begun within an exponential patient time after his arrival. Performance measures such as average queue length, the average number of customers in service, and the proportion of lost customers can be obtained exactly through the proposed numerical solution procedure.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.1
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• pp.30-37
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• 2016

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers' service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

• Journal of Communications and Networks
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• v.8 no.4
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• pp.410-421
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• 2006

In this work, we propose an analytic framework for dimensioning the link capacity of broadband access networks which provide universal broadband access services to a diverse kind of customers such as patient and impatient customers. The proposed framework takes into account the flow-level quality of service (QoS) of a connection as well as the packet-level QoS, via which a simple and systematic provisioning and operation of the network are provided. To that purpose, we first discuss the necessity of flow-aware network dimensioning by reviewing the networking technologies of the current and future access network. Next, we propose an analytic model for dimensioning the link capacity for an access node of broadband convergence networks which takes into account both the flow and packet level QoS requirements. By carrying out extensive numerical experiment for the proposed model assuming typical parameters that represent real network environment, the validity of the proposed method is assessed.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.83-100
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• 2000

Many queueing systems such as M/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers and MAP/M/$\infty$ queue can be modeled by a level dependent quasi-birth-death(LDQBD) process with linear transition rates of the form ${\lambda}_k$={\alpga}{+}{\beta}k$ at each level $\kappa$. The purpose of this paper is to propose an algorithm to find transient distributions for LDQBD processes with linear transition rates based on the adaptive uniformization technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results.

• Proceedings of the Korea Multimedia Society Conference
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• 2012.05a
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• pp.166-167
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• 2012

High packet loss rate and impatience of messages passing through optical switches are essential characteristics in Optical Burst Switching system equipped with Optic Delay Lines buffer, which have not been solved efficiently yet by current existing models. In order to capture both effects, this paper introduces an analytical model from the viewpoint of classical queuing theory with impatient customers. We then apply it to evaluate and compare two wavelength-sharing cases, (1) all delay lines share a common wavelength resource and (2) each wavelength is associated with a number of delay lines. Our numerical results suggest to implement the first case because of lower packet loss rate for a fairly broad range of traffic load.

• Journal of the Korean Society of Clothing and Textiles
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• v.32 no.3
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• pp.362-372
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• 2008

The remarkable tendency shown in recent fashion can be the customer's passiveness, not only their feeling desire for product but also needs for product seem to be made by mass media. So this condition can be thought as the currency of energy for being subjected. The public of fashion eagerly want the fashion style to be suggested for following it. The late Freudian, Erich Fromm said that the reason why individuals demand themselves to follow the masses' move could be explained as the hope against the fear of feeling not being from staying isolated and having no direction. Escaping from this fear, individuals ought to believe the necessity of participation in public. The fashion is willing to be defined as the united condition by individuals in the hope being consolidate in masses against being solitude. Nowadays, people can share many informations with internet, the fastest medium, which makes the individuals impatient not to be isolate, thinking other people must contact the information and should feel pressure of taking part in the currency. Even though the style is considered to be awkward for following it, it's frequent exposure on mass media by celebrities wearing the style could soon make a fashion. This is able to show that many customers should incline to consider less about their style or taste, whereas lean to pursue after masses' authority. Recent consumers have propensity to avoid feeling concern about others' criticism, on the other side, they try to chase of the fashion as masses' choice for feeling peaceful. The reason why people recognize not to have clothing to wear in spite of a large wardrobe, it must reflect their needs promoted from outside influence of introducing for new styles.