• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1659-1671
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• 2013

In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

• Journal of Distribution Science
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• v.17 no.6
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• pp.77-84
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• 2019

Purpose - Although an extensive body of research in psychology and marketing focuses on perceived waiting time, no research has examined the effect of the location of the waiting place on perceived waiting time. In particular, this study suggests that customers who are waiting in a restaurant may have different perceived waiting time depending on whether they are in close proximity to the service area (e.g., dining area) or farther from it. In particular, the author examines how and why the location of the waiting place affects the perceived waiting time of the consumer and reveals the mental simulation as its psychological mechanism. Research design, data, and methodology - This study conducted field surveys with customers waiting in real restaurants. Eighty-eight people participated under two conditions: a restaurant with a waiting place near the dining area and a restaurant with a waiting place far from the dining area. Participants responded to questions about perceived waiting time (the dependent variable), mental simulation (the mediator), and demographic variables. To verify the hypothesis, ANOVA and bootstrapping analysis were performed. Results - The major results from the field study are as follows. First, participants perceived wait time differently depending on the location of the restaurant's waiting place: participants in the restaurant with a waiting place close to the dining area perceived significantly shorter waiting times. Second, the effect of the location of the waiting place on the perceived waiting time was mediated by mental simulation: the closer the wait location is to the dining area, the more imagination the customer exercises about the meal, which in turn distracts attention from time flow and shortens the perceived wait time. Conclusion - This study has a theoretical implication in that it extends research on perceived waiting time as the first study of how and why the location of a waiting place affects a customer's perceived waiting time. It has a practical implication that can be used as a marketing tactics to improve the image of the service provider by changing the location of the waiting place.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.523-533
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• 1999

We consider the M/G/1 queueing model with D-policy. The server is turned off at the end of each busy period and is activated again only when the sum of the service times of all waiting customers exceeds a fixed value D. We obtain the distribution of unfinished work and show that the unfinished work decomposes into two random variables, one of which is the unfinished work of ordinary M/G/1 queue. We also derive the distribution of queue waiting time.

• Journal of the Korea Society for Simulation
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• v.3 no.1
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• pp.99-105
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• 1994

Most of the companies are forced to cut down the manufacturing cost to survive in the competitive environment. Among others, material distribution cost alone takes substantial portion of the total manufacturing cost. In this study, we investigate the waiting phenomenon in the toll gate and propose a new toll booth layout to reduce the waiting time, thereby reduce the total material distribution cost. SIMAN, a simulation language, is employed to evaluate the proposed layout. The experimental results show that the layout reduces the waiting time significantly. Furthermore, the result indicates that determination of the intermediate buffer space affects the performance of the proposed layout.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.749-757
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• 2012

We consider the M/PH,G/1 queue with two classes of customers in which class-1 customers have deterministic impatience time and have preemptive priority over class-2 customers who are assumed to be infinitely patient. The service times of class-1 and class-2 customers have a phase-type distribution and a general distribution, respectively. We obtain performance measures of class-2 customers such as the queue length distribution, the waiting time distribution and the sojourn time distribution, by analyzing the busy period of class-1 customers. We also compute the moments of the queue length and the waiting and sojourn times.

• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.1
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• pp.1-4
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• 2015

This paper presents a heuristic approach to derive the Laplace-Stieltjes transform (LST) and the probability generating function (PGF) of the waiting time distributions of a continuous- and a discrete-time GI/G/1 queue, respectively. This is a new idea to derive the well-known results, the waiting time distribution of GI/G/1 queue, in a different way.

• 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.1 no.1
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• pp.99-103
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• 1975

A procedure for the test of independence of the observations and the null distribution are studied for a waiting-time distribution of the number of Bernoulli trials required to obtain a preassigned number of successes under Markov dependence. Selected critical values for the test statistic are tabulated.

• Journal of Korean Port Research
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• v.5 no.2
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• pp.19-37
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• 1991

This work aims to : establish a model of the container physical distribution system of Pusan port comprising 4 sub-systems of a navigational system, on-dock cargo handling/transfer/storage system, off-dock CY system and an in-land transport system : examine the system regarding the cargo handling capability of the port and analyse the cost of the physical distribution system. The overall findings are as follows : Firstly in the navigational system, average tonnage of the ships visiting the Busan container terminal was 33,055 GRT in 1990. The distribution of the arrival intervals of the ships' arriving at BCTOC was exponential distribution of $Y=e^{-x/5.52}$ with 95% confidence, whereas that of the ships service time was Erlangian distribution(K=4) with 95% confidence, Ships' arrival and service pattern at the terminal, therefore, was Poisson Input Erlangian Service, and ships' average waiting times was 28.55 hours In this case 8berths were required for the arriving ships to wait less than one hour. Secondly an annual container through put that can be handled by the 9cranes at the terminal was found to be 683,000 TEU in case ships waiting time is one hour and 806,000 TEU in case ships waiting is 2 hours in-port transfer capability was 913,000 TEU when berth occupancy rate(9) was 0.5. This means that there was heavy congestion in the port when considering the fact that a total amount of 1,300,000 TEU was handled in the terminal in 1990. Thirdly when the cost of port congestion was not considered optimum cargo volume to be handled by a ship at a time was 235.7 VAN. When the ships' waiting time was set at 1 hour, optimum annual cargo handling capacity at the terminal was calculated to be 386,070 VAN(609,990 TEU), whereas when the ships' waiting time was set at 2 hours, it was calculated to be 467,738 VAN(739,027 TEU). Fourthly, when the cost of port congestion was considered optimum cargo volume to be handled by a ship at a time was 314.5 VAN. When the ships' waiting time was set at I hour optimum annual cargo handling capacity at the terminal was calculated to be 388.416(613.697 TEU), whereas when the ships' waiting time was set 2 hours, it was calculated to be 462,381 VAN(730,562 TEU).