• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.374-378
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• 2001

We present a discrete-time version of the distributional Little's law, of which the continuous-time version is well known. Then we extend it to the queue in which two or more customers may depart at the same time. As a demonstration, we apply this law to various discrete-time queues such as the standard Geom/G/1 queue, the Geom/G/1 queue with vacations, the multi-server Geom/D/c queue, and the bulk-service Geom/$G^b$/1 queue. As a result, we obtain the probability generating functions of the numbers in system/queue and the waiting times in system/queue for those queues.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.405-434
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• 1998

We consider an M/M/c queue with two types of custormers, positive customers and negative customers. Positive customers are ordinary ones who upon arrival, join a queue with the intention of getting served and each arrival of negative customer removes a positive customer in the system, if any presents, and then is disappeared immediately. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions of a tagged customer, joinly with the probability that the tagged customer completes his service without being removed are derived under the combinations of various service displines; FCFS, LCFS and PS and removal strategies; RCF, RCH and RCR.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.14-19
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• 2006

This study examined the effect of waiting in a service queue on the evaluation of service quality focused on its overall process, mediators and moderators The conceptual model of this paper integrates key variables derived from previous studies of consumer waiting behavior. Data obtained from actual customers in service queue at a hospital was used to test the theoretical framework. First, results from the path analysis confirm that negative affect and acceptability of the wait function as mediators in the process that the perceived duration of the wait affects customer's evaluation of overall service quality. Second, the analysis of the data, with the use of moderate regression shows that disconfirmation of wait time expectations, transaction importance, stability of wait time and wait environment work as moderate variables for the relationship between perceived duration of wait and negative affect. For the relationship between perceived wait time and acceptability of the wait, on the other hand, only transaction import ante shows a significant effect as a moderator.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.301-306
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• 2004

We consider the $P_\lambda\;^M$ service policy for an M/G/1 queue in which the service rate is increased from 1 to M at the exponential setup time after the level of workload exceeds $\lambda$. The stationary distribution of the workload is explicitly obtained through the level crossing argument.

• 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 Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.179-186
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• 1993

We derive the arbitrary time point system size distribution of M/ $G^{B}$1 queue in which late arrivals are not allowed to join the on-going service. The distribution is given by P(z) = $P_{4}$(z) $S^{*}$ (.lambda.-.lambda.z) where $P_{4}$ (z) is the probability generating function of the queue size and $S^{*}$(.theta.) is the Laplace-Stieltjes transform of the service time distribution function. We also derive the distribution of the service siez at arbitrary point of time. time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.443-457
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• 2015

We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.

• Journal of the Korea Society for Simulation
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• v.24 no.3
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• pp.27-35
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• 2015

We analyze an M/G/1/K queueing system with queue-length dependent service and arrival rates. There are a single server and a buffer with finite capacity K including a customer in service. The customers are served by a first-come-first-service basis. We put two thresholds $L_1$ and $L_2$($${\geq_-}L_1$$ ) on the buffer. If the queue length at the service initiation epoch is less than the threshold $L_1$, the service time of customers follows $S_1$ with a mean of ${\mu}_1$ and the arrival of customers follows a Poisson process with a rate of ${\lambda}_1$. When the queue length at the service initiation epoch is equal to or greater than $L_1$ and less than $L_2$, the service time is changed to $S_2$ with a mean of $${\mu}_2{\geq_-}{\mu}_1$$. The arrival rate is still ${\lambda}_1$. Finally, if the queue length at the service initiation epoch is greater than $L_2$, the arrival rate of customers are also changed to a value of $${\lambda}_2({\leq_-}{\lambda}_1)$$ and the mean of the service times is ${\mu}_2$. By using the embedded Markov chain method, we derive queue length distribution at departure epochs. We also obtain the queue length distribution at an arbitrary time by the supplementary variable method. Finally, performance measures such as loss probability and mean waiting time are presented.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.343-350
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• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• 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.