• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.95-99
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• 1983

Limiting law for maximum queue length in G/M/1 queue system is derived. Furthermore, a simple approach using mixing sequence is also discussed.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.383-396
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• 2013

We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.691-712
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• 1998

We consider an M$_1$, M$_2$/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.

• Journal of the Korea Society for Simulation
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• v.27 no.3
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• pp.45-52
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• 2018

We consider the busy period of an M/G/1/K queueing system with queue-length-dependent overload control policy. A variant of an oscillating control strategy that was recently analyzed by Choi and Kim (2016) is considered: two threshold values, $L_1({\leq_-}L_2)$ and $L_2({\leq_-}K)$, are assumed, and service rate and arrival rate are adjusted depending on the queue length to alleviate congestion. We investigate the busy period of an M/G/1/K queue with two overload control policies, and present the formulae to obtain the expected length of a busy period for each control policy. Based on the numerical examples, we conclude that the variability and expected value of the service time distribution have the most influence on the length of a busy period.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.25-29
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• 2005

We analyze an M/G/1 queueing system under $P_{\lambda,\tau}^M$ service policy. By using the level crossing theory and solving the corresponding integral equations, we obtain the stationary distribution of the workload in the system explicitly.

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.1-21
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• 2009

We consider an $M^x/G/1$ queueing system with a random setup time under Bernoulli vacation schedule, where the service of the first unit at the completion of each busy period or a vacation period is preceded by a random setup time, on completion of which service starts. However, after each service completion, the server may take a vacation with probability p or remain in the system to provide next service, if any, with probability (1-p). This generalizes both the $M^x/G/1$ queueing system with a random setup time as well as the Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further, attempts have been made to unify the results of related batch arrival vacation models.

• 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 of the Korean Mathematical Society
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• v.10 no.2
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• pp.419-438
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• 1995

We investigate a tansient diffusion approximation of queue size distribution in $M^{X}/G^{Y}/c$ system using the diffusion process with elementary return boundary. We choose an appropriate diffusion process which approxiamtes the queue size in the system and derive the transient solution of Kolmogorov forward equation of the diffusion process. We derive an approximation formula for the transient queue size distribution and mean queue size, and then obtain the stationary solution from the transient solution. Accuracy evalution is presented by comparing approximation results for the mean queue size with the exact results or simulation results numerically.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.1
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• pp.83-90
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• 2006

By defining the partial busy period of the M/M/c/K queueing system as the time interval during which at least one server is in service, we derive the first two moments of both the partial busy period and the number of customers served during it. All expressions are given in explicit forms.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.259-266
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• 2009

We consider an M/G/1 feedback retrial queue with Bernoulli schedule in which after being served each customer either joins the retrial group again or departs the system permanently. Using the supplementary variable method, we obtain the joint generating function of the numbers of customers in two groups.