• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.469-474
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• 2011

In a M/G/I queue where the server alternates between busy and idle periods, we assume that firstly customers arrive at the system according to a Poisson process and the arrival process and customer service times are mutually independent, secondly the system has infinite waiting room, thirdly the server utilization is less than 1 and the system has reached a steady state. With these assumptions, we analyze waiting times on the systems where some vacation policies are considered.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.403-426
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• 1998

We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spa-tially homogeneous except for a finite number of blocks. We treat the MAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.1-12
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• 1998

We consider G/M/1 queues with multiple vacation disci-pline where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vaca-tion time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.389-405
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• 2007

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability ${\gamma}$ and with probability $1-{\gamma}$ leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability ${\delta}\;(<\;1)$ and with probability $1-{\delta}$ leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.3
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• pp.235-241
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• 1994

We consider a B/G/1 queueing with vacations, where the server closes the gate when it begins a vacation. In this system, customers arrive according to a Bernoulli process. The service time and the vacation time follow discrete distributions. We obtain the distribution of the number of customers at a random point in time, and in turn, the distribution of the residence time (queueing time + service time) for a customer. It is observed that solutions for our discret time B/G/1 gated vacation model are analogous to those for the continuous time M/G/1 gated vacation model.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.481-493
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• 1996

We consider a retrial queue with two classes of customers where arrivals of class 1(resp. class 2) customers are MMPP and Poisson process, respectively. In the case taht arriving customers are blocked due to the channel being busy, the class 1 customers are queued in priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrial group in order to try service again after a random amount of time. We consider the following retrial rate control policy, which reduces their retrial rate as more customers join the retrial group; their retrial times are inversely proportional to the number of customers in the retrial group. We find the joint generating function of the numbers of custormers in the two groups by the supplementary variable method.

• Journal of Korean Tunnelling and Underground Space Association
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• v.18 no.1
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• pp.41-52
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• 2016

When the queue length of congestion vehicles in tunnel fire is extended beyond tunnel length, the capacity of smoke control system needs to be increased in line with ventilation resistance. However, the vehicle queue length is not defined, so a rational equation is necessary in current fire prevention guideline. This study is intended to propose an equation to calculate the queue length considering the number of vehicles in queue in tunnel fire and evaluate the applicability by tunnel length as well. When it comes to normal tunnel, it is necessary to compare the vehicle queue length with tunnel length up to the length of 1,200 m in a bid to avoid applying the vehicle queue length excessively in case of fire. As a result of evaluation of applicability to model a tunnel, saving the number of jet fan for smoke control appeared to be effective. Besides, quantitative approach to explain the vehicle queue length through the relationship between the percentage of large vehicles and tunnel length was presented. Consequently, when the queue length of the congestion vehicles exceeds the tunnel length in determining the capacity of smoke control system in case of fire, the number of vehicles beyond the tunnel length needs to be excluded from estimating the ventilation resistance by vehicles.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.189-194
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• 2003

We consider an M/G/1 queueing system under P$_{\lambda}^{M}$-service policy. As soon as the workload exceeds threshold ${\lambda}$ > 0, the service rate is increased from 1 to M ${\geq}$ 1 and is kept until the system becomes empty. After assigning several costs, we show that there exists a unique M minimizing the long-run average cost per unit time.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.4
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• pp.17-24
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• 2004

Call blocking probabilities of streaming data service in CDMA system with access point(AP) of WLAN are analyzed for different cell geometry of base station and AP and queuing is modeled. The considered system leads to successful handoffs between the APs of WLAN. Blocking probabilities are enumerated as a function for ratio of base station and AP sizes, their locations and the number of buffer in the queue. Results show that blocking probability is not influenced by base station and AP locations but mainly by ratio of their sizes. For CDMA system of radius 100m, 5 buffers in the queue and 7㏈ noise rise(NR), in order to obtain 1% call blocking probability, a cell with hot spot of radius 20m has more 0.6Erlang than that of radius 60m.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.203-206
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• 2003

This paper studies constrained optimization of an M/G/1 queue with a server that can be switched on and off. One criterion is an average number of customers in the system and another criterion is an average operating cost per unit time, where operating costs consist of switching and running costs. With the help of queueing theory, we solve the problems of optimization of one of these criteria under a constraint for another one.