• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.541-551
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• 2009

Generalized processor sharing(GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. In a queueing system with single-class traffic, the stationary queue length becomes larger stochastically when the bandwidth (i.e. the service rate) of the system decreases. For a given GPS server, we consider the similar problem to this. We define the monotonicity for the head of the line processor sharing(HLPS) servers in which the units in the heads of the queues are served simultaneously and the bandwidth allocated to each queue are determined by the numbers of units in the queues. GPS is a type of monotonic HLPS. We obtain the HLPS server whose queue length of a class stochastically bounds upper that of corresponding class in the given monotonic HLPS server for all classes. The queue lengths process of all classes in the obtained HLPS server has the stationary distribution of product form. When the given monotonic HLPS server is GPS server, we obtain the explicit form of the stationary queue lengths distribution of the bounding HLPS server. Numerical result shows how tight the stochastic bound is.

• Journal of KIISE:Computing Practices and Letters
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• v.6 no.1
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• pp.103-112
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• 2000

As today's market share of Intelligent Network (IN) service and wireless tele-communication is growing rapidly, the increment in service requests of wireless IN service subscribers and users has to be taken into account for implementing advanced IN services. In this paper, we design Global Service Logic for IN Freephone service, which is one of the commercially most interesting IN services, applied call queuing service feature with mass call processing to enhance call completion rate by considering the mobility of wireless service subscribers with mobile terminals as well as existing wireline service subscribers. Due to the location management of each IN subscribers 'mobile terminals, we design the structure and operation mechanism of Queue Manager which adjusts dynamically service subscribers groups according to their mobility. We optimize the queue size according to the call attempt rate and drop rate, and present the appropriate waiting time in the queue.

• Journal of the Korea Society for Simulation
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• v.25 no.3
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• pp.117-123
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• 2016

This paper presents inference methods for inner operations of a multi-server queue when historical data are limited or system observation is restricted. In a queueing system analysis, autocorrelated arrival and service processes increase the complexity of modeling. Accordingly, numerous analysis methods have been developed. In this paper, we introduce an inference method for specific situations when external observations exhibit autocorrelated structure and and observations of internal operations are difficult. We release an assumption of the previous method and provide lemma and theorem to guarantee the correctness of our proposed inference method. Using only external observations, our proposed method deduces the internal operation of a multi-server queue via non-parametric approach even when the service times are autocorrelated. The main internal inference measures are waiting times and service times of respective customers. We provide some numerical results to verify that our method performs as intended.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.531-540
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• 2012

An approximation for the number of customers at service facility in $M/G/c/K$ retrial queue is provided with the help of the approximations of ordinary $M/G/c/K$ loss system and ordinary $M/G/c$ queue. The interpolation between two ordinary systems is used for the approximation.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.985-1004
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• 2016

We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

• Journal of Communications and Networks
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• v.17 no.3
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• pp.306-320
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• 2015

Due to an explosive growth in services running in different datacenters, there is need for service selection and routing to deliver user requests to the best service instance. In current solutions, it is generally the client that must first select a datacenter to forward the request to before an internal load-balancer of the selected datacenter can select the optimal instance. An optimal selection requires knowledge of both network and server characteristics, making clients less suitable to make this decision. Information-Centric Networking (ICN) research solved a similar selection problem for static data retrieval by integrating content delivery as a native network feature. We address the selection problem for services by extending the ICN-principles for services. In this paper we present Queue and Latency, a network-driven service selection algorithm which maps user demand to service instances, taking into account both network and server metrics. To reduce the size of service router forwarding tables, we present a statistical method to approximate an optimal load distribution with minimized router state required. Simulation results show that our statistical routing approach approximates the average system response time of source-based routing with minimized state in forwarding tables.

• 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 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 Korean Society of Industrial and Systems Engineering
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• v.16 no.28
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• pp.39-47
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• 1993

In this paper, We develop performance evaluation model for Twin fork Automated Storage/Retrieval systems. The system is modeled as a modified bulk service queueing system consisting of one exponential server with limited system capacity. The differance between this model and general bulk service queueing model is the inequality of transition service rate of each stage. The ejective of this model is to provide system characteristics for Twin fork AS/R system design problems, which are the number of customers in system, wait time in system and queue, the system queue size.

• 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.