• Journal of the Korea Society for Simulation
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• v.17 no.2
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• pp.75-82
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• 2008

The times of service commencement and service completion had been used for inferring the queueing systems. However, the service commencement times are difficult to measure because of unobservable nature in queueing systems. In this paper, for inferring queueing systems, the service commencement times are replaced for arrival times which can be easily observed. Determining the service commencement time is very important in our methods. The methods for first come first served(FCFS), last come first served(LCFS) queueing discipline are already developed in our previous work. In this paper, we extend to random selection for service(RSS) queueing discipline. The performance measures we used are mean queueing time and mean service time, the variances of two. The simulation results verify our proposed methods to infer queueing systems under RSS discipline.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.453-460
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• 2006

A discrete-time priority queueing system with place reservation discipline is studied, in which two different types of packets arrive according to batch geometric streams. It is assumed that there is a reserved place in the queue. Whenever a high-priority packet enters the queue, it will seize the reserved place and make a new reservation at the end of the queue. Low-priority arrivals take place at the end of the queue in the usual way. Using the probability generating function method, the joint distribution of system state and the delay distribution for each type are obtained.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.40 no.3
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• pp.66-75
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• 2017

Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.

• Journal of KIISE:Information Networking
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• v.29 no.5
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• pp.553-561
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• 2002

We present a novel service discipline, called linear service discipline, to serve multiple QoS queues sharing a resource and analyze its properties. The linear server makes the output traffic and the queueing dynamics of individual queues as a linear function of its input traffic. In particular, if input traffic is Gaussian, the distributions of queue length and output traffic are also Gaussian with their mean and variance being a function of input mean and input power spectrum (equivalently, autocorrelation function of input). Important QoS measures including buffer overflow probability and queueing delay distribution are also expressed as a function of input mean and input power spectrum. This study explores a new direction for network-wide traffic management based on linear system theories by letting us view the queueing process at each node as a linear filter.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.3
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• pp.32-37
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• 2004

This paper investigates the mathematical model of multi-server retrial queueing system with the Batch Markovian Arrival Process (BMAP), the Phase type (PH) service distribution and the finite buffer. The sufficient condition for the steady state distribution existence and the algorithm for calculating this distribution are presented. Finally, a formula to solve loss probability in the case of complete admission discipline is derived.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.162-170
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• 2012

We propose a new priority discipline called the strict T-preemptive priority discipline, and derive the waiting time distributions of each class in the strict T-preemptive priority M/G/1 queue. Using this queueing analysis, we evaluate the performance of an opportunistic spectrum access in cognitive radio networks, where a communication channel is divided into time slots, a licensed primary user is assigned to one channel, and multiple unlicensed secondary users may opportunistically exploit time slots unused by the primary user. We also present a numerical example of the analysis of the opportunistic spectrum access where the arrival rates and service times distributions of each users are identical.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.12 no.2
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• pp.92-101
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• 1987

Messages which are entered into communication networks are processed according to the priorities manipulated by serveral queueing disciplines. This study is concerned with one of those disciplines, dynamic priority. We analyzed the everage waiting time for the messages be processed by dynamic priority in queue. The priority is variated by the message's waiting time in queue. The dynamic priority discipline can be classified according as messaged have initial priority or not. Difference of above two discriplines were considered.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.1
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• pp.33-40
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• 2007

A multi-server queueing system with finite buffer is considered. The input flow is the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Customers from the BMAP enter the system according to the discipline of partial admission. Besides ordinary (positive) customers, the Markovian flow (MAP) of negative customers arrives to the system. A negative customer can delete an ordinary customer in service if the state of its PH-service process belongs to some given set. In opposite case the ordinary customer is considered to be protected of the effect of negative customers. The stationary distribution and the main performance measures of the considered queueing system are calculated.

• Korean Management Science Review
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• v.9 no.1
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• pp.3-15
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• 1992

In this paper, we study a manufacturing system of serial stages with general service times, in which the production of each stage and the coordination of stages are controlled by Kanban discipline. This Kanban discipline is modeled as a Discrete Event Dynamic System and a system of recursive equations is applied to study the dynamics of the system. The recursive relationship enables us to compare this Kanban discipline with the other blocking disciplines such as transfer blocking, service blocking, block-and-hold b, and block-and-hold K, and the Kanban is shown to be superior to the other disciplines in terms of makespan and throughput. As a special case, two stages Kanban system is modeled as $C_2/C_2/1/N$ queueing system, and a recursive algorithm is developed to calculate the system performance. In optimizing the system performance, the stochastic optimization approach of Robbins-Monro is employed via perturbation analysis, the way to estimate the stochastic partial derivative based on only one sample trajectory of the system, and the required commuting condition is verified. Then the stochastic convexity result is established to provide second-order optimality condition for this parametric optimization problem.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9B
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• pp.783-792
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• 2003

We consider a finite-buffer discrete-time queueing system with fixed-size bulk-service discipline: Geo/ $G^{B}$1/K＋B. The main purpose of this paper is to present a performance analysis of this system that has a wide range of applications in Asynchronous Transfer Mode (ATM) and other related telecommunication systems. For this purpose, we first derive the departure-epoch probabilities based on the embedded Markov chain method. Next, based on simple rate in and rate out argument, we present stable relationships for the steady-state probabilities of the queue length at different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of number of packets in the system at three different epochs and the loss probability. The numerical results are presented for a deterministic service-time distribution - a case that has gained importance in recent years.s.