• 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 Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.89-94
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• 2001

There are many queueing systems where customers wait for service up to a certain amount of time and leave the system if they are not served during that time. This paper considers a finite capacity multi-server queueing system with Poisson input and Erlang service time, where a customer becomes a lost customer when his service has not begun within an exponential patient time after his arrival. Performance measures such as average queue length, the average number of customers in service, and the proportion of lost customers can be obtained exactly through the proposed numerical solution procedure.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.4
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• pp.15-23
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• 1995

In this paper, we evaluate the performance of a transient queueing approximation when it is applied to modeling computer communication networks. An operational computer network that uses the ISO IS-IS(Intermediate System-Intermediate System) routing protocol is modeled as a Jackson network. The primary goal of the approximation pursued in the study was to provide transient queue statistics comparable in accuracy to the results from conventional Monte Carlo simulations. A closure approximation of the M/M/1 queueing system was extended to the general Jackson network in order to obtain transient queue statistics. The performance of the approximation was compared to a discrete event simulation under nonstationary conditions. The transient results from the two simulations are compared on the basis of queue size and computer execution time. Under nonstationary conditions, the approximations for the mean and variance of the number of packets in the queue erer fairly close to the simulation values. The approximation offered substantial speed improvements over the discrete event simulation. The closure approximation provided a good alternative Monte Carlo simulation of the computer networks.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.523-533
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• 2006

We analyze two finite buffers queueing system with priority scheduling dependent upon queue length. Customers are classified into two types ( type-l and type-2 ) according to their characteristics. Here, the customers can be considered as traffics such as voice and data in telecommunication networks. In order to support customers with characteristics of burstiness and time-correlation between interarrival, the arrival of the type-2 customer is assumed to be an Markov- modulated Poisson process(MMPP). The service order of customers in each buffer is determined by the queue length of two buffers. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, performance measures such as loss and mean delay are derived.

• Journal of the Korea Society for Simulation
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• v.13 no.3
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• pp.1-10
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• 2004

The cell loss probability required in the ATM network is in the range of 10$^{-9}$ ∼10$^{-12}$ . If Monte Carlo simulation is used to analyze the performance of the ATM node, an enormous amount of computer time is required. To obtain large speed-up factors, importance sampling may be used. Since the Markov-modulated processes have been used to model various high-speed network traffic sources, we consider discrete time single server queueing systems with Markov-modulated arrival processes which can be used to model an ATM node. We apply importance sampling based on the Large Deviation Theory for the performance evaluation of, MMBP/D/1/K, ∑MMBP/D/1/K, and two stage tandem queueing networks with Markov-modulated arrival processes and deterministic service times. The simulation results show that the buffer overflow probabilities obtained by the importance sampling are very close to those obtained by the Monte Carlo simulation and the computer time can be reduced drastically.

• Journal of the Korea Society for Simulation
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• v.9 no.2
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• pp.89-102
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• 2000

In this paper, we consider an optimal allocation of constant service efforts in queueing network to maximize the system throughput. For this purpose, using the perturbation analysis, we apply a stochastic optimization algorithm to two types of queueing systems. Our simulation results indicate that the estimates obtained from a stochastic optimization algorithm for a two-tandem queuing network are very accurate, and those for closed loop manufacturing system are a little apart from the known optimal allocation. We find that as simulation time increases for obtaining a new gradient (performance measure with respect to decision variables) by perturbation algorithm, the estimates tend to be more stable. Thus, we consider that it would be more desirable to have more accurate sensitivity of performance measure by enlarging simulation time rather than more searching steps with less accurate sensitivity. We realize that more experiments on various types of systems are needed to identify such a relationship with regards to stopping rule, the size of moving step, and updating period for sensitivity.

• Journal of Communications and Networks
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• v.4 no.3
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• pp.209-220
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• 2002

In this paper, we propose a hierarchical packet scheduling technique to closely approximate a hierarchical extension of the generalized processor sharing model, Hierarchical Generalized Processor Sharing (H-GPS). Our approach is to undertake the tasks of service guarantee and hierarchical link sharing in an independent manner so that each task best serves its own objective. The H-GPS model is decomposed into two separate service components: the guaranteed service component to consistently provide performance guarantees over the entire system, and the excess service component to fairly distribute spare bandwidth according to the hierarchical scheduling rule. For tight and harmonized integration of the two service components into a single packet scheduling algorithm, we introduce two novel concepts of distributed virtual time and service credit, and develop a packet version of H-GPS called Hierarchical Fair Queueing (HFQ). We demonstrate the layerindependent performance of the HFQ algorithm through simulation results.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.371-386
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• 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto S policy where as the second model is based on order placement by a fixed quantity Q, where Q = S - s, whenever the inventory level falls to s. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.4
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• pp.51-69
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• 1997

Recently Lee et al[5] developed an approximation algorithm for the performance evaluation of the open queueing networks with blocking. This algorithm, which solves the exponential queueing networks with general configuration is developed based on the symmetrical decomposition approach and is reported to have many advantages over the previous algorithmsf. In addition to being very accurate, this algorithm is reported to be quite simple, pretty fast and solves very general configurations. In this study, we show that if a network has a tree-like configurations, the algorithm developed by Lee at al, always converges to the unique solution. To prove the theoretical results pertaining to the algorithm, some properties associated with symmetrical decomposition approach are exploited. The results obtained in this study such as the proofs of convergence of the algorithm as well as uniquences of the solution would contribute to the theoretical study for the non-tandem configurating of open queueing network.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.2
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• pp.87-95
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• 1991

The exact solution of the closed queueing networks(CQN) is known only for the product form (BCMP) queueing networks. Various computational algorithms are available to derive system throughput(the rate at which a system completes units of computational work) of the networks. However, the computational expense of an exact solution is often excessive when there are multiple classes of cutomers. Instead of computing the exact values, it may be sufficient to derive bounds on the performance measures. Techniques for obtaining bounds on BCMP queueing networks have appeared in the past years. This paper also presents bounds on throughput in CQN models with multiple classes of customers.