• Journal of Korean Institute of Industrial Engineers
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• v.22 no.1
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• pp.3-15
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• 1996

An approximation algorithm is presented for cyclic queueing networks with finite buffers. The algorithm decomposes the queueing network into individual queues with revised arrival and service process and revised queue capacity. Then, each queue is analyzed in isolation. The service process reflects the additional delay a unit might undergo due to blocking and the arrival process is described by a 2-phases Coxian ($C_2$) distribution. The individual queues are modelled as $C_2/C_2$/1/B queues. The parameters of the individual queues are computed approximately using an iterative scheme. The population constraint of the closed network is taken into account by ensuring that the sum of the average queue lengths of the individual queues is equal to the number of customers of the network. Extensive numerical experiments show that this method provides a fairly good estimation of the throughput.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-236
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• 1995

The purpose of this paper is to provide a transient diffusion approximation of queue size distribution for M/G/m/N system. The M/G/m/N system can be expressed as follows. The interarrival times of customers are exponential and the service times of customers have general distribution. The system can hold at most a total of N customers (including the customers in service) and any further arriving customers will be refused entry to the system and will depart immediately without service. The queueing system with finite capacity is more practical model than queueing system with infinite capacity. For example, in the design of a computer system one of the important problems is how much capacity is required for a buffer memory. It its capacity is too little, then overflow of customers (jobs) occurs frequently in heavy traffic and the performance of system deteriorates rapidly. On the other hand, if its capacity is too large, then most buffer memories remain unused.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.6
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• pp.9-17
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• 1994

ATM (Asynchronous Transfer Mode) has a fixed-length packet transport scheme. It is one of the promising proposals in B-ISDN.Since the packet length is fixed, it can be potentially to perform the various service to users. In this paper, a queueing model for an ATM multip`exer loaded by CBR and ON/OFF input sources is considered, and the two-queue system which each type of input sources has a queue with a finite capacity is analyzed. The cell loss probabilities for a performance measures of ATM multiplexer are derived, and are also evaluated through numerical examples. As a result, the cell loss probability of ON/OFF sources for the queue size is rapidly decreased when the multiplexed number and burstiness are increased. Since cells of the CBR source have lower priority than cells of the ON/OFF source, cell loss probabilities of CBR sources are accordingly high independently of CBR cell arrival rate when the number of CBR sources is large.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.26
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• pp.151-157
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• 1992

This paper presents a method for analyzing the transfer lines with finite storage buffers. Each machine spends a random amount of time processing each material. This transfer line can be modeled by the tandem queueing system with finite buffers. The great dimensionality of the state space renders the analysis of such system a formidable task. We propose an efficient algorithm to obtain the marginal state probabilities based on the exact algorithm for the two-machine system. Other performance measures, such as the utilization, the blocking probability, the average sojourn time, and the average queue length, can be easily calculated.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.1 no.1
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• pp.37-44
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• 1978

The purpose of this study is to search for an efficient application method in solving delay-phenomenon problems which influence upon total production cost through case study. The method of this study is an experimental study based on cutting time data in lead cutting operations from "Lead Cutting Machine (Stripper)" and its service rate data from a large electronic products company which utilizes conveyor line system for the products "Car Stereo" The procedure of this experimental study is as follows; 1) Using loading(Man-Hour) analysis technique j,1 order to analyse and evaluate Production capacity, efficiency, operation and idle rate assembly charge, waiting and service cost -when its are controlled by stripper operator(server) 2) Establishing adequate waiting time model of finite population caused by the interference of 4 stripper machine which is drawn from mathematical statistics testing, that is, goodness of fit test in the waiting and service rate and to search for optimal solution by utilizing the above mentioned model The experimental result was that amount to 8,546,618won Per year was brought down, that is, by optimum point, it shows a decrease as compared with Present point. The major limitation of this experimental study is that the Queue in the Finite Population, so to speak. it comes from the interference of 4 stripper machine dealt with this case were limited only on the Car Stereo conveyor line. Further study of application of this application method to the areas such as material handling, personnel management marketing and transportation management is strong1y recommended.trong1y recommended.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.881-889
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• 2005

In this study, we consider characteristics of waiting times in single-server 3-node tandem queues with a Poisson arrival process, finite buffers and deterministic or non-overlapping service times at each queue. There are three buffers: one at the first node is infinite and the others are finite. The explicit expressions of waiting times in all areas of the systems, which are driven as functions of finite buffer capacities, show that the sojourn time does not depend on the finite buffer capacities and also allow one to compute and compare characteristics of waiting times at all areas of the system under two blocking policies: communication and manufacturing blocking. As an application of these results, moreover, an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on waiting times is considered. Some numerical examples are also provided.

• Journal of Information Processing Systems
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• v.7 no.4
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• pp.679-690
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• 2011

In this paper we consider a local area network (LAN) of dual mode service where one is a token bus and the other is a carrier sense multiple access with a collision detection (CSMA/CD) bus. The objective of the paper is to find the overall cell/packet dropping probability of a dual mode LAN for finite length queue M/G/1(m) traffic. Here, the offered traffic of the LAN is taken to be the equivalent carried traffic of a one-millisecond delay. The concept of a tabular solution for two-dimensional Poisson's traffic of circuit switching is adapted here to find the cell dropping probability of the dual mode packet service. Although the work is done for the traffic of similar bandwidth, it can be extended for the case of a dissimilar bandwidth of a circuit switched network.

• Journal of the Korea Society for Simulation
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• v.21 no.4
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• pp.11-24
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• 2012

We compared a DBR(drum-buffer-rope) system with a CONWIP(constant work-in-process) system in a production line with constant processing times. Based on the observation that a WIP-controlled line production system such as DBR and CONWIP is equivalent to a m-node tandem queue with finite buffer, we applied a max-plus algebra based solution method for the tandem queue to evaluate the performance of two systems. Numerical examples with 6 workstations were also used to demonstrate the proposed analysis. The mathematical analyses support that CONWIP outperforms DBR in terms of expected waiting time and WIP. Unlike the CONWIP case, sequencing workstations in a DBR affects the performance of the system. Delaying a bottleneck station in a DBR reduces expected waiting time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.91-105
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• 2019

Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

• The Journal of Engineering Research
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• v.3 no.1
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• pp.85-95
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• 1998

In this study, we consider a recursive procedure to obtain the stationary probability distribution for analyzing Coxian queueing networks with finite queues. This network deals with multiple class customers. Due to the state space representing multiple class customers, the sub-matrices corresponding to states can not be square matrices and can not be inverted. Therefore, we introduce more complex recursive method to avoid the singular problem. The open queueing network that we study consists of 3 parallel first-level sources linked to a single second level queue. We consider two types of schemes for entering a queue. The first scheme is assumed to be the first-blocked-first-enter (FBFE) and the second scheme is the higher-priority-first-enter (HPFE). Arrival and service times are assume to have a Coxian distribution with two phases. Comparison between the resulting using Gauss-Seidel method and recursive procedure will be shown.