• Communications of the Korean Mathematical Society
• /
• v.14 no.3
• /
• pp.611-625
• /
• 1999

We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

• Journal of the Korea Society for Simulation
• /
• v.24 no.2
• /
• pp.11-17
• /
• 2015

Although systems with finite capacities have been the topic of much study, there are as of yet no analytic expressions for (higher) moment and tail probability of stationary waiting times in systems with even constant processing times. The normal queueing theory cannot properly handle such systems due to the difficulties caused by finite capacity. In this study, for a DBR (Drum-Buffer-Rope) line production system with constant processing times, we introduce analytic expressions by using previous results obtained using a max-plus algebraic approach.

• Journal of the Korean Geotechnical Society
• /
• v.34 no.1
• /
• pp.17-24
• /
• 2018

A buffer in a geological disposal system minimizes groundwater inflow from the surrounding rock and protects the disposed high-level waste (HLW) against any mechanical impact. As decay heat of a spent fuel causes temperature variation in the buffer that affects the mechanical performance of the system, an accurate estimation of the temperature variation is substantial. The temperature variation is affected by thermal and material properties of the system such as thermal conductivity, density and specific heat capacity of the buffer, and thus these factors should be properly included in the design of the system. In particular, as the thermal properties are variable depending on the density and water content of the buffer, consideration of the effects should be included in the analysis. Hence, in this study, a numerical model based on finite element method (FEM) which is able to consider the change of density and water content of the buffer was established. In addition, using the numerical model, a parametric study was conducted to investigate the effect of each thermal property on the temperature variation of the buffer.

• Communications of the Korean Mathematical Society
• /
• v.14 no.2
• /
• pp.405-423
• /
• 1999

We consider a statistical multiplexer model with finite buffer capacity and finite number of independent identical 3-state bursty voice sources. The burstiness of the sources is modeled by describing both two different active periods (at the rate of one packet perslot) and the passive periods during which no packets are generated. Assuming a mixture of two geometric distributions for active period and a geometric distribution for passive period and geometric distribution for passive period, we derive the recursive algorithm for the probability mass function of the buffer contents (in packets). We also obtain loss probability and the distribution of packet delay. Numerical results show that the system performance deteriorates considerably as the variance of the active period increases. Also, we see that the loss probability of 2-state Markov models is less than that of 3-state Markov models.

• Journal of the Korea Society for Simulation
• /
• v.28 no.3
• /
• pp.65-74
• /
• 2019

For many years, it has been widely studied on fork-join production systems but there is not much literature focusing on the finite buffer(s) of either individuals or shared, and generally distributed processing times. Usually, it is difficult to handle finite buffer(s) through a standard queueing theoretical approach. In this study, by using the max-plus algebraic approach we studied buffer-shared fork-join production systems with general processing times. However, because it cannot provide proper computational ways for performance measures, we developed simulation models using @RISK software and the expressions derived from max-plus algebra. From the simulation experiments, we compared some properties on waiting time with respect to a buffer capacity under two blocking policies: BBS (Blocking Before Service) and BAS (Blocking After Service).

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.23 no.59
• /
• pp.21-36
• /
• 2000

The drum-buffer-rope(DBR) system is a finite scheduling mechanism that balances the flow of the production system. DBR controls the flow of materials through the plant in order to produce products in accordance with market demand, with a minimum of manufacturing lead time, inventory, and operating expenses. This paper integrates the best of MRP push system and JIT pull system with DBR system, efficiently adapts these logics to capacity constraint resources, and contributes to the evolution of synchronous manufacturing. The purpose of this paper is, thus, threefold. The first objective is to identify the frame of theory of constraints(TOC) and the logic of DBR scheduling. The second objective is to formulate the DBR constraint scheduling problems(DBRCSP) in a job shop environments. Finally, the paper is to suggest the solution procedure of DBRCSP for embedding TOC into MRP/JIT along with an numerical expression. In addition, illustrative numerical example is given.

• Journal of the Korea Society for Simulation
• /
• v.28 no.2
• /
• pp.119-129
• /
• 2019

Although line production systems with finite buffers have been studied over several decades, except for some special cases there are no explicit expressions for system performances such as waiting times(or response time) and blocking probability. Recently, a max-plus algebraic approach for buffer-sharing systems with constant processing times was introduced and it can lead to analytic expressions for (higher) moment and tail probability of stationary waiting. Theoretically this approach can be applied to general processing times, but it cannot give a proper way for computing performance measures. To this end, in this study we developed simulation models using @RISK software and the expressions derived from max-plus algebra, and computed and compared blocking probability, waiting time (or response time) with respect to two blocking policies: communication(BBS: Blocking Before Service) and production(BAS: Blocking After Service). Moreover, an optimization problem which determines the minimum shared-buffer capacity satisfying a predetermined QoS(quality of service) is also considered.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.11 no.3
• /
• pp.179-196
• /
• 1986

In this paper, the peformance of a statistical packet voice/data multiplexer is studied. In ths study we assume that in the packet voice/data multiplexer two separate finite queues are used for voice and data traffics, and that voice traffic gets priority over data. For the performance analysis we divide the output link of the multiplexer into a sequence of time slots. The voice signal is modeled as an (M+1) - state Markov process, M being the packet generation period in slots. As for the data traffic, it is modeled by a simple Poisson process. In our discrete time domain analysis, the queueing behavior of voice traffic is little affected by the data traffic since voice signal has priority over data. Therefore, we first analyze the queueing behavior of voice traffic, and then using the result, we study the queueing behavior of data traffic. For the packet voice multiplexer, both inpur state and voice buffer occupancy are formulated by a two-dimensional Markov chain. For the integrated voice/data multiplexer we use a three-dimensional Markov chain that represents the input voice state and the buffer occupancies of voice and data. With these models, the numerical results for the performance have been obtained by the Gauss-Seidel iteration method. The analytical results have been verified by computer simylation. From the results we have found that there exist tradeoffs among the number of voice users, output link capacity, voic queue size and overflow probability for the voice traffic, and also exist tradeoffs among traffic load, data queue size and oveflow probability for the data traffic. Also, there exists a tradeoff between the performance of voice and data traffics for given inpur traffics and link capacity. In addition, it has been found that the average queueing delay of data traffic is longer than the maximum buffer size, when the gain of time assignment speech interpolation(TASI) is more than two and the number of voice users is small.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.18 no.6
• /
• pp.889-894
• /
• 1993

Asychronous Transfer Mode (ATM) provides the means to transport different types of bursty traffic such as voice, video, and bulk data. To handle more efficiently the traffic sources and to increase the bandwidth utilization as much as possible, flexible statistical multiplexing schemes must be adopted for the ATM networks. This paper presents an efficient computational procedure to calculate the queue state distribution in a finite buffer queueing system with a number of independent input sources, and the cell loss probability is exactly calculated with the use of this recursion computation method. The cell loss probability is related to a ATM multiplexer with a homogeneous ON-OFF source is also investigated through numerical examples.

• Journal of Institute of Control, Robotics and Systems
• /
• v.2 no.3
• /
• pp.220-228
• /
• 1996

This paper presents a extended stochastic Petri net (ESPN) model for CTN(Circulated Token with No duration) service in the data link layer of IEC/ISA fieldbus. It is assumed that a station on the fieldbus has a specified minimum token holding time, a finite capacity buffer, and one transmitter queue with the highest priority. The mean transmission (or service) time at a station and the mean token rotation time for the symmetric fieldbus system atr derived using the presented SPN model and the moment generating function. These performance measures are represented in terms of the minimum token holding time, the number of stations, the arrival rate of messages, and the mean length of messages. The presented performance measure are validated by computer simulations.