• Journal of the Korean Society for Railway
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• v.12 no.2
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• pp.267-275
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• 2009

Max-plus algebra is a nonlinear system comprised of two operations, maximization (max) and addition (Plus), which are corresponding to the addition and the multiplication in conventional algebra, respectively. This methodology is applicable to many discrete event systems containing the state transition with the maximization and addition operation. Timetable with connection is one of such systems. We present the method based on max-plus algebra, which can make up timetable considering transfer and analyse its stability and robustness. In this study, it will be shown how to make up the timetable of the urban train and analyse its stability using Max-Plus algebra.

• Journal of the Korea Society for Simulation
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• v.24 no.2
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• pp.11-17
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• 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 Korea Society for Simulation
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• v.28 no.2
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• pp.119-129
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• 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.

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