• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.1
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• pp.137-146
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• 2007

In this study we consider a CONWIP system studied in Park and Lee [1] in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied Immediately are either backordered or lost according to the number of demands that exist at their arrival instants. For this system using the results in [1] we develop an approximation method to calculate order based performance measures such as the mean time of fulfilling a customer order and the mean number of customer orders. To test the accuracy of the approximation method, the results obtained from the approximation method are compared with those obtained by simulation. Comparisons with simulation have shown that the approximate method provides fairly good results.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.8-12
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• 2004

In this study we consider a CONWIP system in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied are backordered according to the number of demands that exist at their arrival instants. For this system we develop an approximation method to calculate order based performance measures such as the mean time of fulfilling a customer order and the mean number o: customer orders. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interest.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.2
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• pp.111-121
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• 2002

In this paper, we analyze an M$^{x}$ /G/1 with three types of vacation periods including setup time. Three types of vacations are : N-policy, single vacation, and multiple vacation. We consider compound poisson arrival process and general service time, where the server starts his service when a setup is completed. We find the PGF of the number of customers in system and LST of waiting time, with welch we obtain their means. A decomposition property for the system sloe and waiting time is described also.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.3
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• pp.63-79
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• 2006

In this study we consider a CONWIP system in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied immediately are either backordered or lost according to the number of demands that exist at their arrival Instants. For this system we develop an approximation method to calculate performance measures such as steady state probabilities of the number of parts at each station, proportion of lost demands and the mean number of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method. A recursive technique is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method are compared with those obtained by simulation. Comparisons with simulation show that the approximation method provides fairly good results.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.491-507
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• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.