• Journal of the Korea Society for Simulation
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• v.23 no.3
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• pp.1-9
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• 2014

Traditional workflow time analyses have been performed treating an activity as an independent M/M/1queueing system. Using the general forms of performance measures in the M/M/1 system, various aspects of analyses can be performed. Especially, on the time analysis of an AND structure in a workflow system, the mean system sojourn time can be formalized by applying the performance measures of M/M/1 system. In the real workflow system, the AND structure cannot be described correctly under the assumption of independent M/M/1 systems. To overcome this limitation, this research makes the assumption that the all activities for a task starts simultaneously. In this situation, the theoretical solution can be derived using the performance measures of the M/G/1 system. In addition, the simulation modeling method will be proposed to analyze the AND structure of a real workflow system. Finally, some numerical results from the theoretical solutions and simulation models will be provided for verification. The main performance measures used in this research are mean queueing time and mean sojourn time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.2
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• pp.1-10
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• 2016

In this paper, we present a new way to derive the mean cycle time of the G/G/m failure prone queue when the loading of the system approaches to zero. The loading is the relative ratio of the arrival rate to the service rate multiplied by the number of servers. The system with low loading means the busy fraction of the system is low. The queueing system with low loading can be found in the semiconductor manufacturing process. Cluster tools in semiconductor manufacturing need a setup whenever the types of two successive lots are different. To setup a cluster tool, all wafers of preceding lot should be removed. Then, the waiting time of the next lot is zero excluding the setup time. This kind of situation can be regarded as the system with low loading. By employing absorbing Markov chain model and renewal theory, we propose a new way to derive the exact mean cycle time. In addition, using the proposed method, we present the cycle times of other types of queueing systems. For a queueing model with phase type service time distribution, we can obtain a two dimensional Markov chain model, which leads us to calculate the exact cycle time. The results also can be applied to a queueing model with batch arrivals. Our results can be employed to test the accuracy of existing or newly developed approximation methods. Furthermore, we provide intuitive interpretations to the results regarding the expected waiting time. The intuitive interpretations can be used to understand logically the characteristics of systems with low loading.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.3
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• pp.71-77
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• 2009

Using the results of the expected busy periods for the dyadic Min(N, D) and Max(N, D) operating policies in a controllable M/G/1 queueing model, an important relation between them is derived. The derived relation represents the complementary property between two operating policies. This implies that it could be possible to obtained desired system characteristics for one of the two operating policies from the corresponding known system characteristics for the other policy. Then, upper and lower bounds of expected busy periods for both dyadic operating policies are also derived.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.1-18
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• 2006

We consider an $M^x/G/1$ queueing system with Bernoulli vacation schedule under multiple vacation policy. where after each vacation completion or service completion the server takes sequence of vacations until a batch of new customer arrive. This generalizes both $M^x/G/1$ queueing system with multiple vacation as well as M/G/1 Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further attempts have been made to unify the results of related batch arrival vacation models.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.66
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• pp.11-18
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• 2001

In this paper, we analyze an M/G/1 two-phase gated service model with threshold. We consider compound Poison arrival Process and general service time, where the server fives two different modes of services in order, batch and individual services. Server starts his service when the number of arrived customers reaches the predetermined threshold . We find the PGF of the number of customers in system and LST of waiting time, with which we obtain the means of them.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.523-533
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• 1999

We consider the M/G/1 queueing model with D-policy. The server is turned off at the end of each busy period and is activated again only when the sum of the service times of all waiting customers exceeds a fixed value D. We obtain the distribution of unfinished work and show that the unfinished work decomposes into two random variables, one of which is the unfinished work of ordinary M/G/1 queue. We also derive the distribution of queue waiting time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.253-256
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• 2000

In general, Automated Storage/Retrieval Systems (AS/RS ) have racks of equal sized cells to utilize the concept of unit-load. Most of the techniques for the performance estimation of a unit-load AS/RS are a static model or computer simulation. Especially, their models were developed under assumption that the Storage/Retrieval (S/R) machine performs only single command (SC) or dual command (DC). In reality, defending on the operating policy and the status of the system at a particular time, the S/B machine performs a SC or a DC, or becomes .: idle. In order to resolve these weak points, we propose a stochastic model for the performance estimation of unit-load AS/RS by using a single-server queueing model. Expected numbers of waiting storage and retrieval commands are found

• ETRI Journal
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• v.39 no.4
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• pp.558-569
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• 2017

In this study, a non-preemptive M/G/1 queueing model of a spectrum handoff scheme for cognitive wireless networks is proposed. Because spectrum handoff gives secondary users an opportunity to carry on their transmissions, it is crucially important to determine the actions of primary users. In our queueing model, prioritized data traffic is utilized to meet the requirements of the secondary users. These users' packets are categorized into three different priority classes: urgent, real-time, and non-real time. Urgent data packets have the highest priority, while non-real time data packets have the lowest priority. Riverbed (OPNET) Modeler simulation software was used to simulate both reactive and proactive decision spectrum handoff schemes. The simulation results were consistent with the analytical results obtained under different load and traffic conditions. This study also revealed that the cumulative number of handoffs can be drastically decreased by exploiting priority classes and utilizing a decent spectrum handoff strategy, such as a reactive or proactive decision-based strategy.

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.1-21
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• 2009

We consider an $M^x/G/1$ queueing system with a random setup time under Bernoulli vacation schedule, where the service of the first unit at the completion of each busy period or a vacation period is preceded by a random setup time, on completion of which service starts. However, after each service completion, the server may take a vacation with probability p or remain in the system to provide next service, if any, with probability (1-p). This generalizes both the $M^x/G/1$ queueing system with a random setup time as well as the Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further, attempts have been made to unify the results of related batch arrival vacation models.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.111-117
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• 2001

Most of the techniques for the performance estimation of unit-load AS/RS are a static model or computer simulation. Especially, their models have been developed under the assumption that the Storage/Retrieval (S/R) machine performs either single command(SC) or dual command(DC) only. In reality, depending on the operating policy and the status of the system at a particular time, the S/R machine performs a SC or a DC, or becomes idle. In order to resolve this weak point, we propose a stochastic model for the performance estimation of unit-load ASIRS by using a M/G/1 queueing model with a single server and two queues. Server utilization, expected numbers of waiting storage and retrieval commands and mean time spent in queue and system are found.