• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.377-385
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• 2013

We consider a compound Poisson risk model in which the premium rate changes when the surplus exceeds a threshold. The explicit form of the ruin probability for the risk model is obtained by deriving and using the overflow probability of the workload process in the corresponding M/G/1 queueing model.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.10a
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• pp.59-62
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• 2000

Many of the previous researchers have been studied for the performance estimation of an AS/RS with a static model or computer simulation. Especially, they assumes that the storage/retrieval (S/R) machine performs either only single command (SC) or dual command (DC) and their requests are known in advance. However, the S/R machine performs a SC or a DC. or both or becomes idle according to the operating policy and the status of system at an arbitrary point of time. In this paper, we propose a stochastic model for the performance estimation of a unit-load AS/RS by using a M/G/1 queueing model with a single-server and two queues. Expected numbers of waiting storage and retrieval commands, and the waiting time in queues for the storage and retrieval commands are found

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.381-386
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• 1998

We frequently encounter stopped random sums when modelling queueing systems. We also notice occasional mishandling of stopped random sums in the literature. The purpose of this note is to prevent further mistakes by identifying and correcting typical mistakes about stopped random sums. As an example model, we use the two-phase M/G/1 queue with multiple vacations.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.841-844
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• 2002

Recently there has been an increasing interest in queueing models with disasters. Upon arrival of a disaster, all the customers present are noshed out. Queueing models with disasters have been applied to the problems of failure recovery in many computer networks systems, database systems and telecommunication networks in this paper, we suffest the steady state and sojourn time distributions of the M/G/l model with disaster and mass alway when the system is empty.

• Proceedings of the Korea Multimedia Society Conference
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• 2000.11a
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• pp.561-566
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• 2000

Computer-Communication System may be classified into two kinds of systems considering connection capability among terminal and computing facility : time sharing and distributed computer systems According to the different input characteristic, the buffer behavior of two systems is quite different. Here we restrict our study to the analysis of queueing behavior of a demultiplexing buffer of time sharing systems. The analysis shows that M/G/1 queueing model can be used model such behavior.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.405-411
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• 2014

Queueing systems with retrials are widely used to model many problems in call centers, telecommunication networks, and in daily life. We present a very accurate but simple approximate formula for the distribution of the number of retrying customers in the M/G/1 retrial queue.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.1
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• pp.21-29
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• 2015

A steady-state controllable M/G/1 queueing model operating under the {T:Min(T,N)} policy is considered where the {T:Min(T,N)} policy is defined as the next busy period will be initiated either after T time units elapsed from the end of the previous busy period if at least one customer arrives at the system during that time period, or after T time units elapsed without a customer' arrival, the time instant when Nth customer arrives at the system or T time units elapsed with at least one customer arrives at the system whichever comes first. After deriving the necessary system characteristics including the expected number of customers in the system, the expected length of busy period and so on, the total expected cost function per unit time for the system operation is constructed to determine the optimal operating policy. To do so, the cost elements associated with such system characteristics including the customers' waiting cost in the system and the server's removal and activating cost are defined. Then, procedures to determine the optimal values of the decision variables included in the operating policy are provided based on minimizing the total expected cost function per unit time to operate the queueing system under considerations.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.11-17
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• 2001

We consider the M/G/1 with Bernoulli feedback, where the served customers wait in the feedback queue for rework with probability p. It is important to decide the moment of dispatching in feedback systems because of the dispatching cost for rework. Up to date, researches have analyzed for the instantaneous-dispatching model or the case that dispatching epoch is determined by the state of feedback queue. In this paper we deal with a dispatching model whose dispatching epoch depends on main queue. We adopt supplementary variable method for our model and a numerical example is given for clarity.

• Journal of Internet of Things and Convergence
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• v.9 no.3
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• pp.1-6
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• 2023

One of the economical ways to satisfy the quality of service desired by the user in a web service environment is to adjust the size of the object. To this end, this study finds the maximum size of objects that satisfy this constraint when the mean response time is given below an arbitrary threshold for quality of service. It can be inferred that in the steady state of system, the mean response time in the deterministic model by using the round-robin will be the same as that of the queueing model following the general distribution. Based on this, analytical formulas and procedures for finding the maximum object size are obtained. As a service distribution of web traffic, the Pareto distribution is appropriate, so the maximum object size is computed by applying the M/G(Pareto)/1 model and the M/G/1/PS model using exponential distribution as computational experience. Performance evaluation through numerical calculation shows that as the shape parameter in the Pareto distribution increases, the M/G(Pareto)/1 model and M/G/1/PS model have the same maximum object size. The results of this study can be used to environments where objects can be sized for economical web service control.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.2
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• pp.81-87
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• 2000

As for M/G/1 queueing system, we use various control policies, with which we can optimize the system. Up to now the most widely adopted policies are N-Policy, T-Policy, D-Policy, and so on. The existing researches are largely concerned to find an optimal operation condition or to optimize the system under single policy in M/G/1 system. There are, however, few literatures dealing with multiple control policies at once to enhance the flexibility of the model. In this study, we consider M/G/1 system adopting N-Policy and T-Policy simultaneously. If one of two conditions is satisfied, then, the server starts the service. We call this Min(N,T)-Policy. We find the probability distribution of the number of customers and mean waiting time in steady state and derive a cost function. Next, we seek the $N^*$, optimal threshold under various N values. Finally, we reveal the characteristics of cost function.