• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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• pp.244-246
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• 2003

We consider an AS/RS(Automated Storage/ Retrieval System) which performs single and dual commands. In this paper, we also assume that the service times of single and dual commands are differently distributed. We transform the arrival rates of storage and retrieval commands into those of single and dual commands. Using this, we propose a non-preemptive queueing model with priority for the performance analysis of a AS/RS, and obtain approximated means of queue lengths and sojourn times.

• 한국경영과학회지
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• 제30권2호
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• pp.73-80
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• 2005

In this paper, we consider characteristics of waiting times in s1n91e-server 3-node tandem queues with finite buffers, a Poisson arrival process and deterministic service times at all nodes. There are three buffers : one at the first node is infinite and the others are finite. We obtain the fact that sojourn time or departure process is independent of the capacities of the finite buffers and does not depend on the order of service times, which are the same results in the literature. Moreover, the explicit expressions of stationary waiting times in all areas of the systems can be derived as functions of the finite buffer capacities. We also disclose a relationship of waiting times in subareas of the systems between two blocking policies communication and manufacturing. Some numerical examples are also provided.

• 한국경영과학회지
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• 제30권1호
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• pp.149-159
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• 2005

In this study, we consider characteristics of stationary waiting times in single-server 2-node tandem queues with a finite buffer, a Poisson arrival process and deterministic service times. The system has two buffers: one at the first node is infinite and the other one at the second node is finite. We show that the sojourn time or departure process does not depend on the capacity of the finite buffer and on the order of nodes (service times), which are the same as the previous results. Furthermore, the explicit expressions of waiting times at the first node are given as a function of the capacity of the finite buffer and we are able to disclose a relationship of waiting times between under communication blocking and under manufacturing blocking. Some numerical examples are also given.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.881-889
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• 2005

In this study, we consider characteristics of waiting times in single-server 3-node tandem queues with a Poisson arrival process, finite buffers and deterministic or non-overlapping service times at each queue. There are three buffers: one at the first node is infinite and the others are finite. The explicit expressions of waiting times in all areas of the systems, which are driven as functions of finite buffer capacities, show that the sojourn time does not depend on the finite buffer capacities and also allow one to compute and compare characteristics of waiting times at all areas of the system under two blocking policies: communication and manufacturing blocking. As an application of these results, moreover, an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on waiting times is considered. Some numerical examples are also provided.

• 경영과학
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• 제24권1호
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• pp.25-34
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• 2007

In this study, we consider stationary waiting times in finite-buffer 3-node single-server queues in series with a Poisson arrival process and with either constant or non-overlapping service times. We assume that each node has a finite buffer except for the first node. The explicit expressions of waiting times in all areas of the stochastic system were driven as functions of finite buffer capacities. These explicit forms show that a system sojourn time does not depend on the finite buffer sizes, and also allow one to compute and compare characteristics of stationary waiting times at all areas under two blocking rules communication and manufacturing blocking. The goal of this study is to apply these results to an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on stationary waiting times at all nodes. Numerical examples are also provided.

• 대한수학회지
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• 제35권1호
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• pp.207-224
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• 1998

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

• International Journal of Reliability and Applications
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• 제8권1호
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• pp.67-82
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• 2007

This paper deals with the effectiveness analysis of an engineering system, which has two units of different strengths in parallel and one unit as a cold standby unit. Failure times for all the units have negative exponential distribution whereas their repair times have general distribution. Single server caters the need for the system. The effectiveness analysis of the system is done by using regenerative point technique. The different measures of effectiveness such as mean sojourn time, mean time to system failure, availability, busy period, etc, are derived. Cost factors also taken into consideration.

• 한국경영과학회지
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• 제23권4호
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• pp.97-109
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• 1998

In this paper, we propose a new approach to solve stochastic fluid flow models applied to the analysis of ceil loss of an ATM multiplexer. Existing stochastic fluid flow models have been analyzed by using linear differential equations. In case of large state space, however. analyzing stochastic fluid flow model without numerical errors is not easy. To avoid this numerical errors and to analyze stochastic fluid flow model with large state space. we develope a new computational algorithm. Instead of solving differential equations directly, this approach uses iterative and numerical method without calculating eigenvalues. eigenvectors and boundary coefficients. As a result, approximate solutions and upper and lower bounds are obtained. This approach can be applied to stochastic fluid flow model having general Markov chain structure as well as to the superposition of heterogeneous ON-OFF sources it can be extended to Markov process having non-exponential sojourn times.

• 한국경영과학회지
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• 제28권4호
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• pp.145-153
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• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• 산업경영시스템학회지
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• 제26권2호
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• pp.62-67
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• 2003

This paper deals with a First-Come, First-Served queueing model to analyze the behavior of heterogeneous finite source system with a single server Each sources and the processor are assumed to operate in independently Markovian environments, respectively. Each request is characterized by its own exponentially distributed source and service time with parameter depending on the state of the corresponding environment, that is, the arrival and service rates are subject to random fluctuations. Our aim is to get the usual stationary performance measures of the system, such as, utilizations, mean number of requests staying at the server, mean queue lengths, average waiting and sojourn times. In the case of fast arrivals or fast service asymptotic methods can be applied. In the intermediate situations stochastic simulation Is used. As applications of this model some problems in the field of telecommunications are treated.