• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.1
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• pp.101-121
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• 1997

Consider a Jackson type closed queueing network in which each queue has a single exponential server. Assume that N customers are moving among .kappa. queues. We propose a candidata procedure which yields a lower bound of the network throughput which is sharper than those which are currently available : Let (.rho.$_{1}$, ... .rho.$_{\kappa}$) be the loading vector, let x be a real number with 0 .leq. x .leq. N, and let y(x) denote that y is a function of x and be the unique positive solution of the equation. .sum.$_{i = 1}$$^{\kappa}$y(x) .rho.$_{i}$ (N - y(x) x $p_{i}$ ) = 1 Whitt [17] has shown that y(N) is a lower bound for the throughput. In this paper, we present evidence that y(N -1) is also a lower bound. In dosing so, we are led to formulate a rather general conjecture on 'quot;Migrating Critical Points'quot; (MCP). The .MCP. conjecture asserts that zeros of successive derivatives of certain rational functions migrate at an accelerating rate. We provide a proof of MCP in the polynomial case and some other special cases, including that in which the rational function has exactly two real poles and fewer than three real zeros.tion has exactly two real poles and fewer than three real zeros.

• The Transactions of the Korea Information Processing Society
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• v.5 no.5
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• pp.1162-1171
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• 1998

This paper presents a data structure that implements a mergable double-ended priority queue : namely an improved relaxed min-max-pair heap. By means of this new data structure, we suggest a parallel algorithm to merge priority queues organized in two relaxed heaps of different sizes, n and k, respectively. This new data-structure eliminates the blossomed tree and the lazying method used to merge the relaxed min-max heaps in [9]. As a result, employing max($2^{i-1}$,[(m+1/4)]) processors, this algorithm requires O(log(log(n/k))${\times}$log(n)) time. Also, on the MarPar machine, this method achieves a 35.205-fold speedup with 64 processors to merge 8 million data items which consist of two relaxed min-max heaps of different sizes.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.119-128
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• 2010

Let ${X_n,\;n\geq1}$ be a sequence of independent identically distributed (i.i.d.) random variables (r.vs.), defined on a probability space ($\Omega$,A,P), and let ${N_n,\;n\geq1}$ be a sequence of positive integer-valued r.vs., defined on the same probability space ($\Omega$,A,P). Furthermore, we assume that the r.vs. $N_n$, $n\geq1$ are independent of all r.vs. $X_n$, $n\geq1$. In present paper we are interested in asymptotic behaviors of the random sum $S_{N_n}=X_1+X_2+\cdots+X_{N_n}$, $S_0=0$, where the r.vs. $N_n$, $n\geq1$ obey some defined probability laws. Since the appearance of the Robbins's results in 1948 ([8]), the random sums $S_{N_n}$ have been investigated in the theory probability and stochastic processes for quite some time (see [1], [4], [2], [3], [5]). Recently, the random sum approach is used in some applied problems of stochastic processes, stochastic modeling, random walk, queue theory, theory of network or theory of estimation (see [10], [12]). The main aim of this paper is to establish some results related to the asymptotic behaviors of the random sum $S_{N_n}$, in cases when the $N_n$, $n\geq1$ are assumed to follow concrete probability laws as Poisson, Bernoulli, binomial or geometry.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.1
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• pp.30-37
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• 2016

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers' service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.4
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• pp.369-372
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• 2006

Suppose that a customer arrives at the GI/M/1/K queueing system when there are customers in the system, $n,m{\geq}0,\;n+m{\leq}K$. Sooner or later, the number of customers in the system will reach . In this paper, we present the Laplace transform of the remaining interarrival time upon reaching level, for the first time, since a customer arrived when there are customers in the system.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.89-94
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• 2001

There are many queueing systems where customers wait for service up to a certain amount of time and leave the system if they are not served during that time. This paper considers a finite capacity multi-server queueing system with Poisson input and Erlang service time, where a customer becomes a lost customer when his service has not begun within an exponential patient time after his arrival. Performance measures such as average queue length, the average number of customers in service, and the proportion of lost customers can be obtained exactly through the proposed numerical solution procedure.

• Convergence Security Journal
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• v.7 no.2
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• pp.39-47
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• 2007

The scheduling algorithms to provide quality of service (QoS) in broadband convergence network (BcN) are compared and analysed. The main QoS management methods such as traffic classification, traffic processing in the input queue and weighted queueing are first analysed, and then the major scheduling algorithms of round robin, priority and weighted round robin under recently considering for BcN to supply real time multimedia communications are analysed. The simulation results by NS-2 show that the scheduling algorithm with proper weights for each traffic class outperforms the priority algorithm.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.153-162
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• 1997

M/G/1 queueing system is one of the most widely used one to model the real system. When operating a real systems, since it often takes cost, some control policies that change the operation scheme are adopted. In particular, the N-policy is the most popular among many control policies. Almost all researches on queueing system are based on the assumption that the arrival rates of customers into the queueing system is constant, In this paper, we consider the M/G/1 queueing system whose arrival rate varies according to the servers status : idle, set-up and busy states. For this study, we construct the steady state equations of queue lengths by means of the supplementary variable method, and derive the PGF(probability generating function) of them. The L-S-T(Laplace Stieltjes transform) of waiting time and average waiting time are also presented. We also develop an algorithm to find the optimal N-value from which the server starts his set-up. An analysis on the performance measures to minimize total operation cost of queueing system is included. We finally investigate the behavior of system operation cost as the optimal N and arrival rate change by a numerical study.

• Journal of Korean Society of Transportation
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• v.20 no.3
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• pp.149-158
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• 2002

For the purpose of preciously describing real time traffic pattern in urban road network, dynamic network loading(DNL) models able to simulate traffic behavior are required. A number of different methods are available, including macroscopic, microscopic dynamic network models, as well as analytical model. Equivalency minimization problem and Variation inequality problem are the analytical models, which include explicit mathematical travel cost function for describing traffic behaviors on the network. While microscopic simulation models move vehicles according to behavioral car-following and cell-transmission. However, DNL models embedding such travel time function have some limitations ; analytical model has lacking of describing traffic characteristics such as relations between flow and speed, between speed and density Microscopic simulation models are the most detailed and realistic, but they are difficult to calibrate and may not be the most practical tools for large-scale networks. To cope with such problems, this paper develops a new DNL model appropriate for dynamic traffic assignment(DTA), The model is combined with vertical queue model representing vehicles as vertical queues at the end of links. In order to compare and to assess the model, we use a contrived example network. From the numerical results, we found that the DNL model presented in the paper were able to describe traffic characteristics with reasonable amount of computing time. The model also showed good relationship between travel time and traffic flow and expressed the feature of backward turn at near capacity.

• Journal of Fisheries and Marine Sciences Education
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• v.10 no.1
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• pp.1-14
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• 1998

Transportation provides an infrastructure vital to economic growth, and it is also an integral part of production. As a port is regarded as the interface between the maritime transport and domestic transport sectors, it certainly play a key role in any economic development. Ship's delay caused by port congestion has recently has recently attracted attended with the analysis of overall operation in port. In order to analyse complicated port operation which contains large number of variable factors, queueing theory is needed to be adopted, which is applicable to a large scale transportation system in chiding ship's delay in Inchon port in relation to ship's delay problem. The overall findings are as follows ; 1. The stucture of queueing model in this port can be represented as a complex of multi-channel single-phase 2. Ship's arrival and service pattern were Poisson Input Erlangian Service. 3. The suitable formula to calculate the mean delay in this port, namely, $W_q={\frac{{\rho}}{{\lambda}(1-{\rho})}}{\frac{e{\small{N}}({\rho}{\cdot}N)}{D_{N-1}({\rho}{\cdot}N)}}$ Where, ${\lambda}$ : mean arrival rate ${\mu}$ : mean servicing rate N : number of servicing channel ${\rho}$ : utilization rate (l/Nm) $e{\small{N}}$ : the Poisson function $D_{(n-1)}$ : a function of the cumulative Poisson function 4. The utility rate is 95.0 percents in general piers, 75.39 percents in container piers, and watiting time 28.43 hours in general piers, 13.67 hours in container piers, and the length of queue is 6.17 ships in general piers, 0.93 ships in container piers, and the ship turnaround time is 107.03 hours in general piers, 51.93 hours in container piers.