• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.19-29
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• 1995

In this paper, we investigate the asymptotic distributions of maximum queue length for M/G/1 and GI/M/1 systems which are positive recurrent. It is well knwon that for any positive recurrent queueing systems, the distributions of their maxima linearly normalized do not have non-degenerate limits. We show, however, that by concerning an array of queueing processes limiting behaviors of these maximum queue lengths can be established under certain conditions.

• Journal of information and communication convergence engineering
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• v.6 no.1
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• pp.19-23
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• 2008

The AQM (Active Queue Management) starts dropping packets earlier to notify traffic sources about the incipient stage of congestion. The AQM improves fairness between response flow (like TCP) and non-response flow (like UDP), and it can provide high throughput and link efficiency. In this paper, we suggest the QVARED (Queue Variation Adaptive RED) algorithm to respond to bursty traffic more actively. It is possible to provide more smoothness of average queue length and the maximum packet drop probability compared to RED and ARED (Adaptive RED). Therefore, it is highly adaptable to new congestion condition. Our simulation results show that the drop rate of QVARED is decreased by 80% and 40% compare to those of RED and ARED, respectively. This results in shorter end-to-end delay by decreasing the number of retransmitted packets. Also, the QVARED reduces a bias effect over 18% than that of drop-tail method; therefore packets are transmitted stably in the bursty traffic condition.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.95-99
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• 1983

Limiting law for maximum queue length in G/M/1 queue system is derived. Furthermore, a simple approach using mixing sequence is also discussed.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.39-45
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• 2001

Maximum and minimum of rendom variables are frequently encountered in the stochastic modelling for various OR problems. We summarize and extend characteristics of maximum and minimum, emphasizing the case in which random variables are independent and all of them except one are distributed exponential. As an application, we derive a transform-free expression for the M/G/1 queue length distribution.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.1
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• pp.36-43
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• 2002

We analyze bulk service $M/G^{b}/1$ queues using the arrival time approach of Chae et al. (2001). As a result, the decomposition property of the M/G/1 queue with generalized vacations is extended to the $M/G^{b}/1$ queue in which the batch size is exactly a constant b. We also demonstrate that the arrival time approach is useful for relating the time-average queue length PGF to that of the departure time, both for the $M/G^{b}/1$queue in which the batch size is as big as possible but up to the maximum of constant b. The case that the batch size is a random variable is also briefly mentioned.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.1
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• pp.162-172
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• 1997

In this paper, we investigated the performance of a binary feedback switch algorithm for the ABR(Available Bit Rate) service in ATM networks. A binary feedback switch is also called EFCI(Explicit Forward Congestion Indication) switch and can be classificed into input cell processing(IP) scheme according to processing methods for the EFCI bit in data-cell header. We proposed two implementation methods for the binary feedback switch according to EFCI-bit processing schemes, and analyzed the ACR(Allowed Cell Rate) of source and the queue length of switch for each scheme in steady state. In addition, we derived the upper and lower bounds for maximum and minimum queue lengths, respectively, and investigated the impact of ABR parameters on the queue length.

• Journal of Korean Society of Transportation
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• v.23 no.8 s.86
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• pp.181-191
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• 2005

This study developed an algorithm for real-time signal control based on the detection system that can collect sectional travel time. The signal control variable is maximum queue length per cycle and this variable has a sectional meaning. When a individual vehicle pass through the detector, we can gather the vehicle ID and the detected time. Therefor we can compute the travel time of an individual vehicle between consecutive detectors. This travel time informations were bisected including the delay and not. We can compute queue withdrawing time using this bisection and the max queue length is computed using the deterministic delay model. The objective function of the real-time signal control aims equalization of queue length for all direction. The distribution of the cycle is made by queue length ratios.

• Journal of Communications and Networks
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• v.5 no.3
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• pp.275-281
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• 2003

Random Early Detection (RED) [1] is an active queue management scheme which has been deployed extensively to reduce packet loss during congestion. Although RED can improve loss rates, its performance depends severely on the tuning of its operating parameters. The idea of adaptively varying RED parameters to suit the network conditions has been investigated in [2], where the maximum packet dropping probability $max_p$ has been varied. This paper focuses on adaptively varying the queue weight $\omega_q$ in conjunction with $max_p$ to improve the performance. We propose two algorithms viz., $\omega_q$-thresh and $\omega_q$-ewma to adaptively vary $\omega_q$. The performance is measured in terms of the packet loss percentage, link utilization and stability of the instantaneous queue length. We demonstrate that varying $\omega_q$ and $max_p$ together results in an overall improvement in loss percentage and queue stability, while maintaining the same link utilization. We also show that $max_p$ has a greater influence on loss percentage and queue stability as compared to $\omega_q$, and that varying $\omega_q$ has a positive influence on link utilization.

• Journal of Korean Society of Transportation
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• v.18 no.4
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• pp.75-85
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• 2000

The Purpose of this study is to analyze wether the composition of training sample have a relation with the Predictive ability and the learning results of ANNs(Artificial Neural Networks) fur predicting one cycle ahead of the queue length(veh.) in a signalized intersection. In this study, ANNs\` training sample is classified into the assumption of two cases. The first is to utilize time-series(Per cycle) data of queue length which would be detected by one detector (loop or video) The second is to use time-space correlated data(such as: a upstream feed-in flow, a link travel time, a approach maximum stationary queue length, a departure volume) which would be detected by a integrative vehicle detection systems (loop detector, video detector, RFIDs) which would be installed between the upstream node(intersection) and downstream node. The major findings from this paper is In Daechi Intersection(GangNamGu, Seoul), in the case of ANNs\` training sample constructed by time-space correlated data between the upstream node(intersection) and downstream node, the pattern recognition ability of an interrupted traffic flow is better.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1987.10a
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• pp.35-35
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• 1987

Consider a job shop that is modelled as an open queueing network of the Jackson(l957) type. All work stations in the shop have the same number of parallel servers. Two problems are studied : the loading of stations and the assignment of servers, which are represented by loading and assingment vectors, respectively. Ma jorization and arrangement orderings are established to order, respectively, the loading and the assignment vectors. It is shown that reducing the loading vector under ma jorizat ion or increasing the assignment vector under arrangement ordering will reduce the congestion in the shop in terms of reducing the total number of jobs(in the sense of likelihood ratio ordering), the maximum queue length(in the sense of stochastic ordering), and the queue-length vector( in the sense of stochastic majorization). The results can be used to supprot production planning in certain job shops, and to aid the desing of storage capacity. (OPEN QUEUEING NETWORK; WJORIZATION; ARRANGEMENT ORDERINC; LIKELIHOOD RATIO ORDERINC; STOCHASTIC ORDERING)