• Journal of Electrical Engineering and information Science
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• v.2 no.3
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• pp.29-40
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• 1997

Two asymptotic analyses of the queue length distribution at a statistical multiplexor supporting heterogeneous exponential on-off sources are considered. The first analysis is performed by approximating the cell generation rates as a multi-dimensional Ornstein-Uhlenbeck process and then applying the Benes queueing formula. In the second analysis, w state with a system of linear equations derived from the exact expressions of the dominant eigenvalue of the matrix governing the queue length distribution. Assuming that there are a large number of sources, we obtain asymptotic approximations to the dominant eigenvalue. Based on the analyses, we define a traffic descriptor to include the mean and the variance of the cell generation rate and a burstiness measure. A simple expression for the quality of service (QoS) in cell loss rate is derived in terms of the traffic descriptor parameters and the multiplexor parameters (output link capacity and buffer size). The result is then used to quantify the factors determining the required capacity of a call taking the statistical multiplexing gain into consideration. As an application of the analyses, we can use the required capacity calculation for simple yet effective connection admission control(CAC) algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.10
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• pp.1240-1243
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• 2016

In this paper, we analyze the queueing performance of cumulative distribution function (CDF)-based opportunistic scheduling over Nakagami-m Markov fading channels. We derive the formula for the average queueing delay and the queue length distribution by constructing a two-dimensional Markov chain. Using our formula, we investigate the queueing performance for various fading parameters.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.727-740
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• 1998

Controlling traffic lights at a bottleneck, in [5] a time of open passage is called optimal, if it minimizes the first moment of the asymptotic distribution of the queue length. The discussion of the first moment as function of the time of open passage is based on an analysis of the behavior of a fixed point when varying control parameters and delivers theoretical and computational aspects of the traffic problem.

• Journal of Korea Society of Industrial Information Systems
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• v.25 no.1
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• pp.89-99
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• 2020

In this paper, we consider a dyadic server control policy that combines workload control and single vacation. Customer arrives at the system with Bernoulli process, waits until his or her turn, and then receives service on FCFS(First come first served) discipline. If there is no customer to serve in the system, the idle single server spends a vacation of discrete random variable V. If the total service times of the waiting customers at the end of vacation exceeds predetermined workload threshold D, the server starts service immediately, and if the total workload of the system at the end of the vacation is less than or equal to D, the server stands by until the workload exceeds threshold and becomes busy. For the discrete-time Geo/G/1 queueing system operated under this dyadic server control policy, an idle period is analyzed and the steady-state queue length distribution is derived in a form of generating function.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.1A
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• pp.74-80
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• 2000

In this paper, we proposed the MAC protocol and analyzed the performance for CATV/LAN network which was based upon HFC(hybrid optic coaxial) increased abruptly as alternative method of high speed network. Upstream channel which analyzed very deeply for CATV/LAN network have the preferential access property depending upon that position and unidirectional property. To solve this fairness problem, we propose the CSMA-CD/U/P protocol that transm it as $P_i$ probability although data packets is immediately transmitted when it was occurred. As the analytic result and simulation, we obtained $P_i$ value and its average delay time. Also, we get its variance value and queue length distribution. The mean delay time and queue length increase as the load and number of stations increase in the CATV/LAN network.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.41 no.2
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• pp.133-141
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• 2021

The probe vehicle penetration rate is a required parameter in the estimation of entire volume, density, and queue length from probe vehicle data. The previous studies have proposed estimation methods without point detectors, which are based on probability structures for the locations of probe and non-probe vehicles; however, such methods are poorly suited to the case of multi-lane streets. Therefore, this study aimed to estimate the probe vehicle penetration rate at a multi-lane intersection and introduce a probability distribution of the queue length of each lane. Although a gap between estimates and observations was found, the estimates followed the trend of observations; the estimation could be improved by the correction factor hereafter. This study is expected to be used as a basic study for the estimation of entire volume, density, and queue length at multi-lane intersections without point detectors.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9A
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• pp.684-693
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• 2003

This paper analyzes transmissiondelays of a message and a packet in a time-varying and packet-based radio link. The paper assumes that thearrivals of messages have a Bernoulli process and the lengths of the messages a exponential distribution. To reflect the feature of the time-varying radio link, we use a two-state Markov model. From the model the mean transmission delay of and the mean queue length of the packet are analyzed in terms of the packet distribution function, the packet transmission service time, and the PER of the radio link. And the mean message transmission delay time and the mean queue length are derived using the performance indices of the packet. Numerical results show that the message arrival rate and the message length have some bounds to keep the transmission of the message steady and to improve the performance indices of the message. It can be known that the PER of the state influences on the performance indices more than the sojourn time of the state.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9B
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• pp.783-792
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• 2003

We consider a finite-buffer discrete-time queueing system with fixed-size bulk-service discipline: Geo/ $G^{B}$1/K＋B. The main purpose of this paper is to present a performance analysis of this system that has a wide range of applications in Asynchronous Transfer Mode (ATM) and other related telecommunication systems. For this purpose, we first derive the departure-epoch probabilities based on the embedded Markov chain method. Next, based on simple rate in and rate out argument, we present stable relationships for the steady-state probabilities of the queue length at different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of number of packets in the system at three different epochs and the loss probability. The numerical results are presented for a deterministic service-time distribution - a case that has gained importance in recent years.s.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.389-405
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• 1995

Output processes emanating from exit arcs in a mulitple server open Jackson network with node i having $s_i$ servers are determined. Beutler and Melamed (1978) showed, for traffics on all exit arcs of single server open Jackson network in equilibrium, that the customer streams leaving any exit set are Poisson and that the collections over all nodes which yield the Poisson departure processes are mutually independent. In this paper we generalize the above results to multiple servers open Jackson network in equilibrium. While no weak limit result is possible under the equilibrium condition, nonetheless approximations to the distributions of maximum queue lengths for no feedback nodes in multiple servers open Jackson network are established.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.6B
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• pp.895-900
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• 2010

As the diverse telecommunication services have been developed, network designers need to prevent congestion which may be caused by properties of timecorrelation and burstiness, and unpredictable statistical fluctuation of traffic streams. This paper considers the leaky bucket scheme with combined control of arrival and token rates, in which the arrival rate and the token generation interval are controlled according to the queue length. By using the embedded Markov chain and the supplementary variable methods, we obtain the queue length distribution as well as the loss probability and the mean waiting time.