• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.57-66
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• 2005

In this paper, we propose a method to evaluate the solutions of the renewal equations related to SPRT for Erlang distribution. In SPRT, the Average Sample Number(ASN) and type I or type II error probabilities are shown in Fredholm type integral equations. The integral equations are generally solved by the approximation method using Gaussian quadrature. For Erlang distribution, it has been known that the exact solutions of the equations exist. We propose the algorithm to solve the equations.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04d
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• pp.199-201
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• 2003

현재 셀룰러(Cellular) 코어(Core) 망에서의 회선산출은 얼랑(Erlang) B 이론으로부터 출발하고 있다 시도호(attempted call)의 특성이 포아송(Poisson)분포임을 가정한 얼랑 공식으로부터 유도된 얼랑 B 테이블을 통해 각구간의 트래픽 및 목표 호손율(Block Rate)에 맞는 적절한 회선 수를 산출한다. 본 논문에서는 유선 전화망에서 주로 쓰이던 얼랑 B 이론이 이동통신 셀룰러 코어 방에서도 적용될 수 있는지의 여부를 판단하기 위해서 1500만 이상의 가입자를 보유하고 있는 셀룰러 코어 망을 실험대상으로 하였다. 트래픽 분포 및 얼랑 B 호손율을 검증하기 위해 실측 실험을 하였으며, 과금 데이터(Billing Data)를 이용하여 실측 실험과 같은 결과를 얻기 위해 Block Generating Program을 개발하였다. 총 108개 루트(Route)에 대한 측정 실험 결과 50%의 트래픽만이 포아송 분포 특성을 만족함을 알아내었고, 포아송 분포를 벗어난 트래픽에서의 얼랑 B 테이블의 보정 방법을 실제 실험 데이터의 통계특성에 따라 도출하는 방식을 제안한다.

• The Korean Journal of Applied Statistics
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• v.28 no.1
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• pp.33-47
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• 2015

We consider an $M/E_n/1$ queueing model where customers arrive at a facility with a single server according to a Poisson process with customer service times assumed to be independent and identically distributed with Erlang distribution. We concentrate on the overshoot of the workload process in the queue. The overshoot means the excess over a threshold at the moment where the workload process exceeds the threshold. The approximation of the distribution of the overshoot was proposed by Bae et al. (2011); however, but the accuracy of the approximation was unsatisfactory. We derive an advanced approximation using the property of the Erlang distribution. Finally the newly proposed approximation is compared with the results of the previous study.

• 한국정보통신설비학회:학술대회논문집
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• 2003.08a
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• pp.321-324
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• 2003

현재 이동전화 Network 유선구간의 음성회선 산출기법은 얼랑(Erlang) B 이론을 그 바탕으로 하고 있다. 그리고 이러한 얼랑 B이론은 가입자 시도호의 특성이 포아송(Poisson)분포를 하고있음을 기본가정으로 하고 이를 바탕으로 서비스제공자가 목표하는 호손율을 달성하기 위해 필요한 회선수를 얼랑 B 테이블로 제시하고 있다. 본 논문은 실제가입자의 트래픽특성(분포) 및 얼랑 B 이론의 실측특성을 분석하여 이러한 얼랑 B 모델이 상용망에서 적정하게 적용될수 있는지를 검증하였으며 이러한 실측검증을 바탕으로 서비스 제공자의 목표호손율을 일정한 확률(신뢰도) 범위에서 보장하는 보정된 얼랑B 테이블을 제시한다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.8A
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• pp.1311-1321
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• 2001

본 논문에서는 매크로셀/마이크로셀 기반의 셀 구조의 순방향 얼랑 용량 및 outage 확률을 수학적으로 분석하였다. 각 계층 셀에는 음성 및 다양한 속도의 데이터 서비스 사용자가 균일하게 분포되어 있다고 가정하였으며 계층의 자원 분배 방법으로는 각 계층이 동일한 주파수 대역을 사용하는 대역 공유 방식을 적용하였다. 또한, 본 논문에서는 전력 제어의 불완전성에 의한 영향도 고려하였다. 대역 공유 계층셀 구조의 순방향 용량은 계층셀 기지국간 송신 전력비 및 매크로셀 내부에 위치한 마이크로셀의 상대적인 위치와 밀접한 관련이 있다는 결론을 내릴 수 있었으며 모의 실험 결과를 통해 증명하였다. 본 논문에서는 대역폭이 1.2288MHz인 1x 시스템과 광대역 3x 시스템의 순방향 얼랑 용량을 비교 분석하였으며 3x 시스템이 1x 시스템에 비해 3배 이상의 얼랑 용량 증대효과를 가진다는 것을 제시하였다.

• Journal of KIISE:Information Networking
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• v.30 no.3
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• pp.416-423
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• 2003

This paper proposes a continuous-time queuing model of a shared-buffer packet switch and an approximate algorithm. N arrival processes have heterogeneous busty traffic characteristics. The arrival processes are modeled by Coxian distribution with order 2 that is equivalent to Interruped Poisson Process. The service time is modeled by Erlang distribution with r stages. First the approximate algorithm performs the aggregation of N arrival processes as a single state variable. Next the algorithm discompose the queuing system into N subsystems which are represented by aggregated state variables. And the balance equations based on these aggregated state variables are solved for by iterative method. Finally the algorithm is validated by comparing the results with those of simulation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.4
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• pp.387-396
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• 2004

A scheme to evaluate the number of users and cell coverage of a WCDMA supporting multi-rate traffic is newly presented through calculation of the realizable Erlang capacity from a derived blocking probability and the path loss from the COST231 Walfisch-Ikegami(W) model. We evaluate the voice-data Erlang capacities at various data rates of 15 kbps to 960 kbps and it is shown that they have a linear relationship to each other. When the E$\_$b//N$\_$o/ is low from 4 ㏈ to 3 ㏈ in case of voice capacity of 50 Erlang at 8 kbps, the result shows the increase for the data capacity of 10 Erlang and the enlargement of 100 m for the cell coverage at low rate of 15 kbps, and the increase of 0.11 Erlang and the enlargement of 40 m at high rate of 960 kbps. The increase of the blocking probability results in the increase of the Erlang capacity, but not an effect on the cell coverage, and the increase of active users in a cell results in the decrease of the coverage.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.37 no.5
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• pp.1-9
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• 2000

In this paper, for the reverse link of a imperfect power controlled DS/CDMA cellular system when a mobile radio channel is a Rayleigh distributed multipath fading channel, A extended DS/CDMA blocking probability formula considering both shadowing and multipath fading is derived. Erlang capacity and equivalent channel number considering shadowing are analyzed and compared with those considering both shadowing and multipath fading, respectively. The DS/CDMA blocking probability is calculated based on the analysis method that obtains Erlang capacity and ICF(interference correction factor) using the median value of $E_{b(i)}$/ $I_{0}$ corresponding to each reverse link user Assuming that the blocking probability set 2%, it is observed that the Erlang capacity is 19.97 Erlang at the data rate $R_{b}$=9.6 kbps and 11.67 Erlang at the data rate $R_{b}$=14.4 kbps and then is less 16% and 19% than the Erlang capacity considering shadowing only, respectively. It is also shown that the effect of multipath fading must not be ignored and then exact Erlang capacity and equivalent channel numbers that the DS/CDMA cellular system can support are provided.d.d.d.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.4
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• pp.239-246
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• 2009

In this study, we analyze the mean waiting time on the nested open queueing network, where the population within each subnetwork is controlled by a semaphore queue. The queueing network can be transformed into a simpler queueing network in terms of customers waiting time. A major characteristic of this model is that the lower layer flow is halted by the state of higher layer. Since this type of queueing network does not have exact solutions for performance measure, the lower bound and upper bound on the mean waiting time are checked by comparing them with the mean waiting time in the transformed nested queueing network. Simulation estimates are obtained assuming Poisson arrivals and other phase-type arrival process, i.e., Erlang and hyper-exponential distributions. The bounds obtained can be applied to get more close approximation using the suitable approach.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 1998.10a
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• pp.107-115
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• 1998

For the purpose of building the simulation model on cargo handling capacity of container terminal, we composed a model of container logistics system which has a 4 subsystems ; cargo handling, transportation, storage system and Gate complex system. Several date used in simulation gained through spot research and basic statistic analysis using raw data from January to Jane in 1998. The results of this study are as follows ; First, average available ratio of each subsystem was G/C 50%, Y/T 57.5%, storage system 56%, Gate complex 50%, and there was no subsystem occurring specific bottleneck. Second, comparing the results of simulation to the results of basic statistics, we can verify suitability of this simulation model. Third, Comparing the results of this study to the results of existed study, we were able to confirm a change of BCTOC container logistics system under IMF situation.