• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• 한국의료질향상학회지
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• 제1권2호
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• pp.60-72
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• 1994

Background: The number of outpatients visiting large university teaching hospitals has increased drastically with the introduction of a nationwide health care insurance in 1989 and the improvement of the socio-economic status of the population. This resulted in long waiting times for services, particularly prescribed drugs, which have been patients' chief complaints. Hospitals have tried to solve the problem with limited success because their approach lacked comprehensive research. The objective of this study is to investigate associations between waiting times and variables defining a total work system. Methods: Data for the outpatient pharmacy department in a tertiary care university teaching hospital located in Seoul was analyzed to achieve the study objective. Associations of pharmacy system variables -- work load, work force, pharmacist work schedule, machine problems, and inventory control -- with mean and 99th percentile of waiting times were examined by the hierarchical stepwise regression method. Day was a unit of the analyses. Results: The regression models explained 65.8% of variance in the mean waiting time and 61.34% in the 99th percentile of waiting times. The break-down of the printer for drug envelops, Automatic Tablet Counters (ATCs), and main computer system lasted longer than 30 minutes increased the mean for 7.7 minutes, 4.5 minutes, and 7.0 minutes, respectively, and the 99th percentile for 14.8 minutes, 9.0 minutes, and 15.7 minutes, respectively. Concerning the work force, study results showed that there were significant differences in the productivity of pharmacists with work experience more than three years, one to three years, and less than one year, and showed that peak time aid work by pharmacists at job assignments other than the outpatient pharmacy, part-time pharmacists, and the installation of ATCs were effective in reducing waiting times, Finally, study findings indicated that the operational policy of work assignment and rotation schedule, supply and inventory of drugs at work tables, and readiness for undisrupted work during the work hours could have a significant effect on waiting times. Conclusion: The study results indicated that efforts to reduce waiting times for prescribed drugs should be geared toward every components of the pharmacy work system ranging from work schedule of pharmacists and supply of dugs at work tables. These findings should provide hospital managers with right directions in battling the problem.

• 한국통신학회논문지
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• 제14권5호
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• pp.453-461
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• 1989

Bux의 우선도가 없는 토큰링 LAN의 해석 결과와 Cobham의 HOL 우선도의 해석 결과를 사용해서 패킷에 우선도가 있는 토큰링 LAN의 각 노드에서의 각 우선도에 대한 평균대기시간을 근사적으로 해석하였다. IEEE 802.5에 제시된 토큰링 LAN에서의 우선도 예약전송방법은 사용하지 않았다. 본 논문에서 해석한 수학적 결과와 시뮬레이션 결과를 비교하여 +-5%정도의 상대오차율을 확인하였다. 트래픽의 세기, 노드수, 패킷길이, 전송속도, 회선길이, 토큰검색시간, 우선도 동급수, 트래픽 집중율 변화에 따른 각 우선도의 지연을 분석하였다.

• 한국콘텐츠학회논문지
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• 제17권3호
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• pp.589-595
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• 2017

본 논문에서는 다양한 이동통신 서비스의 원활한 데이터 전송을 위한 적정 채널 용량의 산정 방법을 제시한다. 서비스 유형별 패킷 전송에 대한 허용 지연시간 기준을 모두 충족하기 위해서는 적정한 채널용량이 확보되어야 한다. 이러한 채널 산정 과정을 분석하기 위해 디지털 통신시스템의 이산시간 운영특성과 패킷 기반 트래픽의 집단 발생 상황을 $Geo^x$/G/1 비선점형 우선순위 대기행렬로 모델링하였다. 휴리스틱한 평균 대기시간 분석 방법을 이용하여 다양한 전송 우선순위를 갖는 서비스 유형별 평균 대기시간을 도출하였다. 이를 이용하여 무선 서비스 지연에 관한 품질 척도(QoS)를 충족시키는 적정 채널 용량의 산정 과정을 제시하였다. 본 연구 결과인 적정 채널 용량 산정 방법은 이동통신 데이터 서비스의 품질 만족도를 높이고 네트워크의 경제적 운용에 도움이 될 것으로 기대한다.

• 대한산업공학회지
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• 제21권2호
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• pp.267-288
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• 1995

We investigate a multiclass priority system with a mixed service discipline, and propose a new approach to the analysis of performance measures (mean waiting times) of the system. Customers are preferentially served in the order of priority. The service discipline at each station is either gated or exhaustive discipline. We formulate mean waiting times as functions on the state of the system. We first consider the system at an arbitrary system state to obtain explicit formulae for the mean waiting times, and then derive their steady state values by using the property of Poisson arrivals to see time averages and the generalized Little's formula.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.881-892
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• 1999

In this paper we consider a polling system with two classes of stations; high priority and low priority. High priority stations are polled more frequently than low priority stations. We derive an exact and explicit formula for computing the mean waiting times for a message when the arrival processes are batch Poisson. In general the formula requires to solve two sets of simultaneous equations By specializing them to the case of two priority classes we greatly reduce the number equations and provide a simple formula for mean waiting times. We apply the results to a data communication processing system and show that the overall mean waiting time can be reduced by using priority polling.

• Journal of Nutrition and Health
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• 제31권8호
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• pp.1347-1354
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• 1998

The purposes of this study were to : (a) anlayze wating time, service rate, arrival rate, and coustomer expectations/satisfaction in cafeteria business foodservices and (b) identify the differences in those factors between foodservices by menu managmenet systems. The samples were two business foodservices operated by contract management in Seoul. The queue, laptime , service rate, and arrival rate were measured at each foodservice by stopwatch observation. The menu type, delivery system, number of meals served , servide time, and turnover rate of each foodservic was investigated. Questionnaires were developed to survey customer expectations and satisfaction. Satistical data analysis was completed using the SAS package programs for descriptive analysis and t-test. The mean waiting time of island type dafeteria system with separte set -menu was shorter than that of the other. In both foodservices, arrival rates were not significantly different from one another , but sevice rates were significnatly high in dafeteria menu systems. The peak time of the queue was found out at combination set menu line. The separate set menu line had a higher servide rate than the combination set menu line. The mean waiting time of the island type cafeteria line was shorter than that of the straifth type . At the straight type dafeterial line, both arrival rate and service rate were higher than those of island-type. The results of this study suggested that a separate set-menu would be more desirable than a combination set-menu in case of providing set menu with cafeteria menu.

• 한국정보과학회논문지:시스템및이론
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• 제36권4호
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• pp.239-246
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• 2009

각 계층 네트워크가 세마포에 의하여 용량제한을 갖는 중첩형 대기행렬 네트워크의 평균대기시간에 관하여 연구하였다. 중첩형 대기행렬 네트워크는 고객의 대기시간 관점에서 보다 간단한 대기행렬 네트워크로 변환될 수 있다. 이러한 중첩형 대기행렬 네트워크의 가장 중요한 특성은 하위계층의 흐름이 상위 계층의 상태에 의존적이며, 제한을 받는다는 것이다. 이러한 형태의 대기행렬 네트워크는 성능분석을 정확히 할 수 없기 때문에, 변환된 중첩형 대기행렬 네트워크를 이용하여 평균대기시간에 대한 하한과 상한을 분석하고자 한다. 모의실험에 관한 측정은 도착분포가 단계형태 분포로서 포아송, 얼랑 그리고 초지수분포에 관하여 조사하였다. 이렇게 구한 범위는 추후에 좀 더 근접한 근사치를 구하는데 이용할 수 있다.

• 대한수학회논문집
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• 제13권3호
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• pp.603-627
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• 1998

The leaky bucket scheme is a promising method that regulates input traffics for preventive congestion control. In the ATM network, the input traffics are bursty and transmitted at high-speed. In order to get the low loss probability for bursty input traffics, it is known that the leaky bucket scheme with static leaky rate requires larger data buffer and token pool size. This causes the increase of the mean waiting time for an input traffic to pass the policing function, which would be inappropriate for real time traffics such as voice and video. We present the leaky bucket scheme with dynamic leaky rate in which the token generation period changes according to buffer occupancy. In the leaky bucket scheme with dynamic leaky rate, the cell loss probability and the mean waiting time are reduced in comparison with the leaky bucket scheme with static leaky rate. We analyze the performance of the proposed leaky bucket scheme in discrete-time case by assuming arrival process to be Markov-modulated Bernoulli process (MMBP).

• International Journal of Internet, Broadcasting and Communication
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• 제14권3호
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• pp.1-7
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• 2022

This paper aims to compare the mean object size of M/G/1/PS model with that of M/BP/1 model used in the web service. The mean object size is one of important measure to control and manage web service economically. M/G/1/PS model utilizes the processor sharing in which CPU rotates in round-robin order giving time quantum to multiple tasks. M/BP/1 model uses the Bounded Pareto distribution to describe the web service according to file size. We may infer that the mean waiting latencies of M/G/1/PS and M/BP/1 model are equal to the mean waiting latency of the deterministic model using the round robin scheduling with the time quantum. Based on the inference, we can find the mean object size of M/G/1/PS model and M/BP/1 model, respectively. Numerical experiments show that when the system load is smaller than the medium, the mean object sizes of the M/G/1/PS model and the M/BP/1 model become the same. In particular, when the shaping parameter is 1.5 and the lower and upper bound of the file size is small in the M/BP/1 model, the mean object sizes of M/G/1/PS model and M/BP/1 model are the same. These results confirm that it is beneficial to use a small file size in a web service.