• Title/Summary/Keyword: poisson's probability model

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Analysis of an M/M/1 Queue with an Attached Continuous-type (s,S)-inventory ((s,S)-정책하의 연속형 내부재고를 갖는 M/M/1 대기행렬모형 분석)

  • Park, Jinsoo;Lee, Hyeon Geun;Kim, Jong Hyeon;Yun, Eun Hyeuk;Baek, Jung Woo
    • Journal of Korea Society of Industrial Information Systems
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    • v.23 no.5
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    • pp.19-32
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    • 2018
  • This study focuses on an M/M/1 queue with an attached continuous-type inventory. The customers arrive into the system according to the Poisson process, and are served in their arrival order; i.e., first-come-first-served. The service times are assumed to be independent and identically distributed exponential random variable. At a service completion epoch, the customer consumes a random amount of inventory. The inventory is controlled by the traditional (s, S)-inventory policy with a generally distributed lead time. A customer that arrives during a stock-out period assumed to be lost. For the number of customers and the inventory size, we derive a product-form stationary joint probability distribution and provide some numerical examples. Besides, an operational strategy for the inventory that minimizes the long-term cost will also be discussed.

Microbial Risk Assessment of Non-Enterohemorrhagic Escherichia coli in Natural and Processed Cheeses in Korea

  • Kim, Kyungmi;Lee, Heeyoung;Lee, Soomin;Kim, Sejeong;Lee, Jeeyeon;Ha, Jimyeong;Yoon, Yohan
    • Food Science of Animal Resources
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    • v.37 no.4
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    • pp.579-592
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    • 2017
  • This study assessed the quantitative microbial risk of non-enterohemorrhagic Escherichia coli (EHEC). For hazard identification, hazards of non-EHEC E. coli in natural and processed cheeses were identified by research papers. Regarding exposure assessment, non-EHEC E. coli cell counts in cheese were enumerated, and the developed predictive models were used to describe the fates of non-EHEC E. coli strains in cheese during distribution and storage. In addition, data on the amounts and frequency of cheese consumption were collected from the research report of the Ministry of Food and Drug Safety. For hazard characterization, a doseresponse model for non-EHEC E. coli was used. Using the collected data, simulation models were constructed, using software @RISK to calculate the risk of illness per person per day. Non-EHEC E. coli cells in natural- (n=90) and processed-cheese samples (n=308) from factories and markets were not detected. Thus, we estimated the initial levels of contamination by Uniform distribution ${\times}$ Beta distribution, and the levels were -2.35 and -2.73 Log CFU/g for natural and processed cheese, respectively. The proposed predictive models described properly the fates of non-EHEC E. coli during distribution and storage of cheese. For hazard characterization, we used the Beta-Poisson model (${\alpha}=2.21{\times}10^{-1}$, $N_{50}=6.85{\times}10^7$). The results of risk characterization for non-EHEC E. coli in natural and processed cheese were $1.36{\times}10^{-7}$ and $2.12{\times}10^{-10}$ (the mean probability of illness per person per day), respectively. These results indicate that the risk of non-EHEC E. coli foodborne illness can be considered low in present conditions.

Performance Analysis of a Statistical Packet Voice/Data Multiplexer (통계적 패킷 음성 / 데이터 다중화기의 성능 해석)

  • 신병철;은종관
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.11 no.3
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    • pp.179-196
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    • 1986
  • In this paper, the peformance of a statistical packet voice/data multiplexer is studied. In ths study we assume that in the packet voice/data multiplexer two separate finite queues are used for voice and data traffics, and that voice traffic gets priority over data. For the performance analysis we divide the output link of the multiplexer into a sequence of time slots. The voice signal is modeled as an (M+1) - state Markov process, M being the packet generation period in slots. As for the data traffic, it is modeled by a simple Poisson process. In our discrete time domain analysis, the queueing behavior of voice traffic is little affected by the data traffic since voice signal has priority over data. Therefore, we first analyze the queueing behavior of voice traffic, and then using the result, we study the queueing behavior of data traffic. For the packet voice multiplexer, both inpur state and voice buffer occupancy are formulated by a two-dimensional Markov chain. For the integrated voice/data multiplexer we use a three-dimensional Markov chain that represents the input voice state and the buffer occupancies of voice and data. With these models, the numerical results for the performance have been obtained by the Gauss-Seidel iteration method. The analytical results have been verified by computer simylation. From the results we have found that there exist tradeoffs among the number of voice users, output link capacity, voic queue size and overflow probability for the voice traffic, and also exist tradeoffs among traffic load, data queue size and oveflow probability for the data traffic. Also, there exists a tradeoff between the performance of voice and data traffics for given inpur traffics and link capacity. In addition, it has been found that the average queueing delay of data traffic is longer than the maximum buffer size, when the gain of time assignment speech interpolation(TASI) is more than two and the number of voice users is small.

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Performance Analysis of a Packet Voice Multiplexer Using the Overload Control Strategy by Bit Dropping (Bit-dropping에 의한 Overload Control 방식을 채용한 Packet Voice Multiplexer의 성능 분석에 관한 연구)

  • 우준석;은종관
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.18 no.1
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    • pp.110-122
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    • 1993
  • When voice is transmitted through packet switching network, there needs a overload control, that is, a control for the congestion which lasts short periods and occurrs in local extents. In this thesis, we analyzed the performance of the statistical packet voice multiplexer using the overload control strategy by bit dropping. We assume that the voice is coded accordng to (4,2) embedded ADPCM and that the voice packet is generated and transmitted according to the procedures in the CCITT recomendation G. 764. For the performance analysis, we must model the superposed packet arrival process to the multiplexer as exactly as possible. It is well known that interarrival times of the packets are highly correlated and for this reason MMPP is more suited for the modelling in the viewpoint of accuracy. Hence the packet arrival process in modeled as MMPP and the matrix geometric method is used for the performance analysis. Performance analysis is similar to the MMPP IG II queueing system. But the overload control makes the service time distribution G dependent on system status or queue length in the multiplexer. Through the performance analysis we derived the probability generating function for the queue length and using this we derived the mean and standard deviation of the queue length and waiting time. The numerical results are verified through the simulation and the results show that the values embedded in the departure times and that in the arbitrary times are almost the same. Results also show bit dropping reduces the mean and the variation of the queue length and those of the waiting time.

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Heat-Wave Data Analysis based on the Zero-Inflated Regression Models (영-과잉 회귀모형을 활용한 폭염자료분석)

  • Kim, Seong Tae;Park, Man Sik
    • Journal of the Korean Data Analysis Society
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    • v.20 no.6
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    • pp.2829-2840
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    • 2018
  • The random variable with an arbitrary value or more is called semi-continuous variable or zero-inflated one in case that its boundary value is more frequently observed than expected. This means the boundary value is likely to be practically observed more than it should be theoretically under certain probability distribution. When the distribution considered is continuous, the variable is defined as semi-continuous and when one of discrete distribution is assumed for the variable, we regard it as zero-inflated. In this study, we introduce the two-part model, which consists of one part for modelling the binary response and the other part for modelling the variable greater than the boundary value. Especially, the zero-inflated regression models are explained by using Poisson distribution and negative binomial distribution. In real data analysis, we employ the zero-inflated regression models to estimate the number of days under extreme heat-wave circumstances during the last 10 years in South Korea. Based on the estimation results, we create prediction maps for the estimated number of days under heat-wave advisory and heat-wave warning by using the universal kriging, which is one of the spatial prediction methods.

Microbial Risk Assessment of High Risk Vibrio Foodborne Illness Through Raw Oyster Consumption (생굴 섭취로 인한 고병원성 Vibrio균 식중독 위해평가)

  • Ha, Jimyeong;Lee, Jeeyeon;Oh, Hyemin;Shin, Il-Shik;Kim, Young-Mog;Park, Kwon-Sam;Yoon, Yohan
    • Journal of Food Hygiene and Safety
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    • v.35 no.1
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    • pp.37-44
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    • 2020
  • This study investigated the probability of foodborne illness caused by raw oyster consumption contaminated with high risk Vibrio species such as V. vulnificus and V. cholerae. Eighty-eight raw oyster samples were collected from the south coast, west coast and Seoul areas, and examined for the prevalence of high risk Vibrio species. The growth patterns of V. vulnificus and V. cholerae in raw oysters were evaluated, and consumption frequency and amounts for raw oyster were investigated from a Korean National Health and Nutrition Examination Survey. With the collected data, a risk assessment simulation was conducted to estimate the probability of foodborne illness caused by intake of raw oysters, using @RISK. Of 88 raw oysters, there were no V. vulnificus- or V. cholerae-positive samples. Thus, initial contamination levels of Vibrio species in raw oysters were estimated by the statistical methods developed by Vose and Sanaa, and the estimated value for the both Vibrio spp. was -3.6 Log CFU/g. In raw oyster, cell counts of V. vulnificus and V. cholerae remained unchanged. The incidence of raw oyster consumers was 0.35%, and the appropriate probabilistic distribution for the consumption amounts was the exponential distribution. A risk assessment simulation model was developed with the collected data, and the probability of the foodborne illness caused by the consumption of raw oyster was 9.08×10-15 for V. vulnificus and 8.16×10-13 for V. cholerae. Consumption frequency was the first factor, influencing the probability of foodborne illness.

Evaluation of Dynamic Soil Properties Using Dynamic Tests (동적시험에 의한 동적지반특성 평가)

  • Lee, Myung Jae;Shin, Jong Ho;Kang, Ki Young;Chon, Chun Su
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.10 no.2
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    • pp.91-102
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    • 1990
  • The representative tests in this study are performed at a selected site which has the soil layers to analyze the safety and economy of the dynamic analysis for the variable soil conditions. Crosshole test and downhole test of small strain level tests and triaxial test of large strain level test are performed in the soil layers, and in the rock layers, crosshole test and downhole in-situ tests and laboratory sonic test are performed to measure the dynamic shear modulus, damping ratio, and Poisson$\acute{s}$ ratio of the soil and the rock. The correlations between the dynamic soil properties from the tests and the basic soil properties are determined through the regression analysis. The representative design value of the soil is determined by probability analysis of the test results. It is determined from the nonlinear stress-strain model in soils, and the value at small strain level is computed in rocks according to the distribution of the type of soils and the affecting variables. The constitutive value is systematized to be utilized in the analysis of the test results, and computation of the input soil data.

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