• 대한수학회지
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• 제61권4호
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• pp.693-711
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• 2024

A Markov-modulated Bernoulli process is a generalization of a Bernoulli process in which the success probability evolves over time according to a Markov chain. It has been widely applied in various disciplines for modeling and analysis of systems in random environments. This paper focuses on providing analytical characterizations of the Markovmodulated Bernoulli process by introducing key metrics, including success period, failure period, and cycle. We derive expressions for the distributions and the moments of these metrics in terms of the model parameters.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권6호
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• pp.1635-1656
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• 2023

In Bayesian multi-target tracking, the Poisson multi-Bernoulli mixture (PMBM) filter is a state-of-the-art filter based on the methodology of random finite set which is a conjugate prior composed of Poisson point process (PPP) and multi-Bernoulli mixture (MBM). In order to improve the random finite set-based filter utilized in multi-target tracking of sensor scanning, this paper introduces the Poisson multi-Bernoulli mixture filter into time-matching Bayesian filtering framework and derive a tractable and principled method, namely: the time-matching Poisson multi-Bernoulli mixture (TM-PMBM) filter. We also provide the Gaussian mixture implementation of the TM-PMBM filter for linear-Gaussian dynamic and measurement models. Subsequently, we compare the performance of the TM-PMBM filter with other RFS filters based on time-matching method with different birth models under directional continuous scanning and out-of-order discontinuous scanning. The results of simulation demonstrate that the proposed filter not only can effectively reduce the influence of sampling time diversity, but also improve the estimated accuracy of target state along with cardinality.

• 한국통신학회논문지
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• 제19권10호
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• pp.2014-2027
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• 1994

이 논문에서는 서비스 우선순위가 다른 2개의 독자적인 입력 스트림을 가지는 큐잉 모델을 연구하였다. 구체적으로 head-of-line 우선 순위가 적용되는 IBP+BP/D/I시스템을 분석하였는데, 여기에는 IBP는 Interrupted Bernoulli Process를 BP는 Bernoulli Process를 표시한다. BP 스트립은 IBP 스트립에 대하여 서비스 우선권을 가진다. 본 논문은 이 우선 순위 큐에 대하여 시스템 상태의 안정상태분포와 각 클래스 별 고객의 대기 시간분포 및 출발시간 간격분포를 구할 수 잇는 정확한 분석방법을 제공하고 있다. 우선 순위가 다른 두 입력스트림의 다양한 파라미터들이 시스템의 성능에 어떠한 영향을 미치는지 보여줄 수 있는 수치적 예들도 제시하였다.

• 품질경영학회지
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• 제27권4호
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• pp.143-152
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• 1999

In Shewhart control chart, the average run length(ARL) is calculated using the mean of a conventional geometric distribution(CGD) assuming a sequence of identical and independent Bernoulli trials. In this, the success probability of CGB is the probability that any point exceeds the control limits. When the process is in-control state, there is no problem in the above assumption since the probability that any point exceeds the control limits does not change if the in-control state continues. However, if the out-of-control state begins and continues during the process, the probability of exceeding the control limits may take two forms. First, once the out-of-control state begins with exceeding probability p, it continues with the same exceeding probability p. Second, after the out-of-control state begins, the exceeding probabilities may very according to some pattern. In the first case, ARL is the mean of CGD with success probability p as usual. But in the second case, the assumption of a sequence of identical and independent Bernoulli trials is invalid and we can not use the mean of CGD as ARL. This paper concentrate on that point. By adopting one generalized binomial distribution(GBD) model that allows correlated Bernoulli trials, generalized geometric distribution(GGD) is defined and its mean is derived to find an alternative ARL when the process is in out-of-control state and the exceeding probabilities take the second form mentioned in the above. Small-scale simulation is performed to show how an alternative ARL works.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.405-414
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• 2004

This paper considers overload control in telecommunication networks. Markov-modulated Bernoulli process ( MMBP ) has been extensively used to model bursty traffics with time-correlation. Thus, we investigate the transient behavior of the queueing system MMBP/D/l/K queue with two thresholds. The model is analyzed recursively by using the generating function method. We obtain the transient queue length distribution and waiting time distribution at an arbitrary time. The transient behavior of the queueing system helps observing the temporary system behavior.

• 한국수학사학회지
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• 제20권4호
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• pp.71-84
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• 2007

베르누이가 처음으로 자연수 k에 대하여 합 $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$에 관한 공식들을 유도하는 방법을 발견하였다([4]). 그 이후, 리만 제타함수와 관련된 베르누이 수와 오일러 수에 관한 성질들이 연구되어왔다. 최근에 김태균은 $\mathbb{Z}_p$상에서 p-진 q-적분과 관련된 확장된 q-베르누이 수와 q-오일러 수, 연속된 q-정수의 멱수의 합에 관한 성질들을 밝혔다. 본 논문에서는 연속된 q-정수의 멱수의 합에 관한 역사적 배경과 발달과정을 고찰하고, 오일러 및 베르누이 수와 관련된 리만 제타함수가 해석적 함수로써 값을 가지는 문제를 q-확장된 부분의 이론으로 연구되어온 q-오일러 제타함수에 대해 체계적으로 논의한다.

• 식품과학과 산업
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• 제51권2호
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• pp.114-126
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• 2018

The production of high quality oil to meet new standard needs a 'next generation' innovative oil refining tool in paradigm shift. 'Nanoneutralization' using controlled hydrodynamic cavitation-assisted Nanoreactor is successfully being introduced and commercialized into edible oil industry and it plays a key driver for sustainable development of food processing. This emerging technology using bubble dynamics as a consequence of Bernoulli's principle by hydrodynamic cavitation in Venturi-designed multi-flow through cell is radically changing the conventionally chemical-oriented neutralization. Nanoneutralization derived by the creation of nanometer-sized bubbles formed through scientifically structured geometric channels under high pressure has been proven to improve mass transfer and reaction rate so substantially reduce the chemicals required for refined vegetable oil and to increase oil yield while even improving oil quality. More researches on science behind this revolutionary technology will help usto better understand the principle and process hence makes its potential applications expandable in extraction, refining and modification of fats and oils processing.

• International Journal of Computer Science & Network Security
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• 제21권2호
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• pp.229-237
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• 2021

Our modern 'information-hungry' age demands delivery of information at unprecedented fast rates. Timely delivery of noteworthy information about recent events can help people from different segments of life in number of ways. As world has become global village, the flow of news in terms of volume and speed demands involvement of machines to help humans to handle the enormous data. News are presented to public in forms of video, audio, image and text. News text available on internet is a source of knowledge for billions of internet users. Urdu language is spoken and understood by millions of people from Indian subcontinent. Availability of online Urdu news enable this branch of humanity to improve their understandings of the world and make their decisions. This paper uses available online Urdu news data to train machines to automatically categorize provided news. Various machine learning algorithms were used on news headline for training purpose and the results demonstrate that Bernoulli Naïve Bayes (Bernoulli NB) and Multinomial Naïve Bayes (Multinomial NB) algorithm outperformed other algorithms in terms of all performance parameters. The maximum level of accuracy achieved for the dataset was 94.278% by multinomial NB classifier followed by Bernoulli NB classifier with accuracy of 94.274% when Urdu stop words were removed from dataset. The results suggest that short text of headlines of news can be used as an input for text categorization process.

• 한국정보통신학회논문지
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• 제4권3호
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• pp.549-555
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• 2000

본 논문에서는 n개의 버스트 입력 트래픽을 처리하는 이산 시간 큐잉 모형을 분석하기 위한 근사 계산 알고리즘을 제안한다. 입력되는 각각의 버스트 트래픽은 IBP(Interrupted Bernoulli Process)로 모형화된다. 이 알고리즘은 n 개의 입력 프로세스를 하나의 상태 변수로 표시하여 n 개의 입력 프로세스로 표현된 마코프 체인(Markov Chain)의 확률 전이 상태를 단순화한다. 이렇게 단순화된 하나의 상태 변수를 이용하여 큐잉모형의 상태 전이를 표현하고 이를 완전 수치 계산에 의해 해를 구한다. 이러한 절차를 통해 구한 큐 길이, 대기 시간 분포를 시뮬레이션에 의해 구한 값과 비교하여 알고리즘의 타당성을 검증한다.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.589-598
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• 1999

Classification errors are included in sampling -with -re-placement model where items are sampled from a Bernoulli process. Bayesian imperfect inspection model is considered. In addition con-jugate prior and predctive densities for imperfect inspection model are obtained.