• Journal of the Korean Mathematical Society
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• v.61 no.4
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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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• v.17 no.6
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.10
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• pp.2014-2027
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• 1994

A queueing model with two input streams of different service priorities is studied. Specifically, IBP+BP/D/1 with head-of-line priority is analyzed. IBP and BP stand for Interrupted Bernoulli Process and Bernoulli Process respectively. The BP-stream customers have the higher service priority over the IBP-stream customers. An exact analysis of this priority queue is presented to derive the distributions of the state of the system at steady state, the waiting time distributions for each class of customers, and the interdeparture time distributions. The numerical results of the analysis are presented to show how the various parameters of the low and high priority arrival processes affect the performance of the system.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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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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• v.15 no.1_2
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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.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Food Science and Industry
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• v.51 no.2
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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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• v.21 no.2
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.3
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• pp.549-555
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• 2000

We propose an approximate algorithm to analyze the queuing system with n bursty and heterogeneous arrival processes. Each input process is modeled by Interrupted Bernoulli Process(IBP). We approximate N arrival processes by a single state variable and subsequently simplify the transition probability matrix of the Markov chain associated with these N arrival processes. Using this single state variable of arrival processes, we describe the state of the queuing system and analyze the system numerically with the reduced transition probability matrix. We compute the queue length distribution, the delay distribution, and the loss probability. Comparisons with simulation data show that the approximation algorithm has a good accuracy.

• Journal of applied mathematics & informatics
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• v.6 no.2
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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.