• 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.

• 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.

• IE interfaces
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• v.12 no.2
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• pp.312-318
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• 1999

This paper considers the cell loss probability(CLP) in a multiplexer with the superposition of heterogeneous ON/OFF sources. The input traffic is composed of k classes. Traffic of class i is the superposition of M_(i) ON/OFF sources. Recently, the method based on the Markov modulated deterministic process(MMDP) is presented. Basically, it is the discretized model of stochastic fluid flow process(SFFP) and gives the CLP very fast, but under-estimates the CLP especially when the value of estimated CLP is very low. This paper develops the discretized model of Markov modulated Poisson process(MMPP). It is a special type of switched batch Bernoulli process(SBBP). Combining the transition probability matrix of MMDP and SBBP according to the state which is characterized by the arrival rate, this paper presents hybrid algorithm. The hybrid algorithm gives better estimate of CLP than that of MMDP and faster than SBBP.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.45 no.5
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• pp.125-133
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• 2008

In this paper, we propose active queue management mechanism (Active-WRED) to guarantee quality of the high priority service class in multi-class traffic service environment. In congestion situation, this mechanism increases drop probability of low priority traffic and reduces the drop probability of the high priority traffic, therefore it can improve the quality of the high priority service. In order to analyze the performance of our mechanism we introduce the stochastic analysis of a discrete-time queueing systems for the performance evaluation of the Active Queue Management (AQM) based congestion control mechanism called Weighted Random Early Detection (WRED) using a two-state Markov-Modulated Bernoulli arrival process (MMBP-2) as the traffic source. A two-dimensional discrete-time Harkov chain is introduced to model the Active-WRED mechanism for two traffic classes (Guaranteed Service and Best Effort Service) where each dimension corresponds to a traffic class with its own parameters.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.285-295
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• 2001

We consider a queueing system under overload control to support bursty traffic. The queueing system under overload control is modelled by MMBP/D1/K queue with two thresholds on buffer. Arrival of customer is assumed to be a Markov-modulated Bernoulli process (MMBP) by considering burstiness of traffic. Analysis is done in discrete-time case. Using the generating function method, we obtain the stationary queue length distribution. Finally, the loss probability and the waiting time distribution of a customer are given.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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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).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.5A
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• pp.355-362
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• 2009

In real-time communication services, delay constraints are among the most important QoS (Quality of Service) factors. In particular, it is difficult to guarantee the delay requirement over wireless channels, since they exhibit dynamic time-varying behavior and even severe burst-errors during periods of deep fading. Channel throughput may be increased, but at the cost of the additional delays when ARQ (Automatic Repeat Request) schemes are used. For real-time communication services, it is very essential to predict data deliverability. This paper derives the delay distribution and the successful delivery probability within a given delay budget using a priori channel model and a posteriori information from the perspective of queueing theory. The Gilbert-Elliot burst-noise channel is employed as an a Priori channel model, where a two-state Markov-modulated Bernoulli process $(MMBP_2)$ is used. for a posteriori information, the channel parameters, the queue-length and the initial channel state are assumed to be given. The numerical derivation is verified and analyzed via Monte Carlo simulations. This numerical derivation is then applied to a rate control scheme for real-time video transmission, where an optimal encoding rate is determined based on the future channel capacity and the distortion of the reconstructed pictures.