We present a comprehensive model for variable-bit-rate MPEG video streams. This model captures the bit-rate variations at multiple time scales. Long-term variations are captured by incorporating scene changes, which are most noticeable in the fluctuations of I frames. The size of an I frame is modeled by the sum of two random components: a scene-related component and an AR(2) component that accounts for the fluctuations within a scene. Two random processes of i.i.d. rvs are used to model the sizes of P and B frames, respectively. The complete model is then obtained by intermixing the three sub-models according to a given GOP pattern. It is shown that the composite model exhibits long-range dependence (LRD) in the sense that its autocorrelation function is non-summable. The LRD behavior is caused by the repetitive GOP pattern which induces periodic cross-correlations between different types of frames. Using standard statistical methods, we successfully fit our model to several empirical video traces. We then study the queueing performance for video traffic at a statistical multiplexer. The results show that the model is sufficiently accurate in predicting the queueing performance for real video streams.

On the characterization of VBR MPEG streams

Do you need to know what technique to use to evaluate the reliability of an engineered system? This self-contained guide provides comprehensive coverage of all the analytical and modeling techniques currently in use, from classical non-state and state space approaches, to newer and more advanced methods such as binary decision diagrams, dynamic fault trees, Bayesian belief networks, stochastic Petri nets, non-homogeneous Markov chains, semi-Markov processes, and phase type expansions. Readers will quickly understand the relative pros and cons of each technique, as well as how to combine different models together to address complex, real-world modeling scenarios. Numerous examples, case studies and problems provided throughout help readers put knowledge into practice, and a solutions manual and Powerpoint slides for instructors accompany the book online. This is the ideal self-study guide for students, researchers and practitioners in engineering and computer science.

Reliability and Availability Engineering: Modeling, Analysis, and Applications

We propose, in this paper, a new algorithm to compute the performability distribution. Its computational complexity is polynomial and it deals only with nonnegative numbers bounded by one. This important property allows us to determine truncation steps and so to improve the execution time of the algorithm.

/pdf/performability-analysis-a-new-algorithm-3m5z3qmp78.pdf

Performability analysis: a new algorithm

https://www.irisa.fr/dionysos/pages_perso/sericola/PAPIERS/J16.pdf

Transient analysis of stochastic fluid models

In a homogeneous finite-state Markov process, we consider the occupation times, that is, the times spent by the process in given subsets of the state space during a finite interval of time. We first derive the distribution of the occupation time of one subset and then we generalize that result to the joint distribution of occupation times of different subsets of the state space by the use of order statistics from the uniform distribution. Next, we consider the distribution of weighted sums of occupation times. We obtain forward and backward equations describing the behavior of these weighted sums and we show how these lead to simple expressions for that distribution.

/pdf/occupation-times-in-markov-processes-2gksbddev4.pdf

Occupation Times in Markov Processes

An overview on the simplex algorithm

Asymptotic solution of stochastic fluid models

Performability is a composite measure for the performance and reliability, which may be interpreted as the cumulative performance over a nite mission time. The computation of its distribution allows the user to ensure that the system will achieve a given performance level. The system is assumed to be modeled as a Markov process with nite state space and a reward rate (performance measure) is associated with each state. We propose, in this paper, a new algorithm to compute the performability distribution of fault-tolerant computer systems. The main advantage of this new algorithm is its low polynomial computational complexity. Moreover it deals only with non negative numbers bounded by one. This important property allows us to determine truncation steps and so to improve the execution time of the algorithm. Key-words: Fault tolerance, repairable systems, Markov processes, performability, performance, reliability, uniformization

/pdf/performability-analysis-of-fault-tolerant-computer-systems-28j7alr3ul.pdf

Performability analysis of fault-tolerant computer systems

In this paper, transient and asymptotic behaviors of general Markov fluid models are studied and analyzed. The input and output rates are assumed to be modulated by a finite state irreducible Markov process, which can admit states with zero effective input rate. The main advantage of the proposed methods is their accuracy and their numerical stability. For the transient solution, properties of stationary detection lead to reduce considerably the computational complexity of the algorithm. As for the asymptotic solution, it is derived from the transient one's. We apply these methods to a general Markov fluid model and we interpret the numerical results.

Hédi Nabli

Papers

Performability analysis: a new algorithm

An overview on the simplex algorithm

Asymptotic solution of stochastic fluid models

Performability analysis of fault-tolerant computer systems

Transient and Asymptotic Analysis of General Markov Fluid Models