Optimal sampling strategies for multiscale stochastic processes

In this paper, we determine which non-random sampling of fixed size gives the best linear predictor of the sum of a finite spatial population. We employ different multiscale superpopulation models and use the minimum mean-squared error as our optimality criterion. In multiscale superpopulation tree models, the leaves represent the units of the population, interior nodes represent partial sums of the population, and the root node represents the total sum of the population. We prove that the optimal sampling pattern varies dramatically with the correlation structure of the tree nodes. While uniform sampling is optimal for trees with ``positive correlation progression'', it provides the worst possible sampling with ``negative correlation progression.'' As an analysis tool, we introduce and study a class of independent innovations trees that are of interest in their own right. We derive a fast water-filling algorithm to determine the optimal sampling of the leaves to estimate the root of an independent innovations tree.Comment: Published at http://dx.doi.org/10.1214/074921706000000509 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Video traffic : characterization, modelling and transmission

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling of self-similar teletraffic for simulation

Recent studies of real teletraffic data in modern computer networks have shown that teletraffic exhibits self-similar (or fractal) properties over a wide range of time scales. The properties of self-similar teletraffic are very different from the traditional models of teletraffic based on Poisson, Markov-modulated Poisson, and related processes. The use of traditional models in networks characterised by self-similar processes can lead to incorrect conclusions about the performance of analysed networks. These include serious over-estimations of the performance of computer networks, insufficient allocation of communication and data processing resources, and difficulties ensuring the quality of service expected by network users. Thus, full understanding of the self-similar nature in teletraffic is an important issue. Due to the growing complexity of modern telecommunication networks, simulation has become the only feasible paradigm for their performance evaluation. In this thesis, we make some contributions to discrete-event simulation of networks with strongly-dependent, self-similar teletraffic. First, we have evaluated the most commonly used methods for estimating the self-similarity parameter H using appropriately long sequences of data. After assessing properties of available H estimators, we identified the most efficient estimators for practical studies of self-similarity. Next, the generation of arbitrarily long sequences of pseudo-random numbers possessing specific stochastic properties was considered. Various generators of pseudo-random self-similar sequences have been proposed. They differ in computational complexity and accuracy of the self-similar sequences they generate. In this thesis, we propose two new generators of self-similar teletraffic: (i) a generator based on Fractional Gaussian Noise and Daubechies Wavelets (FGN-DW), that is one of the fastest and the most accurate generators so far proposed; and (ii) a generator based on the Successive Random Addition (SRA) algorithm. Our comparative study of sequential and fixed-length self-similar pseudo-random teletraffic generators showed that the FFT, FGN-DW and SRP-FGN generators are the most efficient, both in the sense of accuracy and speed. To conduct simulation studies of telecommunication networks, self-similar processes often need to be transformed into suitable self-similar processes with arbitrary marginal distributions. Thus, the next problem addressed was how well the self-similarity and autocorrelation function of an original self-similar process are preserved when the self-similar sequences are converted into suitable self-similar processes with arbitrary marginal distributions. We also show how pseudo-random self-similar sequences can be applied to produce a model of teletraffic associated with the transmission of VBR JPEG /MPEG video. A combined gamma/Pareto model based on the application of the FGN-DW generator was used to synthesise VBR JPEG /MPEG video traffic. Finally, effects of self-similarity on the behaviour of queueing systems have been investigated. Using M/M/1/∞ as a reference queueing system with no long-range dependence, we have investigated how self-similarity and long-range dependence in arrival processes affect the length of sequential simulations being executed for obtaining steady-state results with the required level of statistical error. Our results show that the finite buffer overflow probability of a queueing system with self-similar input is much greater than the equivalent queueing system with Poisson or a short-range dependent input process, and that the overflow probability increases as the self-similarity parameter approaches one