Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

Techniques for the Fast Simulation of Models of Highly dependable Systems

With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system

On Efficiency and Validity of Previous Homeplug MAC Performance Analysis

The Medium Access Control protocol of Power Line Communication networks (defined in Homeplug and IEEE 1901 standards) has received relatively modest attention from the research community. As a consequence, there is only one analytic model that complies with the standardised MAC procedures and considers unsaturated conditions. We identify two important limitations of the existing analytic model: high computational expense and predicted results just prior to the predicted saturation point do not correspond to long-term network performance. In this work, we present a simplification of the previously defined analytic model of Homeplug MAC able to substantially reduce its complexity and demonstrate that the previous performance results just before predicted saturation correspond to a transitory phase. We determine that the causes of previous misprediction are common analytical assumptions and the potential occurrence of a transitory phase, that we show to be of extremely long duration under certain circumstances. We also provide techniques, both analytical and experimental, to correctly predict long-term behaviour and analyse the effect of specific Homeplug/IEEE 1901 features on the magnitude of misprediction errors

Global design of analog cells using statistical optimization techniques

We present a methodology for automated sizing of analog cells using statistical optimization in a simulation based approach. This methodology enables us to design complex analog cells from scratch within reasonable CPU time. Three different specification types are covered: strong constraints on the electrical performance of the cells, weak constraints on this performance, and design objectives. A mathematical cost function is proposed and a bunch of heuristics is given to increase accuracy and reduce CPU time to minimize the cost function. A technique is also presented to yield designs with reduced variability in the performance parameters, under random variations of the transistor technological parameters. Several CMOS analog cells with complexity levels up to 48 transistors are designed for illustration. Measurements from fabricated prototypes demonstrate the suitability of the proposed methodology