A Survey of Probabilistic Schedulability Analysis Techniques for Real-Time Systems

With the deregulation of power industry in many countries, the traditionally vertically integrated power systems have been experiencing dramatic changes leading to competitive electricity markets. Power system planning in such an environment are now facing increasing requirements and challenges because of the deregulation. The traditional deterministic power system analyses techniques have been found in many cases have limited capability to reveal the increasing uncertainties in today's power systems. The power system operation and planning are demonstrating probabilistic characteristics which requires emphasizes on probabilistic techniques. A key probabilistic power system analysis technique is the probabilistic power system small signal stability assessment technique. With the many factors such as demand uncertainty, market price elasticity and unexpected system congestions, it is more appropriate to have probabilistic power system stability assessment results rather than a deterministic one especially for the sake of risk management in a competitive electricity market. We present a framework of probabilistic power system small signal stability assessment technique in this paper supported with detailed probabilistic analysis and case studies. The results of this paper can be used as a valuable reference for utility power system small signal stability assessment probabilistically and reliably.

This survey covers probabilistic timing analysis techniques for real-time systems. It reviews and critiques the key results in the field from its origins in 2000 to the latest research published up to the end of August 2018. The survey provides a taxonomy of the different methods used, and a classification of existing research. A detailed review is provided covering the main subject areas: static probabilistic timing analysis, measurement-based probabilistic timing analysis, and hybrid methods. In addition, research on supporting mechanisms and techniques, case studies, and evaluations is also reviewed. The survey concludes by identifying open issues, key challenges and possible directions for future research.

The reliability of OFHC (Oxygen Free High Conductivity) copper and NARloy-Z thrust chambers is assessed by applying probabilistic structural analysis techniques to incorporate design parameter variability and uncertainty. Thrust chambers specifically evaluated are the cylindrical test fixtures employed in a plug-nozzle configuration at the NASA Lewis Research Center. Direct sampling Monte Carlo simulations based on a simplified life prediction methodology established probability densities of firing cycles to structural failure. Simulated cyclic lives demonstrated modest agreement to experiment. Similarly, regions of high structural failure probability were determined using a limit state approach employing calculated cumulative distribution functions for effective stress response and an assumed material strength distribution. A probability of failure of 0.012 was calculated at the center of the coolant channel hot-gas-side wall for an OFHC milled channel. Structural response was found to be sensitive to the uncertainties in the thrust chamber thermal environment and the material's thermal expansion coefficient.

In pursuit of identifying the most accurate and efficient uncertainty modelling (UM) techniques, this paper provides an extensive review and classification of the available UM techniques for probabilistic power system stability analysis. The increased penetration of system uncertainties related to renewable energy sources, new types of loads and their fluctuations, and deregulation of the electricity markets necessitates probabilistic power system analysis. The abovementioned factors significantly affect the power system stability, which requires computationally intensive simulation, including frequency, voltage, transient, and small disturbance stability. Altogether 40 UM techniques are collated with their characteristics, advantages, disadvantages, and application areas, particularly highlighting their accuracy and efficiency (as both are crucial for power system stability applications). This review recommends the most accurate and efficient UM techniques that could be used for probabilistic stability analysis of renewable-rich power systems.

Probabilistic and statistical temporal analyses have been developed as a means of determining the worst-case execution and response times of real-time software for decades. A number of such methods have been proposed in the literature, of which the majority claim to be able to provide worst-case timing scenarios with respect to a given likelihood of a certain value being exceeded. Further, such claims are based on either some estimates associated with a probability, or probability distributions with a certain level of confidence. However, the validity of the claims are very much dependent on a number of factors, such as the achieved samples and the adopted distributions for analysis. This paper is the first one that puts side by side existing state of the art statistical and probabilistic analysis techniques, using the probabilistic analysis as the ground truth in order to asses the applicability and performance of the statistical technique. The evaluation clearly shows that for the experiments performed the approach can identify clear differences between a range of techniques and that these differences can be considered valid based on the trends expected from the academic theory.

The paper presents a comparison study of the rough sets approach and probabilistic techniques, in particular, discriminant analysis and probabilistic inductive learning, to data analysis on a common set of medical data. This study completes the comparison done in [9], by taking into account, in addition to the location model of discriminant analysis, the linear Fisherian discrimination and Bayesian tree classifiers derived via inductive learning approach. A general discussion on similarities and differences among compared methods is given. Particular attention is paid to data reduction and creation of decision rules. The outcomes of a computational experiment on the common set of data are described and discussed.

One of the most critical phases of software engineering is requirements elicitation and analysis. Success in a software project is influenced by the quality of requirements and their associated analysis since their outputs contribute to higher level design and verification decisions. Real-time software systems are event driven and contain temporal and resource limitation constraints. Natural-language-based specification and analysis of such systems are then limited to identifying functional and non-functional elements only. In order to design an architecture, or to be able to test and verify these systems, a comprehensive understanding of dependencies, concurrency, response times, and resource usage are necessary. Scenario-based analysis techniques provide a way to decompose requirements to understand the said attributes of real-time systems. However they are in themselves inadequate for providing support for all real-time attributes. This paper discusses and evaluates the suitability of certain scenario-based models in a real-time software environment and then proposes an approach, called timed automata, that constructs a formalised view of scenarios that generate timed specifications. This approach represents the operational view of scenarios with the support of a formal representation that is needed for real-time systems. Our results indicate that models with notations and semantic support for representing temporal and resource usage of scenario provide a better analysis domain.

Asthma is a chronic-episodic disease characterised by acute, symptomatic episodes of varying severity. We developed a Markov model that can be used to estimate the cost effectiveness of alternative asthma treatments. Because of the costs they incur, asthma exacerbations ('attacks') requiring intervention by a healthcare professional were a central consideration in the development of the model. Treatment success was assessed as asthma control, a composite measure based on goals defined in world-wide asthma management guidelines and in terms of quality-adjusted life-years (QALYs). The data from which the transition probabilities were derived came from patients with asthma who received either salmeterol/fluticasone propionate combination (SFC) 50/100microg or fluticasone propionate (FP) 100microg, administered twice daily via an inhaler, in a 12-week, randomised, double-blind, clinical trial. Costs were estimated from resource profiles defined for each of the model states. A key aspect of the model was the use of probabilistic sensitivity analysis techniques to examine the uncertainty in the cost-effectiveness results. Distributions were fitted to transition probabilities and to cost input parameters and values were sampled at random from these distributions using a second order Monte Carlo simulation technique. This produced a distribution for incremental cost effectiveness that was employed to construct 95% uncertainty intervals and to construct cost effectiveness acceptability curves. In this analysis, the model was run over a 12-week period using transition probabilities derived from the trial data. The results showed that treatment with SFC resulted in a higher proportion of successfully controlled weeks per patient than treatment with FP (66 vs 47%), and higher mean weekly direct asthma management costs (pound sterling 15.77 vs pound sterling 11.83; 2000 values). The average incremental cost per successfully controlled week with SFC was pound sterling 20.83. Probabilistic sensitivity analysis showed that the 95% uncertainty intervals for the incremental cost-effectiveness ratio was - pound sterling 64.94 to pound sterling 112.66. In approximately 25% of cases, SFC was dominant (more effective and less costly), but in the remaining cases, it was both more effective and more costly. It was shown that if decision makers are willing to pay approximately pound sterling 45 for an additional successfully controlled week, SFC will be the more cost-effective strategy in this patient population for 80% of the time. This is one of the first decision-analytic models of asthma to incorporate probabilistic sensitivity analysis techniques to explore uncertainty. The model's flexible yet standardised framework permits the cost effectiveness of alternative asthma management strategies in different healthcare settings to be established.

The rigorous application of static timing analysis requires a large and costly amount of detail knowledge on the hardware and software components of the system. Probabilistic Timing Analysis has potential for reducing the weight of that demand. In this paper, we present a sound measurement-based probabilistic timing analysis technique based on Extreme Value Theory. In all the experiments made as part of this work, the timing bounds determined by our technique were less than 15% pessimistic in comparison with the tightest possible bounds obtainable with any probabilistic timing analysis technique. As a point of interest to industrial users, our technique also requires a comparatively low number of measurement runs of the program under analysis, less than 650 runs were needed for the benchmarks presented in this paper.

In this paper we show how symbolic probabilistic analysis techniques for finite state systems can be successfully used to perform quantitative verification of properties and performance evaluation of communication protocols and, more in general, of entire protocol stacks and complete communication networks. In particular, we first outline our approach to the problem of verifying communication protocols, and then we present an application example of the proposed methodology to the simple Alternating Bit Protocol.

This report provides an introduction to the various probabilistic methods developed roughly between 1956--1985 for performing reliability or probabilistic uncertainty analysis on complex systems. This exposition does not include the traditional reliability methods (e.g. parallel-series systems, etc.) that might be found in the many reliability texts and reference materials (e.g. and 1977). Rather, the report centers on the relatively new, and certainly less well known across the engineering community, analytical techniques. Discussion of the analytical methods has been broken into two reports. This particular report is limited to those methods developed between 1956--1985. While a bit dated, methods described in the later portions of this report still dominate the literature and provide a necessary technical foundation for more current research. A second report (Analytical Techniques 2) addresses methods developed since 1985. The flow of this report roughly follows the historical development of the various methods so each new technique builds on the discussion of strengths and weaknesses of previous techniques. To facilitate the understanding of the various methods discussed, a simple 2-dimensional problem is used throughout the report. The problem is used for discussion purposes only; conclusions regarding the applicability and efficiency of particular methods are based on secondary analyses and a number of years of experience by the author. This document should be considered a living document in the sense that as new methods or variations of existing methods are developed, the document and references will be updated to reflect the current state of the literature as much as possible. For those scientists and engineers already familiar with these methods, the discussion will at times become rather obvious. However, the goal of this effort is to provide a common basis for future discussions and, as such, will hopefully be useful to those more intimate with probabilistic analysis and design techniques. There are clearly alternative methods of dealing with uncertainty (e.g. fuzzy set theory, possibility theory), but this discussion will be limited to those methods based on probability theory.

Here the author reviewed the previous works in literature for low power at gate level logic transformation in synthesis process. I applied the probabilistic power analysis technique with an example f = b(a+c) and same is proved using MATLAB 7.10.0 (R2010a). I showed the advantage of Binary Decision Diagram (BDD) for computing the probability of given Boolean function. The effect of technology mapping is reviewed with an example f = ab + cd using the cost metric of minimum area and minimum power mapping. The area mapped circuit has less area than the power mapped circuit but it has 22% higher switched capacitance as reported in literature. I observed that the area mapped circuit has ≈ 28 % less area and power cost has also been reduced three times of power mapped circuit for the same circuit with probability P (a, b, c = 1) = 0.5. The reason for this effective change is the transition probability (Pt). I found that in minimum area mapping the lower transition probability (Pt = 0.058) point is driven by AOI22 library having high intrinsic and load capacitance while in minimum power mapping case the lower transition probability point is driven by a much lower capacitance of G3, a NAND2 gate. Beside that internal switching capacitance of G1 and G2 is included to make the power cost so high. I also showed that a tree structure consume more power than a chain structure with an example f = abcd, the same is used to show the effect of pin ordering on transition probabilities that directly affect the dynamic power.

Most nonrandomized epidemiologic studies, and even some randomized studies [1, 2], are susceptible to more than one threat to validity (i.e., multiple biases). Bias analysis applied to these studies requires a strategy to address each important threat to yield a reasonable estimate of the total bias affecting the study and the impact that it has on the magnitude and direction of the estimate of effect. The methods described in earlier chapters can be applied separately. to adjust for one source of bias at a time; that is, a bias analysis would be conducted separately for misclassification and then for confounding and then for selection bias. Alternatively, they can be applied serially one after the other (with some important caveats on how this is done) to simultaneously quantify the biases and their associated uncertainties. Either type of adjustment, one at a time or serially, can be conducted using simple bias analysis techniques that do not produce simulation intervals or using probabilistic bias analysis techniques that do provide such intervals. In this chapter we will discuss serial adjustment using simple techniques and serial adjustment using probabilistic techniques.

Experience with Mobile Offshore Drilling Units (MODUs) in recent hurricanes in the Gulf of Mexico (GOM) has indicated the need to reassess where and how these units are sited. During hurricane Andrew (1992), several of these units moved significant distances (up to ISO km) from their original locations. In several instances there were collisions with platforms and pipelines. Also, in the case of hurricanes weather conditions can deteriorate rapidly, and timely decisions are critical to allow proper securing and evacuation of MODU's. This is particularly crucial in areas with high storm intensity and low predictability. The primary objective of this research was to develop an analytical model to evaluate MODUs' movements in response to the combined load effects of hurricane winds, waves and currents, then use a Monte-Carlo simulation process to evaluate the probability of collisions between the MODU and surrounding large facilities. The computer simulation program was developed, and has been used to investigate alternative siting strategies. The strategies investigated include location of the MODU relative to nearby facilities, capacities of the mooring systems, and incorporation of intentional 'weak links' in the mooring system to cause either the mooring to the anchor connections to break, or the anchors to drag. The results of the parametric studies of alternative siting and mooring strategies are summarized. The second objective of this research was to use probabilistic risk analysis techniques to develop a computer model to help evaluate operation and evacuation systems for MODUs. Results from the evacuation simulation model are intended to assist in developing decision criteria for securing and evacuating MODUs. Approach Fig. I summarizes the approach used to develop, verify and implement the simulation models. Based on fundamentals of statistics, hurricane forecasting and modeling, fluid dynamics, mooring strength analysis, and Monte Carlo techniques, the first step was to develop a basic simulation model, to evaluate the movement of MODUs in hurricanes. The program was then used to develop siting strategies for Mobile Offshore Drilling Units. The simulation model incorporates models of hurricane winds, waves, currents, and tracks; storm wind, wave and current forces; mooring capacity characteristics, and finally, a model of movement characteristics that takes into account free floating, intermittent grounding ('skipping'), collision 'holding', and anchor dragging characteristics of MODUs. The program allows the user to specify hurricane characteristics in a probabilistic or deterministic manner. A Monte-Carlo simulation model is utilized to perform probabilistic calculations. The model includes a Markov model to describe the probabilities associated with changes in the tracks of the hurricanes. The model incorporates variable hurricane parameters and their correlation, the storm spatial geometry, and shallow water shoaling effects. The developed program allows one to define the locations and sizes of 'critical facilities' near the MODU location, and then evaluate the probabilities of collisions between the MODU and the critical facilities. The organization and theoretical basis for the program will be detailed later in this paper. Based on the project management and network simulation techniques, a computer simulation model was developed to help evaluate operation and evacuation systems for MODUs in hurricanes. Probabilistic risk analysis and Monte Carlo techniques are used in the model to address the large uncertainties in hurricane forecasts and in the evacuation process.

Missing data are commonly thought to impede a resolved or accurate reconstruction of phylogenetic relationships, and probabilistic analysis techniques are increasingly viewed as less vulnerable to the negative effects of data incompleteness than parsimony analyses. We test both assumptions empirically by conducting parsimony and Bayesian analyses on an approximately 1.5 × 106 -cell (27 965 characters × 52 species) mustelid-procyonid molecular supermatrix with 62.7% missing entries. Contrary to the first assumption, phylogenetic relationships inferred from our analyses are fully (Bayesian) or almost fully (parsimony) resolved topologically with mostly strong support and also largely in accord with prior molecular estimations of mustelid and procyonid phylogeny derived with parsimony, Bayesian, and other probabilistic analysis techniques from smaller but complete or nearly complete data sets. Contrary to the second assumption, we found no compelling evidence in support of a relationship between the inferior performance of parsimony and taxon incompleteness (i.e. the proportion of missing character data for a taxon), although we found evidence for a connection between the inferior performance of parsimony and character incompleteness (i.e. no overlap in character data between some taxa). The relatively good performance of our analyses may be related to the large number of sampled characters, so that most taxa (even highly incomplete ones) are represented by a sufficient number of characters allowing both approaches to resolve their relationships. © The Willi Hennig Society 2009.