Analysis of Markov-modulated infinite-server queues in the central-limit regime

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\ge 0$, in the asymptotic regime in which the arrival rates $\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\alpha$, with $\alpha \in \mathbb R^+$. The specific value of $\alpha$ has a crucial impact on the result: (i) for $\alpha>1$ the system essentially behaves as an M/M/$\infty$ queue, and in the central limit theorem the centered process has to be normalized by $\sqrt{N}$; (ii) for $\alpha<1$, the centered process has to be normalized by $N^{{1-}\alpha/2}$, with the deviation matrix appearing in the expression for the variance

Bridging the Gap between Enumerative and Symbolic Model Checkers

We present a method to perform symbolic state space generation for languages with existing enumerative state generators. The method is largely independent from the chosen modelling language. We validated this on three different types of languages and tools: state-based languages (PROMELA), action-based process algebras (muCRL, mCRL2), and discrete abstractions of ODEs (Maple).\ud Only little information about the combinatorial structure of the\ud underlying model checking problem need to be provided. The key enabling data structure is the "PINS" dependency matrix. Moreover, it can be provided gradually (more precise information yield better results).\ud \ud Second, in addition to symbolic reachability, the same PINS matrix contains enough information to enable new optimizations in state space generation (transition caching), again independent from the chosen modelling language. We have also based existing optimizations, like (recursive) state collapsing, on top of PINS and hint at how to support partial order reduction techniques.\ud \ud Third, PINS allows interfacing of existing state generators to, e.g., distributed reachability tools. Thus, besides the stated novelties, the method we propose also significantly reduces the complexity of building modular yet still efficient model checking tools.\ud \ud Our experiments show that we can match or even outperform existing tools by reusing their own state generators, which we have linked into an implementation of our ideas

Hard sphere colloidal dispersions: Mechanical relaxation pertaining to thermodynamic forces

The complex viscosity of sterically stabilized (hard) silica spheres in cyclohexane has been measured between 80 Hz and 170 kHz with torsion pendulums and a nickel tube resonator. The observed relaxation behaviour can be attributed to the interplay of hydrodynamic and thermodynamic forces. The validity of the Cox-Merz rule is checked

R.F. planar magnetron sputtered ZnO films II: Electrical properties

The electrical properties of r.f. planar magnetron sputtered ZnO films are studied by means of current-voltage, capacitance-voltage and Van der Pauw measurements.\ud \ud These films are applied as piezoelectric transducers in micromechanical sensors and actuators. Their piezoelectric behaviour strongly depends on the electric properties.\ud \ud A conduction model for the polycrystalline ZnO layers is presented. This model gives a good description of the electrical behaviour, and is useful in understanding the piezoelectric properties of the films studied

A functional central limit theorem for a Markov-modulated infinite-server queue

The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under specific time-scaling; the background process is sped up by $N^{\alpha}$, the arrival rates are scaled by $N$, for $N$ large. A functional central limit theorem is derived for $M$, which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on $\alpha$ is observed. For $\alpha\leq1$ the parameters of the limiting process contain the deviation matrix associated with the background process.Comment: 4 figure

Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking

The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade.\ud \ud An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states.\ud \ud To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced.\ud \ud To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies

Optically activated ZnO/Sio2/Si cantilever beams

The photomechanical effect induced by periodically varying sub-bandgap illumination in thin ZnO films deposited on oxidized Si has been demonstrated for the first time. The efficiency of this effect is at least one order of magnitude higher as compared to the photothermal activation of Si. Thus it can be considered as a powerful optical drive for resonant sensors. A phenomenological model of the mechanisms involved in the process is proposed. The optomechanical effect can also be used as a complementary method in determination of the surface state parameters of ZnO films

Homocysteine levels and treatment effect in the prospective study of pravastatin in the elderly at risk

Objectives: To assess the effect of preventive pravastatin treatment on coronary heart disease (CHD) morbidity and mortality in older persons at risk for cardiovascular disease (CVD), stratified according to plasma levels of homocysteine.&lt;p&gt;&lt;/p&gt; Design: A post hoc subanalysis in the PROspective Study of Pravastatin in the Elderly at Risk (PROSPER), started in 1997, which is a double-blind, randomized, placebo-controlled trial with a mean follow-up of 3.2 years.&lt;p&gt;&lt;/p&gt; Setting: Primary care setting in two of the three PROSPER study sites (Netherlands and Scotland).&lt;p&gt;&lt;/p&gt; Participants: Individuals (n = 3,522, aged 70–82, 1,765 male) with a history of or risk factors for CVD were ranked in three groups depending on baseline homocysteine level, sex, and study site.&lt;p&gt;&lt;/p&gt; Intervention: Pravastatin (40 mg) versus placebo.&lt;p&gt;&lt;/p&gt; Measurements: Fatal and nonfatal CHD and mortality.&lt;p&gt;&lt;/p&gt; Results: In the placebo group, participants with a high homocysteine level (n = 588) had a 1.8 higher risk (95% confidence interval (CI) = 1.2–2.5, P = .001) of fatal and nonfatal CHD than those with a low homocysteine level (n = 597). The absolute risk reduction in fatal and nonfatal CHD with pravastatin treatment was 1.6% (95% CI = −1.6 to 4.7%) in the low homocysteine group and 6.7% (95% CI = 2.7–10.7%) in the high homocysteine group (difference 5.2%, 95% CI = 0.11–10.3, P = .046). Therefore, the number needed to treat (NNT) with pravastatin for 3.2 years for benefit related to fatal and nonfatal CHD events was 14.8 (95% CI = 9.3–36.6) for high homocysteine and 64.5 (95% CI = 21.4–∞) for low homocysteine.&lt;p&gt;&lt;/p&gt; Conclusion: In older persons at risk of CVD, those with high homocysteine are at highest risk for fatal and nonfatal CHD. With pravastatin treatment, this group has the highest absolute risk reduction and the lowest NNT to prevent fatal and nonfatal CHD.&lt;p&gt;&lt;/p&gt

Interviewer Effects on Nonresponse

In face-to-face surveys interviewers play a crucial role in making contact with and gaining cooperation from sample units. While some analyses investigate the influence of interviewers on nonresponse, they are typically restricted to single-country studies. However, interviewer training, contacting and cooperation strategies as well as survey climates may differ across countries. Combining call-record data from the European Social Survey (ESS) with data from a detailed interviewer questionnaire on attitudes and doorstep behavior we find systematic country differences in nonresponse processes, which can in part be explained by differences in interviewer characteristics, such as contacting strategies and avowed doorstep behavior.

Sea Bed Sand Waves Studied To Help Pipeline Planners

The article cites a study that offers information on the variability of sand wave characteristics in the North Sea. The sand waves variability includes a statement that pipelines may start vibrating due to turbulence generated under the free span and navigational channels often need to be dredged for ships to pass safely. The study used multi-beam measurement of three fields in the North Sea in which sand waves occur. Moreover, the study concludes that understanding the variability of sand waves can help determine the optimal depth of a pipeline trench