Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavy-traffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n\approx r+\beta \sqrtr for some scalar \beta. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.

A new subsurface record of the Pliensbachian-Toarcian, Lower Jurassic, of Yorkshire

Here, we describe the upper Pliensbachian to middle Toarcian stratigraphy of the Dove's Nest borehole, which was drilled near Whitby, North Yorkshire, in 2013. The core represents a single, continuous vertical section through unweathered, immature Lower Jurassic sedimentary rocks. The thickness of the Lias Group formations in the Dove's Nest core is approximately the same as that exposed along the North Yorkshire coast between Hawsker Bottoms and Whitby. The studied succession consists of epeiric-neritic sediments and comprises cross-laminated very fine sandstones, (oolitic) ironstones, and argillaceous mudstones. Dark argillaceous mudstone is the dominant lithology. These sediments were deposited in the Cleveland Basin, a more subsident area of an epeiric sea, the Laurasian Sea. We present a set of geochemical data that includes organic carbon isotope ratios (δ13Corg) and total organic carbon (TOC). The δ13Corg record contains a negative excursion across the Pliensbachian–Toarcian boundary and another in the lower Toarcian that corresponds to the Toarcian Oceanic Anoxic Event (T-OAE). Below the T-OAE negative excursion, δ13Corg values are less 13C-depleted than above it. We find no evidence of a long-term δ13Corg positive excursion. TOC values below the T-OAE negative excursion are lower than above it. Sedimentary evidence suggests that, during much of the Pliensbachian–Toarcian interval, the seafloor of the Cleveland Basin was above storm wave-base and that storm-driven bottom currents were responsible for much sediment erosion, transport, and redeposition during the interval of oceanic anoxia. The abrupt shifts observed in the δ13Corg record (lower Toarcian) are likely to reflect the impact of erosion by storms on the morphology of the δ13C record of the T-OAE

Probing the Z = 6 spin-orbit shell gap with (p,2p) quasi-free scattering reactions

The evolution of the traditional nuclear magic numbers away from the valley of stability is an active field of research. Experimental efforts focus on providing key spectroscopic information that will shed light into the structure of exotic nuclei and understanding the driving mechanism behind the shell evolution. In this work, we investigate the Z=6 spin-orbit shell gap towards the neutron dripline. To do so, we employed NA(p,2p)CA−1 quasi-free scattering reactions to measure the proton component of the 21+ state of 16,18,20C. The experimental findings support the notion of a moderate reduction of the proton 1p1/2−1p3/2 spin-orbit splitting, at variance to recent claims for a prevalent Z=6 magic number towards the neutron dripline.</p

Determinants and prognostic implications of Cardiac Troponin T measured by a sensitive assay in Type 2 Diabetes Mellitus

<p>Abstract</p> <p>Background</p> <p>The cardiac troponins are biomarkers used for diagnosis of myocardial injury. They are also powerful prognostic markers in many diseases and settings. Recently introduced high-sensitivity assays indicate that chronic cardiac troponin elevations are common in response to cardiovascular (CV) morbidity. Type 2 diabetes mellitus (T2DM) confers a high risk of CV disease, but little is known about chronic cardiac troponin elevations in diabetic subjects. Accordingly, we aimed to understand the prevalence, determinants, and prognostic implications of cardiac troponin T (cTnT) elevations measured with a high-sensitivity assay in patients with T2DM.</p> <p>Methods</p> <p>cTnT was measured in stored, frozen serum samples from 124 subjects enrolled in the Asker and Bærum Cardiovascular Diabetes trial at baseline and at 2-year follow-up, if availabe (96 samples available). Results were analyzed in relation to baseline variables, hospitalizations, and group assignment (multifactorial intensive versus conventional diabetes care for lowering CV risk).</p> <p>Results</p> <p>One-hundred thirteen (90 %) had detectable cTnT at baseline and of those, 22 (18 % of the total population) subjects had values above the 99th percentile for healthy controls (13.5 ng/L). Levels at baseline were associated with conventional CV risk factors (age, renal function, gender). There was a strong correlation between cTnT levels at the two time-points (r = 0.92, p > 0.001). Risk for hospitalizations during follow-up increased step-wise by quartiles of hscTnT measured at baseline (p = 0.058).</p> <p>Conclusions</p> <p>Elevations of cTnT above the 99th percentile measured by a highly sensitive assay were encountered frequently in a population of T2DM patients. cTnT levels appeared to be stable over time and associated with conventional CV risk factors. Although a clear trend was present, no statistically robust associations with adverse outcomes could be found.</p

Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle

Large deviations for polling systems

Related INRIA Research report available at : http://hal.inria.fr/docs/00/07/27/62/PDF/RR-3892.pdfInternational audienceWe aim at presenting in short the technical report, which states a sample path large deviation principle for a resealed process n-1 Qnt, where Qt represents the joint number of clients at time t in a single server 1-limited polling system with Markovian routing. The main goal is to identify the rate function. A so-called empirical generator is introduced, which consists of Q t and of two empirical measures associated with S t the position of the server at time t. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program

Effect of oral β-blocker treatment on mortality in contemporary post-myocardial infarction patients: a systematic review and meta-analysis

Aims: Guidelines concerning β-blocker treatment following acute myocardial infarction (AMI) are based on studies undertaken before the implementation of reperfusion and secondary prevention therapies. We aimed to estimate the effect of oral β-blockers on mortality in contemporary post-AMI patients with low prevalence of heart failure and/or reduced left ventricular ejection fraction. Methods and results: A random effects model was used to synthetize results of 16 observational studies published between 1 January 2000 and 30 October 2017. Publication bias was evaluated, and heterogeneity between studies examined by subgroup and random effects meta-regression analyses considering patient-related and study-level variables. The pooled estimate showed that β-blocker treatment [among 164 408 (86.8%) patients, with median follow-up time of 2.7 years] was associated with a 26% reduction in all-cause mortality [rate ratio (RR) 0.74, 95% confidence interval (CI) 0.64-0.85] with moderate heterogeneity (I2 = 67.4%). The patient-level variable mean age of the cohort explained 31.5% of between study heterogeneity. There was presence of publication bias, or small study effect, and when controlling for bias by the trim and fill simulation method, the effect disappeared (adjusted RR 0.90, 95% CI 0.77-1.04). Also, small study effect was demonstrated by a cumulative meta-analysis starting with the largest study showing no effect, with increasing effect as the smaller studies were accumulated. Conclusion: Evidence from this study suggests that there is no association between β-blockers and all-cause mortality. A possible beneficial effect in AMI survivors needs to be tested by large randomized clinical trials

Batch and continuous removal of heavy metals from industrial effluents using microbial consortia

Bio-removal of heavy metals, using microbial biomass, increasingly attracting scientific attention due to their significant role in purification of different types of wastewaters making it reusable. Heavy metals were reported to have a significant hazardous effect on human health, and while the conventional methods of removal were found to be insufficient; microbial biosorption was found to be the most suitable alternative. In this work, an immobilized microbial consortium was generated using Statistical Design of Experiment (DOE) as a robust method to screen the efficiency of the microbial isolates in heavy metal removal process. This is the first report of applying Statistical DOE to screen the efficacy of microbial isolates to remove heavy metals instead of screening normal variables. A mixture of bacterial biomass and fungal spores was used both in batch and continuous modes to remove Chromium and Iron ions from industrial effluents. Bakery yeast was applied as a positive control, and all the obtained biosorbent isolates showed more significant efficiency in heavy metal removal. In batch mode, the immobilized biomass was enclosed in a hanged tea bag-like cellulose membrane to facilitate the separation of the biosorbent from the treated solutions, which is one of the main challenges in applying microbial biosorption at large scale. The continuous flow removal was performed using fixed bed mini-bioreactor, and the process was optimized in terms of pH (6) and flow rates (1 ml/min) using Response Surface Methodology. The most potential biosorbent microbes were identified and characterized. The generated microbial consortia and process succeeded in the total removal of Chromium ions and more than half of Iron ions both from standard solutions and industrial effluents

Non-Equilibrium Statistical Physics of Currents in Queuing Networks

We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition rates between nodes. For such systems, we ask the question ``What is the most likely way for large currents to accumulate over time in a network ?'', where time is large compared to the system correlation time scale. We identify two interesting regimes. In the first regime, in which the accumulation of currents over time exceeds the expected value by a small to moderate amount (moderate large deviation), we find that the large-deviation distribution of currents is universal (independent of the interaction details), and there is no long-time and averaged over time accumulation of particles (condensation) at any nodes. In the second regime, in which the accumulation of currents over time exceeds the expected value by a large amount (severe large deviation), we find that the large-deviation current distribution is sensitive to interaction details, and there is a long-time accumulation of particles (condensation) at some nodes. The transition between the two regimes can be described as a dynamical second order phase transition. We illustrate these ideas using the simple, yet non-trivial, example of a single node with feedback.Comment: 26 pages, 5 figure

Subjective and objective outcome in congenital clubfoot; a comparative study of 204 children

<p>Abstract</p> <p>Background</p> <p>Outcome following management of congenital talipes equinovarus (clubfoot) can be assessed in a number of ways. Bjonness stated simply that <it>"the patient is the final judge of whether he has a good foot</it>"; a purely subjective assessment. Others have employed objective measures. Combining subjective evaluation with a more objective assessment of movement and position of the foot, is likely to give a more comprehensive picture of the final result of clubfoot. The purpose of this study was to compare subjective and objective outcome following management of clubfoot, and evaluate sex differences in outcome.</p> <p>Methods</p> <p>We used a patient-administered subjective assessment of outcome following treatment of clubfoot and compared it with objective anthropometry and range of movement of the ankle to assess and compare subjective and objective outcome in clubfoot. Statistical analysis was performed using Pearson correlation coefficients. Significance was tested using Student's t-test test.</p> <p>Results</p> <p>Objective outcome can be assessed using length of the foot, calf circumference and range of movement at the ankle. These are easy to measure, reproducible, and correlate well with subjective outcome. Objective outcome is comparable for boys and girls. However, subjectively, female patients and their parents are less happy with the results of management of clubfoot.</p> <p>Conclusion</p> <p>There is a correlation between the anthropometric measures and the subjective outcome and an objective grading can be designed using foot length, calf muscle bulk and range of movement at the ankle.</p