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.

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

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

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

Quasi-free (p,pN) scattering of light neutron-rich nuclei around N = 14

Background: For many years, quasifree scattering reactions in direct kinematics have been extensively used to study the structure of stable nuclei, demonstrating the potential of this approach. The RB3 collaboration has performed a pilot experiment to study quasifree scattering reactions in inverse kinematics for a stable C12 beam. The results from that experiment constitute the first quasifree scattering results in inverse and complete kinematics. This technique has lately been extended to exotic beams to investigate the evolution of shell structure, which has attracted much interest due to changes in shell structure if the number of protons or neutrons is varied. Purpose: In this work we investigate for the first time the quasifree scattering reactions (p,pn) and (p,2p) simultaneously for the same projectile in inverse and complete kinematics for radioactive beams with the aim to study the evolution of single-particle properties from N=14 to N=15. Method: The structure of the projectiles O23, O22, and N21 has been studied simultaneously via (p,pn) and (p,2p) quasifree knockout reactions in complete inverse kinematics, allowing the investigation of proton and neutron structure at the same time. The experimental data were collected at the R3B-LAND setup at GSI at beam energies of around 400 MeV/u. Two key observables have been studied to shed light on the structure of those nuclei: the inclusive cross sections and the corresponding momentum distributions. Conclusions: The knockout reactions (p,pn) and (p,2p) with radioactive beams in inverse kinematics have provided important and complementary information for the study of shell evolution and structure. For the (p,pn) channels, indications of a change in the structure of these nuclei moving from N=14 to N=15 have been observed, i.e., from the 0d5/2 shell to the 1s1/2. This supports previous observations of a subshell closure at N=14 for neutron-rich oxygen isotopes and its weakening for the nitrogen isotopes

Strong neutron pairing in core+4n nuclei

The emission of neutron pairs from the neutron-rich N=12 isotones C18 and O20 has been studied by high-energy nucleon knockout from N19 and O21 secondary beams, populating unbound states of the two isotones up to 15 MeV above their two-neutron emission thresholds. The analysis of triple fragment-n-n correlations shows that the decay N19(-1p)C18∗→C16+n+n is clearly dominated by direct pair emission. The two-neutron correlation strength, the largest ever observed, suggests the predominance of a C14 core surrounded by four valence neutrons arranged in strongly correlated pairs. On the other hand, a significant competition of a sequential branch is found in the decay O21(-1n)O20∗→O18+n+n, attributed to its formation through the knockout of a deeply bound neutron that breaks the O16 core and reduces the number of pairs

Nuclear astrophysics with radioactive ions at FAIR

The nucleosynthesis of elements beyond iron is dominated by neutron captures in the s and r processes. However, 32 stable, proton-rich isotopes cannot be formed during those processes, because they are shielded from the s-process flow and r-process, β-decay chains. These nuclei are attributed to the p and rp process. For all those processes, current research in nuclear astrophysics addresses the need for more precise reaction data involving radioactive isotopes. Depending on the particular reaction, direct or inverse kinematics, forward or time-reversed direction are investigated to determine or at least to constrain the desired reaction cross sections. The Facility for Antiproton and Ion Research (FAIR) will offer unique, unprecedented opportunities to investigate many of the important reactions. The high yield of radioactive isotopes, even far away from the valley of stability, allows the investigation of isotopes involved in processes as exotic as the r or rp processes