On exceedance times for some processes with dependent increments

Let ${Z_n}_{n\ge 0}$ be a random walk with a negative drift and i.i.d. increments with heavy-tailed distribution and let $M=\sup_{n\ge 0}Z_n$ be its supremum. Asmussen & Kl{\"u}ppelberg (1996) considered the behavior of the random walk given that $M>x$, for $x$ large, and obtained a limit theorem, as $x\to\infty$, for the distribution of the quadruple that includes the time \rtreg=\rtreg(x) to exceed level $x$, position Z_{\rtreg} at this time, position Z_{\rtreg-1} at the prior time, and the trajectory up to it (similar results were obtained for the Cram\'er-Lundberg insurance risk process). We obtain here several extensions of this result to various regenerative-type models and, in particular, to the case of a random walk with dependent increments. Particular attention is given to describing the limiting conditional behavior of $\tau$. The class of models include Markov-modulated models as particular cases. We also study fluid models, the Bj{\"o}rk-Grandell risk process, give examples where the order of $\tau$ is genuinely different from the random walk case, and discuss which growth rates are possible. Our proofs are purely probabilistic and are based on results and ideas from Asmussen, Schmidli & Schmidt (1999), Foss & Zachary (2002), and Foss, Konstantopoulos & Zachary (2007).Comment: 17 page

Stabilization of an overloaded queueing network using measurement-based admission control

Admission control can be employed to avoid congestion in queueing networks subject to overload. In distributed networks the admission decisions are often based on imperfect measurements on the network state. This paper studies how the lack of complete state information affects the system performance by considering a simple network model for distributed admission control. The stability region of the network is characterized and it is shown how feedback signaling makes the system very sensitive to its parameters.Comment: Published at http://dx.doi.org/10.1239/jap/1143936256 in the Journal of Applied Probability (http://projecteuclid.org/jap) by the Applied Probability Trust (http://www.appliedprobability.org/

Regular Variation in a Fixed-Point Problem for Single- and Multiclass Branching Processes and Queues

Tail asymptotics of the solution $R$ to a fixpoint problem of type $R =_{st} Q + \sum_1^N R_m$ is derived under heavy-tailed conditions allowing both dependence between $Q$ and $N$ and the tails to be of the same order of magnitude. Similar results are derived for a $K$-class version with applications to multitype branching processes and busy periods in multiclass queues.Comment: 19 pages, 1 figur

Experiments and analysis of a compact electrothermal thruster

The description and experimental performance of a compact microwave electrothermal thruster (MET) are presented. This thruster uses a coaxial applicator to couple microwave power into a high pressure discharge. Unlike earlier experiments, it uses no fused quartz in the discharge chamber or the nozzle. This allows high temperatures in the discharge chamber without quartz erosion and melting, thereby improving thruster performance and lifetime. The thruster design is compact, enhancing its potential as a space engine. Experimental tests using nitrogen and helium propellants with input powers levels of 200 W to 1.5 kW are presented. Experimental results, which produce energy efficiencies of 20 to 60 percent and specific impulse of 250 to 450 sec, compare favorably to previous experimental MET performance

Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon g−2g-2

The well-known discrepancy in the muon $g-2$ between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon $g-2$ using full QCD.Comment: 8 pages, 11 figures, 1 table, Lattice 2017 proceedings, Granada, Spai

A "poor man's" approach to topology optimization of natural convection problems

Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational effort by use of a reduced-order model governed by simplified physics. The proposed method models the fluid flow using a potential flow model, which introduces an additional fluid property. This material property currently requires tuning of the model by comparison to numerical Navier-Stokes based solutions. Topology optimization based on the reduced-order model is shown to provide qualitatively similar designs, as those obtained using a full Navier-Stokes based model. The number of DOFs is reduced by 50% in two dimensions and the computational complexity is evaluated to be approximately 12.5% of the full model. We further compare to optimized designs obtained utilizing Newton's convection law.Comment: Preprint version. Please refer to final version in Structural Multidisciplinary Optimization https://doi.org/10.1007/s00158-019-02215-