Asymptotic optimality of maximum pressure policies in stochastic processing networks

We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89--148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5--25] from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks.Comment: Published in at http://dx.doi.org/10.1214/08-AAP522 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion-type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity.Comment: 29 page

Building fault detection and diagnostics: Achieved savings, and methods to evaluate algorithm performance

Fault detection and diagnosis (FDD) represents one of the most active areas of research and commercial product development in the buildings industry. This paper addresses two questions concerning FDD implementation and advancement 1) What are today's users of FDD saving and spending on the technology? 2) What methods and datasets can be used to evaluate and benchmark FDD algorithm performance? Relevant to the first question, 26 organizations that use FDD across a total 550 buildings and 97 M sf achieved median savings of 8%. Twenty-seven FDD users reported that the median base cost for FDD software, annual recurring software cost, and annual labor cost were $8,$2.7 and $8 per monitoring point, with a median implementation size of approximately 1300 points. To address the second question, this paper describes a systematic methodology for evaluating the performance of FDD algorithms, curates an initial test dataset of air handling unit (AHU) system faults, and completes a trial to demonstrate the evaluation process on three sample FDD algorithms. The work provided a first step toward a standard evaluation of different FDD technologies. It showed the test methodology is indeed scalable and repeatable, provided an understanding of the types of insights that can be gained from algorithm performance testing, and highlighted the priorities for further expanding the test dataset

Optimization of double drive pulse pumping in Ne-like Ge x-ray lasers

Pumping of the Ne-like Ge x-ray laser with two 100 ps duration pulses (a prepulse and main pulse) is investigated using a fluid and atomic physics code coupled to a 3D ray tracing postprocessor code. The modeling predicts the optimum ratio of the irradiance of the two pulses for the maximum x-ray laser output resulting from the balance between the relative lower electron density gradients and wider gain region which is produced with a larger prepulse and the higher peak gain coefficients produced with a small prepulse. With a longer pulse interval between prepulse and main pulse, a relatively lower optimum pulse ratio is found. The threshold irradiance of the main driving pulse with a prepulse required to make an order of magnitude enhancement of laser output compared to irradiation without a prepulse is also found at 3-4x10(13) W/cm(2) for Ne-like Ge. (C) 1998 American Institute of Physics

Low Redshift QSO Lyman alpha Absorption Line Systems Associated with Galaxies

In this paper we present Monte-Carlo simulations of Lyman alpha absorption systems which originate in galactic haloes, galaxy discs and dark matter (DM) satellites around big central haloes. It is found that for strong Lyman alpha absorption lines galactic haloes and satellites can explain ~20% and 40% of the line number density of QSO absorption line key project respectively. If big galaxies indeed possess such large numbers of DM satellites and they possess gas, these satellites may play an important role for strong Lyman alpha lines. However the predicted number density of Lyman-limit systems by satellites is \~0.1 (per unit redshift), which is four times smaller than that by halo clouds. Including galactic haloes, satellites and HI discs of spirals, the predicted number density of strong lines can be as much as 60% of the HST result. The models can also predict all of the observed Lyman-limit systems. The average covering factor within 250 kpc/h is estimated to be ~0.36. And the effective absorption radius of a galaxy is estimated to be ~150 kpc/h. The models predict W_r propto rho^{-0.5} L_B^{0.15} (1+z)^{-0.5}. We study the selection effects of selection criteria similar to the imaging and spectroscopic surveys. We simulate mock observations through known QSO lines-of-sight and find that selection effects can statistically tighten the dependence of line width on projected distance. (abridged)Comment: 23 pages, 9 postscript figures; references updated, minor change in section

Scattering by a contact potential in three and lower dimensions

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur