Approximating class-departure variability in tandem queues with downtime events: Regression-based variability function

Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in distribution to a Brownian motion as n goes to infinity. In particular this implies that the Brownian motion is an attractive invariant measure for the Brownian queueing operator. Our proof exploits the relationship between Brownian queues in tandem and the last-passage Brownian percolation model, developing a coupling technique in the second setting. The result is also interpreted in the related context of Brownian particles acting under one-sided reflection.

Due to the analytical intractability of general tandem queues, we develop methods to quantify the dependence among servers through simulation. Dependence is defined by the contribution queue time at each server, and contribution factors are developed based on the insight from Friedman's reduction method and Jackson networks. In a tandem queue, the dependence among stations can be either diffusion or blocking, and their impact depends on the positions relative to the bottlenecks.

We consider a tandem queueing system with m stages and finite intermediate buffer storage spaces. Each stage has a single server and the service times are independent and exponentially distributed. There is an unlimited supply of customers in front of the first stage. For this system we show that the number of customers departing from each of the m stages during the time interval [0, t] for any t ≧ 0 is strongly stochastically increasing and concave in the buffer storage capacities. Consequently the throughput of this tandem queueing system is an increasing and concave function of the buffer storage capacities. We establish this result using a sample path recursion for the departure processes from the m stages of the tandem queueing system, that may be of independent interest. The concavity of the throughput is used along with the reversibility property of tandem queues to obtain the optimal buffer space allocation that maximizes the throughput for a three-stage tandem queue.

The authors consider the problem of dynamic channel allocation in cellular networks. Each cell can use any channel, subject to the interference constraints. Channel allocation algorithms are executed by the network switch in a centralized way. The authors show how to design and use objective functions aimed at proper channel allocation and improvement of network performance. As a figure of merit of network performance, they consider the blocking probability in the network as a whole, and the maximum blocking probability in any particular cell of the network ("hot-spot" in the network). They designed three specific channel allocation policies, based on three different objective functions. Compared with two other benchmark policies, the approach shows significant improvement. Performance analysis of various channel allocation policies is virtually impossible without simulations, which are prohibitively time-consuming in the case of small blocking probabilities. The authors propose an original approximate method based on a short simulation and an analytic approximation. The method exhibits good accuracy and significant improvement in efficiency.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The approximation of normal moveout is essential for estimating the anisotropy parameters of anisotropic media. The generalized nonhyperbolic moveout approximation (GMA) brings considerable improvement in accuracy compared with known analytical approximations. However, this is still prone to relatively large errors in the presence of relatively long offsets and large anisotropic parameters, which would degrade the inversion accuracy due to error accumulation in velocity analysis. We optimize the constant coefficients for all possible groupings of the anellipticity parameter and the offset-to-depth ratio (O/D) within practical ranges. Theoretical analyses and numerical experiments indicate that the traditional optimization scheme, using the two-norm objective function solved by the least-squares method, could not provide an error-constrained result; in addition, a direct optimization without constant-coefficient extension would not lead to a satisfactory accuracy improvement. We construct the objective function using the maximum norm and solve it by using a simulated annealing algorithm; in addition, we extend the total number of constant coefficients in the GMA to achieve additional significant improvements in the accuracy. We use a normalized traveltime and offset so that the optimized constant coefficients are independent of the model. The optimized constant coefficients are obtained over a fine grid of the anellipticity parameter (0–0.5) and the O/D (0–4) that covers most practical ranges. Our optimization scheme does not increase the computational complexity but can significantly improve the accuracy. The relative error after optimization is always below a given tolerable error threshold 0.01%, which is better than the original error 0.21% of GMA. Scanning of the velocity and anellipticity parameter indicates that the original GMA has relatively large errors; in contrast, the optimized GMA can obtain more accurate results, which are essential for flattening the moveout and helpful for reducing error accumulations.

A new analytical approximation to the extended Brinkman equation

An analytical approximation of target zone exchange rate functions: the technique of collocation

Presurgical Planning With CT-Derived Fabrication of Surgical Guides

To analyze networks of queues, it is important to be able to analyze departure processes from single queues. For the M/M/s and M/G/∞ models, the stationary departure process is simple (Poisson), but in general the stationary departure process is quite complicated. As a basis for approximations, this paper shows that the stationary departure process is approximately Poisson when there are many busy slow servers in a large class of stationary G/GI/s congestion models having s servers, infinite waiting room, the first-come first-served discipline, and mutually independent and identically distributed service times that are independent of a stationary arrival process. Limit theorems are proved for the departure process in a G/GI/s system in which the number of servers and the offered load (arrival rate divided by the service rate) both increase. The asymptotic behavior of the departure process depends on the way the arrival rate changes. If the arrival rate is held fixed, so that the offered load increases by slowing down the service rate, then the departure process converges to a Poisson process. For this result, the service-time distribution is assumed to be phase-type. Other limiting behavior occurs if the arrival rate approaches zero or infinity. Convergence is established in each case by applying previous heavy-traffic limit theorems.

In the computation of turbulent boundary-layer flows and internal flows, a substantial amount of mesh points and computational effort is required to adequately resolve the intense temperature and velocity profile variations in the near wall region. In this study, analytical profile approximations are obtained for the mean velocity and temperature distribution in the wall layer; these profiles are based upon consideration of the observed coherent structure of the time-dependent wall-layer flow. The profile approximations are relatively simple analytical formulae which satisfy all the required compatibility conditions at the wall and the logarithmic behavior at the edge of the wall layer. The Reynolds analogy for heat transfer is not used in the present theory. A general method for utilizing the present wall-layer profile models in a prediction method is indicated.

Fission-fusion adaptivity in finite elements for nonlinear dynamics of shells

It is widely accepted that variations in manufacturing processes are inevitable and should be taken into account during analysis and design processes. However, estimating uncertainty propagation in an end-product caused by these variations is a very challenging task, especially when a computationally expensive effort is already needed in deterministic models, such as simulations of sheet metal forming. The focus of this article is on the variance estimation of a system response using sensitivity-based methods. A weighted three-point-based strategy for efficiently and effectively estimating the variance of a system response is proposed. Three first-order derivatives of each variable are used to describe the non-linear behaviour and estimate the variance of a system. A methodology for determining the optimal locations and weights of the three points along each axis is proposed and illustrated for the cases where each variable follows either a normal distribution or a uniform distribution. An extension of the weighted three-point-based strategy is introduced to take into account the interaction between parameters. In addition, an extension is given for mean estimation of the system response without requiring more data. The considerable improvement in accuracy compared with the traditional first-order approximation is demonstrated in a number of test problems. The proposed method requires significantly less computational effort than the Monte Carlo method.

Contradictory trends in the industrial design environment have increased uncertainty while decreasing the tolerance to uncertainty. Worst case design techniques, still widely used in industry, do not provide the accuracy required to design under these conditions. On the other hand, statistical design techniques do provide a significant improvement in accuracy, by virtue of their adaptive behavior, but at a substantial cost in computational effort. One practical solution to improving the accuracy of worst case design without sacrificing efficiency is considered here. It integrates an efficient statistical circuit simulator with worst case design tools into a hierarchical performance design process. It employs two stages of worst case analysis, calibrated with statistical circuit simulation, serving as filters to screen out circuits that easily meet their performance requirements. This focuses the use of statistical circuit simulation on those circuits for which the improved accuracy provides significant benefit. This methodology has been applied with outstanding results in design and manufacturing. >

The objective of this project was to improve numerical simulation and forecasting of regional climate by incorporating recent advances in the understanding and modeling of atmospheric aerosols, clouds, and precipitation mechanisms in an advanced regional-global numerical model. We utilized the Ocean-Land-Atmosphere Model (OLAM), which is a global model that is partly derived from the Regional Atmospheric Modeling System (RAMS). OLAM’s global grid can be configured with a high resolution locally-refined region that provides seamless two-way communication between global and regional scales of motion. The full interaction between regional and global climate is a major improvement in accuracy and applicability over conventional regional climate models (RCMs) that are one-way nested within global climate models (GCMs). When OLAM is applied as a RCM, most computational effort is concentrated in its high-resolution region, and the lower-resolution remainder of its global domain adds relatively minor computational cost while providing significant benefits.

Multidisciplinary design optimization (MDO) can be used in computer aided engineering (CAE) to efficiently improve and balance performance of automotive structures. However, large-scale MDO is not yet generally integrated within automotive product development due to several challenges, of which excessive computing times is the most important one. In this thesis, a metamodel-based MDO process that fits normal company organizations and CAE-based development processes is presented. The introduction of global metamodels offers means to increase computational efficiency and distribute work without implementing complicated multi-level MDO methods. The presented MDO process is proven to be efficient for thickness optimization studies with the objective to minimize mass. It can also be used for spot weld optimization if the models are prepared correctly. A comparison of different methods reveals that topology optimization, which requires less model preparation and computational effort, is an alternative if load cases involving simulations of linear systems are judged to be of major importance. A technical challenge when performing metamodel-based design optimization is lack of accuracy for metamodels representing complex responses including discontinuities, which are common in for example crashworthiness applications. The decision boundary from a support vector machine (SVM) can be used to identify the border between different types of deformation behaviour. In this thesis, this information is used to improve the accuracy of feedforward neural network metamodels. Three different approaches are tested; to split the design space and fit separate metamodels for the different regions, to add estimated guiding samples to the fitting set along the boundary before a global metamodel is fitted, and to use a special SVM-based sequential sampling method. Substantial improvements in accuracy are observed, and it is found that implementing SVM-based sequential sampling and estimated guiding samples can result in successful optimization studies for cases where more conventional methods fail.