scholarly journals Generalized Truncated Methods for an Efficient Solution of Retrial Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Ma Jose Domenech-Benlloch ◽  
Jose Manuel Gimenez-Guzman ◽  
Vicent Pla ◽  
Jorge Martinez-Bauset ◽  
Vicente Casares-Giner
Keyword(s):  
Closed Form ◽  
State Space ◽  
Efficient Solution ◽  
Analytic Solution ◽  
Computational Cost ◽  
Retrial Queues ◽  
Performance Parameters ◽  
Approximate Methods ◽  
Closed Form Solutions ◽  
Wide Range

We are concerned with the analytic solution of multiserver retrial queues including the impatience phenomenon. As there are not closed-form solutions to these systems, approximate methods are required. We propose two different generalized truncated methods to effectively solve this type of systems. The methods proposed are based on the homogenization of the state space beyond a given number of users in the retrial orbit. We compare the proposed methods with the most well-known methods appeared in the literature in a wide range of scenarios. We conclude that the proposed methods generally outperform previous proposals in terms of accuracy for the most common performance parameters used in retrial systems with a moderated growth in the computational cost.

scholarly journals A Semidefinite Relaxation Method for Elliptical Location

Electronics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 128
Author(s):  
Xin Wang ◽  
Ying Ding ◽  
Le Yang
Keyword(s):  
Maximum Likelihood ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Communication Systems ◽  
Computational Cost ◽  
Semidefinite Relaxation ◽  
Noise Levels ◽  
Likelihood Estimator ◽  
Closed Form Solutions ◽  
Wide Range

Wireless location is a supporting technology in many application scenarios of wireless communication systems. Recently, an increasing number of studies have been conducted on range-based elliptical location in a variety of backgrounds. Specifically, the design and implementation of position estimators are of great significance. The difficulties arising from implementing a maximum likelihood estimator for elliptical location come from the nonconvexity of the negative log-likelihood functions. The need for computational efficiency further enhances the difficulties. Traditional algorithms suffer from the problems of high computational cost and low initialization justifiability. On the other hand, existing closed-form solutions are sensitive to the measurement noise levels. We recognize that the root of these drawbacks lies in an oversimplified linear approximation of the nonconvex model, and accordingly design a maximum likelihood estimator through semidefinite relaxation for elliptical location. We relax the elliptical location problems to semidefinite programs, which can be solved efficiently with interior-point methods. Additionally, we theoretically analyze the complexity of the proposed algorithm. Finally, we design and carry out a series of simulation experiments, showing that the proposed algorithm outperforms several widely used closed-form solutions at a wide range of noise levels. Extensive results under extreme noise conditions verify the deployability of the algorithm.

Incipient Slip Conditions in the Rolling Contact of Tyred Wheels

2010 ◽  
Vol 224 (10) ◽  
pp. 2049-2054 ◽  
Author(s):  
S Reina ◽  
D A Hills ◽  
D Dini
Keyword(s):  
Contact Problem ◽  
Closed Form ◽  
Rolling Contact ◽  
Simplified Model ◽  
Practical Case ◽  
Closed Form Solutions ◽  
Steel Wheel ◽  
State Of Stress ◽  
Wide Range ◽  
Tractive Rolling

The contact problem of a driving tyred wheel, pressed and rolling over an elastically similar half-plane, is considered. Although applicable to a wide range of shrink-fitted assemblies, the simplified model is solved to study the practical case of an elastically similar steel tyre mounted on a locomotive steel wheel subjected to tractive rolling. The behaviour of the system at the tyre—substrate interface is studied using closed-form solutions to calculate the state of stress within the tyre. Conditions leading to incipient slip and/or plasticity are identified and mapped for different loads and geometries.

scholarly journals Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts

2019 ◽  
Vol 6 (4) ◽  
pp. 629-646
Author(s):  
Eyyup Aras
Keyword(s):  
Closed Form ◽  
Rotation Axis ◽  
Computational Cost ◽  
Industrial Applications ◽  
Machining Process ◽  
Moving Frames ◽  
Factors Affecting ◽  
Tube Cross Section ◽  
Closed Form Solutions ◽  
Characteristic Points

Abstract Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed. Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.

WORST-OF OPTIONS AND CORRELATION SKEW UNDER A STOCHASTIC CORRELATION FRAMEWORK

2012 ◽  
Vol 15 (07) ◽  
pp. 1250051 ◽  
Author(s):  
JACINTO MARABEL ROMO
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Term Structure ◽  
Stochastic Volatility Model ◽  
Closed Form Solutions ◽  
Stochastic Correlation ◽  
Term Structures ◽  
Volatility Model ◽  
Wide Range ◽  
Correlation Term

This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the underlying assets, as well as between their volatilities. The model accounts for the existence of correlation term structure and correlation skew. The article shows that the Wishart specification can generate different patterns corresponding to the correlation skew for a wide range of correlation term structures. Another advantage of the model is that it is analytically tractable and, hence, it is possible to obtain semi-closed-form solutions for the prices of plain vanilla options, as well as for the price of exotic derivatives. In this sense, this article develops semi-closed-form formulas for the price of European worst-of options with barriers and/or forward-start features. To motivate the introduction of the Wishart volatility model, the article compares the prices obtained under this model and under a multi-asset stochastic volatility model with constant instantaneous correlations. The results reveal the existence of a stochastic correlation premium and show that the consideration of stochastic correlation is a key element for the valuation of these structures.

scholarly journals Efficient Method to Approximately Solve Retrial Systems with Impatience

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Jose Manuel Gimenez-Guzman ◽  
M. Jose Domenech-Benlloch ◽  
Vicent Pla ◽  
Jorge Martinez-Bauset ◽  
Vicente Casares-Giner
Keyword(s):  
State Space ◽  
Decision Process ◽  
Analytic Solution ◽  
Computational Cost ◽  
Continuous Time Markov Chain ◽  
Kolmogorov Equations ◽  
Novel Technique ◽  
Polynomial Extrapolation ◽  
Markov Decision ◽  
Infinite State

We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady-state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.

scholarly journals A Robust Controlled Backward Reach Tube with (Almost) Analytic Solution for Two Dubins Cars

10.29007/mx3f ◽  
2020 ◽  
Author(s):  
Ian Mitchell
Keyword(s):  
Nonlinear Dynamics ◽  
Closed Form ◽  
Analytic Solution ◽  
High Accuracy ◽  
Reachability Problem ◽  
Game Analysis ◽  
Closed Form Solutions ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Future Challenges

Benchmark Proposal: We describe how a well-known backward reachability problem with nonlinear dynamics and adversarial inputs—based on a pursuit evasion game with two identical vehicles that have Dubins car dynamics—can be viewed as a robust controlled backward reach tube. The resulting set is nonconvex with a surface that is nondifferentiable in places, yet (mostly explicit) closed form solutions for points on the surface of this set have been derived based on a classical differential game analysis, and so these points can be sampled with high accuracy at arbitrary density. We propose this problem as a benchmark because few existing reachability algorithms can tackle robust controlled backward reach tubes despite their potential for proving the robust safety of systems, and this (almost) analytic solution exists against which to compare prospective solutions. We then describe some extensions to the problem to provide additional future challenges. Code is provided.

scholarly journals Dynamic Catalysis Fundamentals: I. Fast calculation of limit cycles in dynamic catalysis

2021 ◽  
Author(s):  
Brandon Foley ◽  
Neil Razdan
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Closed Form ◽  
Linear Systems ◽  
Computational Cost ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Closed Form Solutions ◽  
Non Linear ◽  
Non Linear Systems

Dynamic catalysis—the forced oscillation of catalytic reaction coordinate potential energy surfaces (PES)—has recently emerged as a promising method for the acceleration of heterogeneously-catalyzed reactions. Theoretical study of enhancement of rates and supra-equilibrium product yield via dynamic catalysis has, to-date, been severely limited by onerous computational demands of forward integration of stiff, coupled ordinary differential equations (ODEs) that are necessary to quantitatively describe periodic cycling between PESs. We establish a new approach that reduces, by ≳108×, the computational cost of finding the time-averaged rate at dynamic steady state (i.e. the limit cycle for linear and nonlinear systems of kinetic equations). Our developments are motivated by and conceived from physical and mathematical insight drawn from examination of a simple, didactic case study for which closed-form solutions of rate enhancement are derived in explicit terms of periods of oscillation and elementary step rate constants. Generalization of such closed-form solutions to more complex catalytic systems is achieved by introducing a periodic boundary condition requiring the dynamic steady state solution to have the same periodicity as the kinetic oscillations and solving the corresponding differential equations by linear algebra or Newton-Raphson-based approaches. The methodology is well-suited to extension to non-linear systems for which we detail the potential for multiple solutions or solutions with different periodicities. For linear and non-linear systems alike, the acute decrement in computational expense enables rapid optimization of oscillation waveforms and, consequently, accelerates understanding of the key catalyst properties that enable maximization of reaction rates, conversions, and selectivities during dynamic catalysis.

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