Heavy-traffic asymptotic expansions for the asymptotic decay rates in theBMAP/G/1 queue

1994 ◽  
Vol 10 (2) ◽  
pp. 453-498 ◽  
Author(s):  
Gagan L. Choudhury ◽  
Ward Whitt
Keyword(s):  
Asymptotic Expansions ◽  
Heavy Traffic ◽  
Decay Rates ◽  
Asymptotic Decay

Accurate bounds for the asymptotic constant in a statistical multiplexer with homogeneous generalized binary Markov sources

2003 ◽  
Vol 40 (02) ◽  
pp. 273-292
Author(s):  
J. Xue ◽  
Attahiru Sule Alfa
Keyword(s):  
Initial Phase ◽  
Decay Rates ◽  
Upper And Lower Bounds ◽  
Asymptotic Decay ◽  
Tail Distribution ◽  
Asymptotic Constant ◽  
Phase Combination ◽  
Statistical Multiplexer ◽  
Asymptotic Decay Rate ◽  
Markov Sources

This paper considers the asymptotic tail distribution of the number of cells queued in a statistical multiplexer fed with homogeneous generalized binary Markov sources. As the asymptotic decay rate is easy to obtain, we focus our effort on bounding the asymptotic constant, which is dependent on the initial phase combination of the sources and is hard to compute even for a moderate number of sources. We derive upper and lower bounds for the asymptotic constant, taking the initial phase combination into account. Numerical experiments show the accuracy of these bounds. They also show that, while the asymptotic decay rates are the same, the variation of initial phase combination of the sources may significantly affect the asymptotic constants.

Asymptotic decay to relaxation shock fronts in two dimensions

2001 ◽  
Vol 131 (6) ◽  
pp. 1385-1410 ◽  
Author(s):  
Hailiang Liu
Keyword(s):  
Shock Front ◽  
Initial Perturbation ◽  
Two Dimensions ◽  
Decay Rates ◽  
Front Solution ◽  
Asymptotic Decay ◽  
Planar Shock ◽  
Spatial Dimensions ◽  
Shock Front Solution ◽  
Shock Fronts

We prove nonlinear stability of planar shock fronts for certain relaxation systems in two spatial dimensions. If the subcharacteristic condition is assumed and the initial perturbation is sufficiently small and the mass carried by the perturbations is not necessarily finite, then the solution converges to a shifted planar shock front solution as time t ↑ ∞. The asymptotic phase shift of shock fronts is, in general, non-zero and governed by a similarity solution to the heat equation. The asymptotic decay rate to the shock front is proved to be t−1/4 in L∞(R2) without imposing extra decay rates in space for the initial perturbations. The proofs are based on an elementary weighted energy analysis to the error equation.

Lp time asymptotic decay for general hyperbolic–parabolic balance laws with applications

2019 ◽  
Vol 16 (04) ◽  
pp. 663-700
Author(s):  
Yanni Zeng
Keyword(s):  
Lower Order ◽  
Order Term ◽  
General System ◽  
Decay Rates ◽  
Lower Order Term ◽  
Logistic Growth ◽  
Balance Laws ◽  
Asymptotic Decay ◽  
Decay Of Solutions ◽  
Special Cases

We study the time asymptotic decay of solutions for a general system of hyperbolic–parabolic balance laws in one space dimension. The system has a physical viscosity matrix and a lower-order term for relaxation, damping or chemical reaction. The viscosity matrix and the Jacobian matrix of the lower-order term are rank deficient. For Cauchy problem around a constant equilibrium state, existence of solution global in time has been established recently under a set of reasonable assumptions. In this paper, we obtain optimal [Formula: see text] decay rates for [Formula: see text]. Our result is general and applies to models such as Keller–Segel equations with logarithmic chemotactic sensitivity and logistic growth, and gas flows with translational and vibrational non-equilibrium. Our result also recovers or improves the existing results in literature on the special cases of hyperbolic–parabolic conservation laws and hyperbolic balance laws, respectively.

Accurate bounds for the asymptotic constant in a statistical multiplexer with homogeneous generalized binary Markov sources

2003 ◽  
Vol 40 (02) ◽  
pp. 273-292
Author(s):  
J. Xue ◽  
Attahiru Sule Alfa
Keyword(s):  
Initial Phase ◽  
Decay Rates ◽  
Upper And Lower Bounds ◽  
Asymptotic Decay ◽  
Tail Distribution ◽  
Asymptotic Constant ◽  
Phase Combination ◽  
Statistical Multiplexer ◽  
Asymptotic Decay Rate ◽  
Markov Sources

This paper considers the asymptotic tail distribution of the number of cells queued in a statistical multiplexer fed with homogeneous generalized binary Markov sources. As the asymptotic decay rate is easy to obtain, we focus our effort on bounding the asymptotic constant, which is dependent on the initial phase combination of the sources and is hard to compute even for a moderate number of sources. We derive upper and lower bounds for the asymptotic constant, taking the initial phase combination into account. Numerical experiments show the accuracy of these bounds. They also show that, while the asymptotic decay rates are the same, the variation of initial phase combination of the sources may significantly affect the asymptotic constants.

scholarly journals Definition and properties of disequilibria within nuclear-mitochondrial-chloroplast and other nuclear-dicytoplasmic systems.

Genetics ◽  
1989 ◽  
Vol 123 (1) ◽  
pp. 199-215
Author(s):  
A Schnabel ◽  
M A Asmussen
Keyword(s):  
Dynamical Behavior ◽  
Extreme Case ◽  
Decay Rates ◽  
Initial Increase ◽  
Mixed Mating ◽  
Asymptotic Decay ◽  
Sign Change ◽  
Sign Patterns ◽  
Self Fertilization ◽  
Nuclear Locus

Abstract We define and determine the interrelationships among five sets of disequilibrium parameters that measure two- and three-locus nonrandom associations in nuclear-dicytoplasmic systems. These assume a diploid nuclear locus and two haploid cytoplasmic loci, with special reference to nuclear-mitochondrial-chloroplast systems. Three sets of two-locus disequilibria measure the association between haplotypes at the two cytoplasmic loci (DMC) and associations between each cytoplasmic locus and nuclear alleles or genotypes (DM, D1M, D2M, D3M; DC, D1C, D2C, D3C). In addition, we present two classes of higher-order disequilibria that measure nonrandom allelic or genotypic associations involving all three loci. The first class quantifies associations between the nuclear locus and the two cytoplasmic loci taken jointly (DA/MC, DAA/MC, DAa/MC, Daa/MC, etc.), whereas the second measures only those associations remaining after all two-locus associations have been taken into account (DA/M/C, DAA/M/C, DAa/M/C, Daa/M/C). Based on combinations of these five sets of measures, we suggest a variety of parameterizations of three-locus, nuclear-dicytoplasmic systems. The dynamics of these disequilibria are then investigated under models of random and mixed mating, either with both cytoplasmic genomes inherited through the same parent or through opposite parents. Except for associations between the cytoplasmic haplotypes, which are constant when the two cytoplasmic genomes are inherited through the same parent, all disequilibria ultimately decay to zero. These randomizations do not necessarily occur monotonically, however, and in some cases are preceded by an initial increase in magnitude or sign change. For both inheritance patterns, the asymptotic decay rates are steadily retarded by increasing levels of self-fertilization. This behavior contrasts with that in the extreme case of complete selfing, for which only the heterozygote disequilibria always decay to zero. For all models considered, the dynamics of the two-locus cytonuclear subsystems are solely a function of the mating system, whereas the dynamical behavior and sign patterns of the cytoplasmic and three-locus disequilibria also depend strongly on the mode of cytoplasmic inheritance.

Analisis Daya Dukung Tanah Dan Bahan Pondasi Tiang Pancang Pada Pembangunan Jembatan Kab. Jombang

2020 ◽  
Vol 9 (1) ◽  
pp. 32-37
Author(s):  
Ruslan Hidayat ◽  
Saiful Arfaah
Keyword(s):  
Carrying Capacity ◽  
Pile Foundation ◽  
Heavy Traffic ◽  
Traffic Volume ◽  
Material Strength ◽  
Cone Penetrometer ◽  
The Village

One of the most important factors in the structure of the pile foundation in the construction of the bridge is the carrying capacity of the soil so as not to collapse. Construction of a bridge in the village of Klitik in Jombang Regency to be built due to heavy traffic volume. The foundation plan to be used is a pile foundation with a diameter of 50 cm, the problem is what is the value of carrying capacity of soil and material. The equipment used is the Dutch Cone Penetrometer with a capacity of 2.50 tons with an Adhesion Jacket Cone. The detailed specifications of this sondir are as follows: Area conus 10 cm², piston area 10 cm², coat area 100 cm², as for the results obtained The carrying capacity of the soil is 60.00 tons for a diameter of 30 cm, 81,667 tons for a diameter of 35 cm, 106,667 tons for a diameter of 40 cm, 150,000 tons for a diameter of 50 cm for material strength of 54,00 tons for a diameter of 30 cm, 73,500 tons for a diameter of 35 cm, 96,00 tons for a diameter of 40 cm, 166,666 tons for a diameter of 50 cm

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