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.

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 TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS

2008 ◽  
Vol 18 (04) ◽  
pp. 511-541 ◽  
Author(s):  
WENLIANG GAO ◽  
CHANGJIANG ZHU
Keyword(s):  
Cauchy Problem ◽  
Maximum Principle ◽  
Coupled System ◽  
Model System ◽  
Two Dimensions ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
The Maximum Principle ◽  
The Cauchy Problem ◽  
Asymptotic Decay Rate

In this paper, we consider the asymptotic decay rate towards the planar rarefaction waves to the Cauchy problem for a hyperbolic–elliptic coupled system called as a model system of the radiating gas in two dimensions. The analysis based on the standard L2-energy method, L1-estimate and the monotonicity of profile obtained by the maximum principle.

Economies of scale in queues with sources having power-law large deviation scalings

1996 ◽  
Vol 33 (3) ◽  
pp. 840-857 ◽  
Author(s):  
N. G. Duffield
Keyword(s):  
Power Law ◽  
Generating Functions ◽  
Economies Of Scale ◽  
Shape Function ◽  
Large Deviation ◽  
Rate Function ◽  
Uhlenbeck Process ◽  
Asymptotic Decay ◽  
Potential Structure ◽  
Asymptotic Decay Rate

We analyse the queue QL at a multiplexer with L sources which may display long-range dependence. This includes, for example, sources modelled by fractional Brownian motion (FBM). The workload processes W due to each source are assumed to have large deviation properties of the form P[Wt/a(t) > x] ≈ exp[– v(t)K(x)] for appropriate scaling functions a and v, and rate-function K. Under very general conditions limL→xL–1 log P[QL > Lb] = – I(b), provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. For power-law scalings v(t) = tv, a(t) = ta (such as occur in FBM) we analyse the asymptotics of the shape function limb→xb–u/a(I(b) – δbv/a) = vu for some exponent u and constant v depending on the sources. This demonstrates the economies of scale available though the multiplexing of a large number of such sources, by comparison with a simple approximation P[QL > Lb] ≈ exp[−δLbv/a] based on the asymptotic decay rate δ alone. We apply this formula to Gaussian processes, in particular FBM, both alone, and also perturbed by an Ornstein–Uhlenbeck process. This demonstrates a richer potential structure than occurs for sources with linear large deviation scalings.

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

2021 ◽  
pp. 1-34
Author(s):  
Yuhui Chen ◽  
Minling Li ◽  
Qinghe Yao ◽  
Zheng-an Yao
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Convergence Rates ◽  
Splitting Method ◽  
Mhd Flow ◽  
Decay Rates ◽  
Upper And Lower Bounds ◽  
Time Decay ◽  
Large Solutions ◽  
Time Decay Rates

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p ( R 2 ) ∩ L 2 ( R 2 ). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized.

scholarly journals Quick Performance Assessment of Improved Nyquist Pulses

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Nicolae Dumitru Alexandru ◽  
Felix Diaconu
Keyword(s):  
Energy Distribution ◽  
Error Probability ◽  
Figure Of Merit ◽  
Timing Error ◽  
Asymptotic Decay ◽  
Figures Of Merit ◽  
Timing Offset ◽  
Nyquist Pulses ◽  
The Difference ◽  
Asymptotic Decay Rate

An explanation is proposed for the improved behavior of the improved Nyquist pulses with an asymptotic decay rate of t-2 when sampled with a timing offset. Three figures of merit that indicate the energy distribution into the sidelobes of the time response and allow a quick assessment of their performance in terms of error probability when the impulse response is sampled with a timing error have been proposed and verified on several improved Nyquist pulses reported in the literature. In order to check the validity of the proposed figures of merit a novel family of Nyquist pulses denoted as power sine was introduced. Using the proposed approach the design process was expedited as the volume of necessary calculations was significantly decreased. To explain the difference in close pulse performance a figure of merit based on limited ISI distortion was introduced.

scholarly journals SOJOURN TIMES IN THE M/G/1 FB QUEUE WITH LIGHT-TAILED SERVICE TIMES

2005 ◽  
Vol 19 (3) ◽  
pp. 351-361 ◽  
Author(s):  
M. Mandjes ◽  
M. Nuyens
Keyword(s):  
Decay Rate ◽  
Sojourn Time ◽  
Busy Period ◽  
Service Discipline ◽  
Asymptotic Decay ◽  
Sojourn Times ◽  
Service Times ◽  
Asymptotic Decay Rate

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the foreground–background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times, the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimizes the decay rate in the class of work-conserving disciplines.

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES OF SOLUTIONS FOR VISCOUS CONSERVATION LAWS IN SEVERAL SPACE DIMENSIONS

1996 ◽  
Vol 06 (03) ◽  
pp. 315-338 ◽  
Author(s):  
KAZUO ITO
Keyword(s):  
Conservation Laws ◽  
Decay Rate ◽  
Energy Method ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
One Dimensional ◽  
Viscous Conservation Laws ◽  
Asymptotic Decay Rate

This paper gives the asymptotic decay rate toward the planar rarefaction waves of the solutions for the scalar viscous conservation laws in two or more space dimensions. This is proved by a result on the decay rate of solutions for one-dimensional scalar viscous conservation laws and by using an L2-energy method with a weight of time.

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