Exact and asymptotic solutions to a PDE that arises in time-dependent queues

2000 ◽  
Vol 32 (1) ◽  
pp. 256-283 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Limit Theorems ◽  
Asymptotic Properties ◽  
Mathematical Physics ◽  
Linear Functions ◽  
Time Dependent ◽  
One Dimension ◽  
Asymptotic Results ◽  
Piecewise Constant ◽  
Space And Time ◽  
Diffusion Problems

We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

Exact and asymptotic solutions to a PDE that arises in time-dependent queues

2000 ◽  
Vol 32 (01) ◽  
pp. 256-283 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Limit Theorems ◽  
Asymptotic Properties ◽  
Mathematical Physics ◽  
Linear Functions ◽  
Time Dependent ◽  
One Dimension ◽  
Asymptotic Results ◽  
Piecewise Constant ◽  
Space And Time ◽  
Diffusion Problems

We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients

2017 ◽  
Vol 44 (3) ◽  
pp. 617-635 ◽  
Author(s):  
Abdelkamel Alj ◽  
Rajae Azrak ◽  
Christophe Ley ◽  
Guy Mélard
Keyword(s):  
Asymptotic Properties ◽  
Time Dependent

A time-dependent model for high-pressure discharges in narrow ablative capillaries

1993 ◽  
Vol 50 (1) ◽  
pp. 51-70 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman ◽  
J. Ashkenazy ◽  
M. Caner ◽  
Z. Kaplan
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Time Dependent ◽  
Dimensional Model ◽  
Plasma Sources ◽  
One Dimensional ◽  
Space And Time ◽  
Dependent Model ◽  
Energy Equations ◽  
Time Dependent Model

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

Multivariate linear time series models

1984 ◽  
Vol 16 (3) ◽  
pp. 492-561 ◽  
Author(s):  
E. J. Hannan ◽  
L. Kavalieris
Keyword(s):  
Limit Theorems ◽  
Analysis Of Algorithms ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Real Data ◽  
Rates Of Convergence ◽  
Structure Theory ◽  
Time Series Models ◽  
Transfer Model ◽  
Rational Transfer

This paper is in three parts. The first deals with the algebraic and topological structure of spaces of rational transfer function linear systems—ARMAX systems, as they have been called. This structure theory is dominated by the concept of a space of systems of order, or McMillan degree, n, because of the fact that this space, M(n), can be realised as a kind of high-dimensional algebraic surface of dimension n(2s + m) where s and m are the numbers of outputs and inputs. In principle, therefore, the fitting of a rational transfer model to data can be considered as the problem of determining n and then the appropriate element of M(n). However, the fact that M(n) appears to need a large number of coordinate neighbourhoods to cover it complicates the task. The problems associated with this program, as well as theory necessary for the analysis of algorithms to carry out aspects of the program, are also discussed in this first part of the paper, Sections 1 and 2.The second part, Sections 3 and 4, deals with algorithms to carry out the fitting of a model and exhibits these algorithms through simulations and the analysis of real data.The third part of the paper discusses the asymptotic properties of the algorithm. These properties depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record, T. The necessary limit theorems and the analysis of the algorithms are given in Section 5. Many of these results are of interest independent of the algorithms being studied.

THE TEMPERATURE DISTRIBUTION PRODUCED BY ACOUSTIC ABSORPTION: I. MACROSCOPIC TREATMENT

1966 ◽  
Vol 44 (12) ◽  
pp. 3001-3011 ◽  
Author(s):  
S. Simons
Keyword(s):  
Temperature Distribution ◽  
Acoustic Wave ◽  
Numerical Results ◽  
Time Dependent ◽  
Acoustic Absorption ◽  
Space And Time

A calculation is given of the temperature distribution in space and time produced by the absorption of an acoustic wave propagated inside a medium, under conditions in which the situation may be described macroscopically. The problem is considered for various geometries, and for both constant and time-dependent energies of the incident acoustic wave. Numerical results are obtained, and a discussion is given of their relevance to various experiments.

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

Sign in / Sign up

Export Citation Format

Share Document