65 research outputs found
Continuity theorems for the queueing system
In this paper continuity theorems are established for the number of losses
during a busy period of the queue. We consider an queueing
system where the service time probability distribution, slightly different in a
certain sense from the exponential distribution, is approximated by that
exponential distribution. Continuity theorems are obtained in the form of one
or two-sided stochastic inequalities. The paper shows how the bounds of these
inequalities are changed if further assumptions, associated with specific
properties of the service time distribution (precisely described in the paper),
are made. Specifically, some parametric families of service time distributions
are discussed, and the paper establishes uniform estimates (given for all
possible values of the parameter) and local estimates (where the parameter is
fixed and takes only the given value). The analysis of the paper is based on
the level crossing approach and some characterization properties of the
exponential distribution.Comment: Final revision; will be published as i
A special family of Galton-Watson processes with explosions
The linear-fractional Galton-Watson processes is a well known case when many
characteristics of a branching process can be computed explicitly. In this
paper we extend the two-parameter linear-fractional family to a much richer
four-parameter family of reproduction laws. The corresponding Galton-Watson
processes also allow for explicit calculations, now with possibility for
infinite mean, or even infinite number of offspring. We study the properties of
this special family of branching processes, and show, in particular, that in
some explosive cases the time to explosion can be approximated by the Gumbel
distribution
Rearranging Edgeworth-Cornish-Fisher Expansions
This paper applies a regularization procedure called increasing rearrangement
to monotonize Edgeworth and Cornish-Fisher expansions and any other related
approximations of distribution and quantile functions of sample statistics.
Besides satisfying the logical monotonicity, required of distribution and
quantile functions, the procedure often delivers strikingly better
approximations to the distribution and quantile functions of the sample mean
than the original Edgeworth-Cornish-Fisher expansions.Comment: 17 pages, 3 figure
Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model
This paper deals with a one--dimensional model for granular materials, which
boils down to an inelastic version of the Kac kinetic equation, with
inelasticity parameter . In particular, the paper provides bounds for
certain distances -- such as specific weighted --distances and the
Kolmogorov distance -- between the solution of that equation and the limit. It
is assumed that the even part of the initial datum (which determines the
asymptotic properties of the solution) belongs to the domain of normal
attraction of a symmetric stable distribution with characteristic exponent
\a=2/(1+p). With such initial data, it turns out that the limit exists and is
just the aforementioned stable distribution. A necessary condition for the
relaxation to equilibrium is also proved. Some bounds are obtained without
introducing any extra--condition. Sharper bounds, of an exponential type, are
exhibited in the presence of additional assumptions concerning either the
behaviour, near to the origin, of the initial characteristic function, or the
behaviour, at infinity, of the initial probability distribution function
Queues with Lévy input and hysteretic control
We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009
Special Libraries, April 1933
Volume 24, Issue 3https://scholarworks.sjsu.edu/sla_sl_1933/1002/thumbnail.jp
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