867 research outputs found
On input/output maps for nonlinear systems via continuity in a locally convex topology
In this paper we show that the output of a nonlinear system with inputs in () whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results
Randomized Assignment of Jobs to Servers in Heterogeneous Clusters of Shared Servers for Low Delay
We consider the job assignment problem in a multi-server system consisting of
parallel processor sharing servers, categorized into ()
different types according to their processing capacity or speed. Jobs of random
sizes arrive at the system according to a Poisson process with rate . Upon each arrival, a small number of servers from each type is
sampled uniformly at random. The job is then assigned to one of the sampled
servers based on a selection rule. We propose two schemes, each corresponding
to a specific selection rule that aims at reducing the mean sojourn time of
jobs in the system.
We first show that both methods achieve the maximal stability region. We then
analyze the system operating under the proposed schemes as which
corresponds to the mean field. Our results show that asymptotic independence
among servers holds even when is finite and exchangeability holds only
within servers of the same type. We further establish the existence and
uniqueness of stationary solution of the mean field and show that the tail
distribution of server occupancy decays doubly exponentially for each server
type. When the estimates of arrival rates are not available, the proposed
schemes offer simpler alternatives to achieving lower mean sojourn time of
jobs, as shown by our numerical studies
Reduced-dimension linear transform coding of distributed correlated signals with incomplete observations
We study the problem of optimal reduced-dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal. In the mean square estimation context this involves finding he optimal signal representation based on multiple incomplete or only partial observations that are correlated. In particular this leads to the study of finding the optimal Karhunen-Loeve basis based on the censored observations. The problem has been considered previously by Gestpar, Dragotti and Vitterli in the context of jointly Gaussian random variables based on using conditional covariances. In this paper, we derive the estimation results in the more general setting of second-order random variables with arbitrary distributions, using entirely different techniques based on the idea of innovations. We explicitly solve the single transform coder case, give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problm
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