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\title{Implementable Bounds for a Neural Networks Algorithm in 
Communication Traffic Control}

\author{Alexandru Murgu}

\pagestyle{myheadings}

\markright{APIC'95, El Paso,
Extended Abstracts,
A Supplement to the international journal of {\rm Reliable
Computing}\ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ }

\maketitle

\auffil{The author is with Department of Mathematics,
University of Jyvaskyla,
FIN-40351 Jyvaskyla, FINLAND,
Email murgu@julia.math.jyu.fi.}

\begin{abstract}
The traffic control problem for communication networks has been 
widely considered either
from  the standpoint  of traffic assignment, including  
linearizations of  the nonlinear 
traffic  pattern  around the  ``nominal'' regime and variational 
inequalities approach, or 
from  the more classical standpoint of flow networks theory. 
When the traffic  stream is 
time  varying, additional computational  effort is  required, 
and the  problem complexity 
becomes NP-hard, even when we want to solve some of its discrete time 
approximations (it is also NP-hard if we have interval uncertainty in
some of the parameters). 

In this paper,
an  idea from  continuous  bounding  approach often  
encountered in  Linear  Programming 
(deterministic or stochastic)  is  used  to  build  a  
learning  algorithm for the bound
movement  over  the  successive approximation of the true  
solution, trying to  capture a 
``local''  landscape  of a  convex  functional. We implement  the 
learning  algorithm in a 
feedforward neural network (FNN) based on some merit function 
discriminating the quality
of the solution bounds.  Because the traffic pattern (that we want to 
control by  
using this learning 
mechanism) is stochastic, we need to check the convergence 
properties ensuring that 
the  learning algorithm is  asymptotically stable.  For that,
a  suitably chosen 
stochastic Lyapunov function is used.  
Finally, we report some 
simulation  results for a 
Gaussian flow pattern, and we draw the main conclusions of this research. 
\end{abstract}

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