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## Copyright (C) 2008, 2009, 2010, 2011, 2012, 2016 Moreno Marzolla
##
## This file is part of the queueing toolbox.
##
## The queueing toolbox is free software: you can redistribute it and/or
## modify it under the terms of the GNU General Public License as
## published by the Free Software Foundation, either version 3 of the
## License, or (at your option) any later version.
##
## The queueing toolbox is distributed in the hope that it will be
## useful, but WITHOUT ANY WARRANTY; without even the implied warranty
## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with the queueing toolbox. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{Xl}, @var{Xu}, @var{Rl}, @var{Ru}] =} qnosbsb (@var{lambda}, @var{D})
## @deftypefnx {Function File} {[@var{Xl}, @var{Xu}, @var{Rl}, @var{Ru}] =} qnosbsb (@var{lambda}, @var{S}, @var{V})
##
## @cindex bounds, balanced system
## @cindex open network
##
## Compute Balanced System Bounds for single-class, open networks with
## @math{K} service centers.
##
## @strong{INPUTS}
##
## @table @code
##
## @item @var{lambda}
## overall arrival rate to the system (scalar, @code{@var{lambda} @geq{} 0}).
##
## @item @var{D}(k)
## service demand at center @math{k} (@code{@var{D}(k) @geq{} 0}).
##
## @item @var{S}(k)
## service time at center @math{k} (@code{@var{S}(k) @geq{} 0}).
##
## @item @var{V}(k)
## mean number of visits at center @math{k} (@code{@var{V}(k) @geq{} 0}).
##
## @item @var{m}(k)
## number of servers at center @math{k}. This function only supports
## @math{M/M/1} queues, therefore @var{m} must be
## @code{ones(size(S))}.
##
## @end table
##
## @strong{OUTPUTS}
##
## @table @code
##
## @item @var{Xl}
## @item @var{Xu}
## Lower and upper bounds on the system throughput. @var{Xl} is always
## set to @math{0}, since there can be no lower bound on open
## networks throughput.
##
## @item @var{Rl}
## @itemx @var{Ru}
## Lower and upper bounds on the system response time.
##
## @end table
##
## @seealso{qnosaba}
##
## @end deftypefn
## Author: Moreno Marzolla <moreno.marzolla(at)unibo.it>
## Web: http://www.moreno.marzolla.name/
function [X_lower X_upper R_lower R_upper] = qnosbsb( varargin )
if ( nargin < 2 || nargin > 4 )
print_usage();
endif
[err lambda S V m] = qnoschkparam( varargin{:} );
isempty(err) || error(err);
all(m==1) || ...
error("this function supports M/M/1 servers only");
D = S .* V;
D_max = max(D);
D_tot = sum(D);
D_ave = mean(D_tot);
X_upper = 1/D_max;
X_lower = 0;
R_lower = D_tot / (1-lambda*D_ave);
R_upper = D_tot / (1-lambda*D_max);
endfunction
%!test
%! fail( "qnosbsb( 0.1, [] )", "vector" );
%! fail( "qnosbsb( 0.1, [0 -1])", "nonnegative" );
%! fail( "qnosbsb( 0, [1 2] )", "lambda" );
%! fail( "qnosbsb( -1, [1 2])", "lambda" );
%!test
%! [Xl Xu Rl Ru] = qnosbsb(0.1,[1 2 3]);
%! assert( Xl, 0 );
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