1## Copyright (C) 2008, 2009, 2010, 2011, 2012, 2016 Moreno Marzolla 2## 3## This file is part of the queueing toolbox. 4## 5## The queueing toolbox is free software: you can redistribute it and/or 6## modify it under the terms of the GNU General Public License as 7## published by the Free Software Foundation, either version 3 of the 8## License, or (at your option) any later version. 9## 10## The queueing toolbox is distributed in the hope that it will be 11## useful, but WITHOUT ANY WARRANTY; without even the implied warranty 12## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 13## General Public License for more details. 14## 15## You should have received a copy of the GNU General Public License 16## along with the queueing toolbox. If not, see <http://www.gnu.org/licenses/>. 17 18## -*- texinfo -*- 19## 20## @deftypefn {Function File} {[@var{Xl}, @var{Xu}, @var{Rl}, @var{Ru}] =} qnosaba (@var{lambda}, @var{D}) 21## @deftypefnx {Function File} {[@var{Xl}, @var{Xu}, @var{Rl}, @var{Ru}] =} qnosaba (@var{lambda}, @var{S}, @var{V}) 22## @deftypefnx {Function File} {[@var{Xl}, @var{Xu}, @var{Rl}, @var{Ru}] =} qnosaba (@var{lambda}, @var{S}, @var{V}, @var{m}) 23## 24## @cindex bounds, asymptotic 25## @cindex open network 26## 27## Compute Asymptotic Bounds for open, single-class networks with @math{K} service centers. 28## 29## @strong{INPUTS} 30## 31## @table @code 32## 33## @item @var{lambda} 34## Arrival rate of requests (scalar, @code{@var{lambda} @geq{} 0}). 35## 36## @item @var{D}(k) 37## service demand at center @math{k}. 38## (vector of length @math{K}, @code{@var{D}(k) @geq{} 0}). 39## 40## @item @var{S}(k) 41## mean service time at center @math{k}. 42## (vector of length @math{K}, @code{@var{S}(k) @geq{} 0}). 43## 44## @item @var{V}(k) 45## mean number of visits to center @math{k}. 46## (vector of length @math{K}, @code{@var{V}(k) @geq{} 0}). 47## 48## @item @var{m}(k) 49## number of servers at center @math{k}. 50## This function only supports @math{M/M/1} queues, therefore 51## @var{m} must be @code{ones(size(S))}. 52## 53## @end table 54## 55## @strong{OUTPUTS} 56## 57## @table @code 58## 59## @item @var{Xl} 60## @item @var{Xu} 61## Lower and upper bounds on the system throughput. @var{Xl} is 62## always set to @math{0} since there can be no lower bound on the 63## throughput of open networks (scalar). 64## 65## @item @var{Rl} 66## @item @var{Ru} 67## Lower and upper bounds on the system response time. @var{Ru} 68## is always set to @code{+inf} since there can be no upper bound on the 69## throughput of open networks (scalar). 70## 71## @end table 72## 73## @seealso{qnomaba} 74## 75## @end deftypefn 76 77## Author: Moreno Marzolla <moreno.marzolla(at)unibo.it> 78## Web: http://www.moreno.marzolla.name/ 79 80function [X_lower X_upper R_lower R_upper] = qnosaba( varargin ) 81 if ( nargin < 2 || nargin > 4 ) 82 print_usage(); 83 endif 84 85 [err lambda S V m] = qnoschkparam( varargin{:} ); 86 isempty(err) || error(err); 87 88 all(m==1) || ... 89 error("this function supports M/M/1 servers only"); 90 91 D = S .* V; 92 93 X_lower = 0; 94 X_upper = 1/max(D); 95 R_lower = sum(D); 96 R_upper = +inf; 97endfunction 98 99%!test 100%! fail( "qnosaba( 0.1, [] )", "vector" ); 101%! fail( "qnosaba( 0.1, [0 -1])", "nonnegative" ); 102%! fail( "qnosaba( 0, [1 2] )", "lambda" ); 103%! fail( "qnosaba( -1, [1 2])", "lambda" ); 104%! fail( "qnosaba( 1, [1 2 3], [1 2] )", "incompatible size"); 105%! fail( "qnosaba( 1, [1 2 3], [-1 2 3] )", "nonnegative"); 106 107%!test 108%! [Xl Xu Rl Ru] = qnosaba( 1, [1 1] ); 109%! assert( Xl, 0 ); 110%! assert( Ru, +inf ); 111