1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
|
## Copyright (C) 2012, 2016, 2018 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}] =} qnomaba (@var{lambda}, @var{D})
## @deftypefnx {Function File} {[@var{Xl}, @var{Xu}, @var{Rl}, @var{Rl}] =} qnomaba (@var{lambda}, @var{S}, @var{V})
##
## @cindex bounds, asymptotic
## @cindex open network
## @cindex multiclass network, open
##
## Compute Asymptotic Bounds for open, multiclass networks with @math{K}
## service centers and @math{C} customer classes.
##
## @strong{INPUTS}
##
## @table @code
##
## @item @var{lambda}(c)
## class @math{c} arrival rate to the system (vector of length
## @math{C}, @code{@var{lambda}(c) > 0}).
##
## @item @var{D}(c, k)
## class @math{c} service demand at center @math{k} (@math{C \times K}
## matrix, @code{@var{D}(c, k) @geq{} 0}).
##
## @item @var{S}(c, k)
## mean service time of class @math{c} requests at center @math{k}
## (@math{C \times K} matrix, @code{@var{S}(c, k) @geq{} 0}).
##
## @item @var{V}(c, k)
## mean number of visits of class @math{c} requests at center @math{k}
## (@math{C \times K} matrix, @code{@var{V}(c, k) @geq{} 0}).
##
## @end table
##
## @strong{OUTPUTS}
##
## @table @code
##
## @item @var{Xl}(c)
## @item @var{Xu}(c)
## lower and upper bounds of class @math{c} throughput.
## @code{@var{Xl}(c)} is always @math{0} since there can be no lower
## bound on the throughput of open networks (vector of length
## @math{C}).
##
## @item @var{Rl}(c)
## @item @var{Ru}(c)
## lower and upper bounds of class @math{c} response time.
## @code{@var{Ru}(c)} is always @code{+inf} since there can be no
## upper bound on the response time of open networks (vector of length
## @math{C}).
##
## @end table
##
## @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] = qnomaba( lambda, S, V )
if ( nargin < 2 || nargin > 3 )
print_usage();
endif
(isvector(lambda) && length(lambda)>0) || ...
error( "lambda must be a nonempty vector" );
all(lambda > 0) || ...
error( "lambda must contain positive values" );
lambda = lambda(:)';
C = length(lambda);
( ismatrix(S) && rows(S)==C ) || ...
error( "S/D must be a matrix >=0 with %d rows", C );
all(S(:)>=0) || ...
error( "S/D must contain nonnegative values" );
K = columns(S);
if ( nargin < 3 )
V = ones(size(S));
else
( ismatrix(V) && size_equal(S,V) ) || ...
error( "V must be a %d x %d matrix", C, K);
all(V(:)>=0) || ...
error( "V must contain nonnegative values" );
endif
D = S.*V;
X_lower = zeros(1,C);
X_upper = 1./max(D,[],2)';
R_lower = sum(D,2)';
R_upper = +inf(1,C);
endfunction
%!test
%! fail( "qnomaba( [1 1], [1 1 1; 1 1 1; 1 1 1] )", "2 rows" );
|
