/* $Id$ */
-
/* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. All rights reserved. */
-
/* This program is free software; you can redistribute it and/or modify it
* under the terms of the license (GNU LGPL) which comes with this package. */
-
/*
* Modelling the proportional fairness using the Lagrange Optimization
* Approach. For a detailed description see:
XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
-
/*
* Local prototypes to implement the lagrangian optimization with optimal step, also called dicotomi.
*/
double partial_diff_mu (double mu, void * param_var);
//computes the value of the differential of constraint param_cnst applied to lambda
double partial_diff_lambda (double lambda, void * param_cnst);
-
+//auxiliar function to compute the partial_diff
+double diff_aux(lmm_variable_t var, double x);
void lagrange_solve(lmm_system_t sys)
/*
* Lagrange Variables.
*/
- int max_iterations= 100;
- double epsilon_min_error = 1e-4;
+ int max_iterations= 10000;
+ double epsilon_min_error = 1e-4;
double dicotomi_min_error = 1e-8;
double overall_error = 1;
-
/*
* Variables to manipulate the data structure proposed to model the maxmin
* fairness. See docummentation for more details.
xbt_swag_t elem_list = NULL;
lmm_element_t elem = NULL;
-
xbt_swag_t cnst_list = NULL;
lmm_constraint_t cnst = NULL;
xbt_swag_t var_list = NULL;
lmm_variable_t var = NULL;
-
/*
* Auxiliar variables.
*/
DEBUG1("#### Minimum error tolerated : %e", epsilon_min_error);
DEBUG1("#### Minimum error tolerated (dicotomi) : %e", dicotomi_min_error);
-
if ( !(sys->modified))
return;
*/
var_list = &(sys->variable_set);
i=0;
- xbt_swag_foreach(var, var_list) { if((var->bound > 0.0) || (var->weight <= 0.0)){
- DEBUG1("#### NOTE var(%d) is a boundless variable", i);
- var->mu = -1.0;
- } else{
- var->mu = 1.0;
- var->new_mu = 2.0;
- }
- DEBUG2("#### var(%d)->mu : %e", i, var->mu);
- DEBUG2("#### var(%d)->weight: %e", i, var->weight);
- i++;
+ xbt_swag_foreach(var, var_list) {
+ if((var->bound > 0.0) || (var->weight <= 0.0)){
+ DEBUG1("#### NOTE var(%d) is a boundless variable", i);
+ var->mu = -1.0;
+ } else{
+ var->mu = 1.0;
+ var->new_mu = 2.0;
+ }
+ DEBUG2("#### var(%d)->mu : %e", i, var->mu);
+ DEBUG2("#### var(%d)->weight: %e", i, var->weight);
+ i++;
}
/*
* Initialize lambda.
*/
cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst, cnst_list) {
+ xbt_swag_foreach(cnst, cnst_list){
cnst->lambda = 1.0;
cnst->new_lambda = 2.0;
DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
iteration++;
DEBUG1("************** ITERATION %d **************", iteration);
-
/*
* Compute the value of mu_i
*/
if((var->bound >= 0) && (var->weight > 0) ){
var->new_mu = dicotomi(var->mu, partial_diff_mu, var, dicotomi_min_error);
if(var->new_mu < 0) var->new_mu = 0;
+ var->mu = var->new_mu;
}
}
//forall lambda_i in lambda_1, lambda_2, ..., lambda_n
xbt_swag_foreach(cnst, cnst_list) {
cnst->new_lambda = dicotomi(cnst->lambda, partial_diff_lambda, cnst, dicotomi_min_error);
- if(cnst->new_lambda < 0) cnst->new_lambda = 0;
- }
-
-
- /*
- * Update values of mu and lambda
- */
- //forall mu_i in mu_1, mu_2, ..., mu_n
- xbt_swag_foreach(var, var_list) {
- var->mu = var->new_mu ;
- }
-
- //forall lambda_i in lambda_1, lambda_2, ..., lambda_n
- xbt_swag_foreach(cnst, cnst_list) {
+ DEBUG2("====> cnst->lambda (%p) = %e", cnst, cnst->new_lambda);
cnst->lambda = cnst->new_lambda;
}
-
/*
* Now computes the values of each variable (\rho) based on
* the values of \lambda and \mu.
if(var->weight <=0)
var->value = 0.0;
else {
+ //compute sigma_i + mu_i
tmp = 0;
for(i=0; i<var->cnsts_number; i++){
tmp += (var->cnsts[i].constraint)->lambda;
if(var->bound > 0)
tmp+=var->mu;
}
- //computes de overall_error
- if(overall_error < fabs(var->value - 1.0/tmp)){
- overall_error = fabs(var->value - 1.0/tmp);
+
+ //uses the partial differential inverse function
+ tmp = var->func_fpi(var, tmp);
+
+ //computes de overall_error using normalized value
+ if(overall_error < (fabs(var->value - tmp)/tmp) ){
+ overall_error = (fabs(var->value - tmp)/tmp);
}
- var->value = 1.0 / tmp;
+
+ var->value = tmp;
}
DEBUG4("======> value of var %s (%p) = %e, overall_error = %e", (char *)var->id, var, var->value, overall_error);
}
}
}
-
//verify the KKT property of each flow
xbt_swag_foreach(var, var_list){
}
-
if(overall_error <= epsilon_min_error){
DEBUG1("The method converge in %d iterations.", iteration);
}else{
double min, max;
double overall_error;
double middle;
-
+ double min_diff, max_diff, middle_diff;
+
min = max = init;
+
+ if(init == 0){
+ min = max = 1;
+ }
+
+ min_diff = max_diff = middle_diff = 0.0;
overall_error = 1;
- //DEBUG0("STARTING DICOTOMI... Debugging, format used [min, max], [D(min),D(max)]");
+ if(diff(0.0, var_cnst) > 0){
+ DEBUG1("====> returning 0.0 (diff = %e)", diff(0.0, var_cnst));
+ return 0.0;
+ }
+
+ DEBUG0("====> not detected positive diff in 0");
while(overall_error > min_error){
- //DEBUG4("====> [%e, %e] , [%e,%e]", min, max, diff(min, var_cnst), diff(max, var_cnst));
- if( diff(min, var_cnst) > 0 && diff(max, var_cnst) > 0 ){
+ min_diff = diff(min, var_cnst);
+ max_diff = diff(max, var_cnst);
+
+ DEBUG2("DICOTOMI ===> min = %e , max = %e", min, max);
+ DEBUG2("DICOTOMI ===> diffmin = %e , diffmax = %e", min_diff, max_diff);
+
+ if( min_diff > 0 && max_diff > 0 ){
if(min == max){
min = min / 2.0;
}else{
max = min;
}
- }else if( diff(min, var_cnst) < 0 && diff(max, var_cnst) < 0 ){
+ }else if( min_diff < 0 && max_diff < 0 ){
if(min == max){
max = max * 2.0;
}else{
min = max;
}
- }else if( diff(min, var_cnst) < 0 && diff(max, var_cnst) > 0 ){
+ }else if( min_diff < 0 && max_diff > 0 ){
middle = (max + min)/2.0;
-
- if( diff(middle, var_cnst) < 0 ){
+ middle_diff = diff(middle, var_cnst);
+ overall_error = fabs(min - max);
+
+ if( middle_diff < 0 ){
min = middle;
- }else if( diff(middle, var_cnst) > 0 ){
+ }else if( middle_diff > 0 ){
max = middle;
}else{
WARN0("Found an optimal solution with 0 error!");
overall_error = 0;
+ return middle;
}
- overall_error = fabs(min - max);
- }else{
- WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
+
+ }else if(min_diff == 0){
+ return min;
+ }else if(max_diff == 0){
+ return max;
+ }else if(min_diff > 0 && max_diff < 0){
+ WARN0("The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
}
}
+
+ DEBUG1("====> returning %e", (min+max)/2.0);
return ((min+max)/2.0);
}
+/*
+ *
+ */
double partial_diff_mu(double mu, void *param_var){
double mu_partial=0.0;
+ double sigma_mu=0.0;
lmm_variable_t var = (lmm_variable_t)param_var;
int i;
- //for each link with capacity cnsts[i] that uses flow of variable var do
+ //compute sigma_i
for(i=0; i<var->cnsts_number; i++)
- mu_partial += (var->cnsts[i].constraint)->lambda + mu;
+ sigma_mu += (var->cnsts[i].constraint)->lambda;
+
+ //compute sigma_i + mu_i
+ sigma_mu += var->mu;
- mu_partial = (-1.0/mu_partial) + var->bound;
+ //use auxiliar function passing (sigma_i + mu_i)
+ mu_partial = diff_aux(var, sigma_mu) ;
+
+ //add the RTT limit
+ mu_partial += var->bound;
return mu_partial;
}
-
+/*
+ *
+ */
double partial_diff_lambda(double lambda, void *param_cnst){
- double tmp=0.0;
int i;
xbt_swag_t elem_list = NULL;
lmm_element_t elem = NULL;
lmm_variable_t var = NULL;
lmm_constraint_t cnst= (lmm_constraint_t) param_cnst;
double lambda_partial=0.0;
-
+ double sigma_mu=0.0;
elem_list = &(cnst->element_set);
+
+ DEBUG2("Computting diff of cnst (%p) %s", cnst, (char *)cnst->id);
xbt_swag_foreach(elem, elem_list) {
var = elem->variable;
if(var->weight<=0) continue;
- tmp = 0;
+ //initilize de sumation variable
+ sigma_mu = 0.0;
+
+ //compute sigma_i of variable var
for(i=0; i<var->cnsts_number; i++){
- tmp += (var->cnsts[i].constraint)->lambda;
+ sigma_mu += (var->cnsts[i].constraint)->lambda;
}
- if(var->bound > 0)
- tmp += var->mu;
-
- tmp = tmp - cnst->lambda + lambda;
-
- //avoid a disaster value of lambda
- if(tmp==0) lambda_partial = 10e-8;
+ //add mu_i if this flow has a RTT constraint associated
+ if(var->bound > 0) sigma_mu += var->mu;
+
+ //replace value of cnst->lambda by the value of parameter lambda
+ sigma_mu = (sigma_mu - cnst->lambda) + lambda;
- lambda_partial += (-1.0 /tmp);
+ //use the auxiliar function passing (\sigma_i + \mu_i)
+ lambda_partial += diff_aux(var, sigma_mu);
}
lambda_partial += cnst->bound;
return lambda_partial;
}
+
+
+double diff_aux(lmm_variable_t var, double x){
+ double tmp_fp, tmp_fpi, tmp_fpip, result;
+
+ xbt_assert0(var->func_fp, "Initialize the protocol functions first create variables before.");
+
+ tmp_fp = var->func_fp(var, x);
+ tmp_fpi = var->func_fpi(var, x);
+ tmp_fpip = var->func_fpip(var, x);
+
+ result = tmp_fpip*(var->func_fp(var, tmp_fpi));
+ result = result - tmp_fpi;
+
+ result = result - (tmp_fpip * x);
+
+ return result;
+}
+
+
+
+
+
+
+
+
