}
std::unordered_map<int, std::vector<int>>
-simgrid::kernel::lmm::BmfSystem::get_alloc(const Eigen::VectorXd& fair_sharing) const
+simgrid::kernel::lmm::BmfSystem::get_alloc(const Eigen::VectorXd& fair_sharing, bool initial) const
{
std::unordered_map<int, std::vector<int>> alloc;
for (int player_idx = 0; player_idx < A_.cols(); player_idx++) {
- int selected_resource = -1;
- double min_share = 0;
+ int selected_resource = NO_RESOURCE;
+ double bound = idx2Var_.at(player_idx)->get_bound();
+ double min_share = (bound <= 0 || initial) ? -1 : bound;
for (int cnst_idx = 0; cnst_idx < A_.rows(); cnst_idx++) {
if (A_(cnst_idx, player_idx) <= 0.0)
continue;
double share = fair_sharing[cnst_idx] / A_(cnst_idx, player_idx);
- if (selected_resource == -1 || double_positive(min_share - share, sg_maxmin_precision)) {
+ if (min_share == -1 || double_positive(min_share - share, sg_maxmin_precision)) {
selected_resource = cnst_idx;
min_share = share;
}
return debug.str();
}
+double simgrid::kernel::lmm::BmfSystem::get_resource_capacity(int resource,
+ const std::vector<int>& bounded_players) const
+{
+ double capacity = C_[resource];
+ for (int p : bounded_players) {
+ capacity -= A_(resource, p) * idx2Var_.at(p)->get_bound();
+ }
+ return capacity;
+}
+
Eigen::VectorXd
simgrid::kernel::lmm::BmfSystem::equilibrium(const std::unordered_map<int, std::vector<int>>& alloc) const
{
// if so, they must have a fair sharing of this resource, adjust A_p and C_p accordingly
int last_row = n_players - 1;
int first_row = 0;
+ std::vector<int> bounded_players;
for (const auto& e : alloc) {
// add one row for the resource with A[r,]
int cur_resource = e.first;
+ if (cur_resource == NO_RESOURCE) {
+ bounded_players.insert(bounded_players.end(), e.second.begin(), e.second.end());
+ continue;
+ }
A_p.row(first_row) = A_.row(cur_resource);
- C_p[first_row] = C_[cur_resource];
+ C_p[first_row] = get_resource_capacity(cur_resource, bounded_players);
first_row++;
if (e.second.size() > 1) {
int i = e.second[0]; // first player
}
}
}
+ /* clear players which are externally bounded */
+ for (int p : bounded_players) {
+ A_p.col(p).setZero();
+ }
XBT_DEBUG("A':\n%s", debug_eigen(A_p).c_str());
XBT_DEBUG("C':\n%s", debug_eigen(C_p).c_str());
- return Eigen::FullPivLU<Eigen::MatrixXd>(A_p).solve(C_p);
+ Eigen::VectorXd rho = Eigen::FullPivLU<Eigen::MatrixXd>(A_p).solve(C_p);
+ for (int p : bounded_players) {
+ rho[p] = idx2Var_.at(p)->get_bound();
+ }
+ return rho;
}
bool simgrid::kernel::lmm::BmfSystem::is_bmf(const Eigen::VectorXd& rho) const
bmf = bmf && (not std::any_of(remaining.data(), remaining.data() + remaining.size(),
[](double v) { return double_positive(v, sg_maxmin_precision); }));
- // 2) at least 1 resource is saturated
- bmf = bmf && (std::any_of(remaining.data(), remaining.data() + remaining.size(),
- [](double v) { return double_equals(v, 0.0, sg_maxmin_precision); }));
// 3) every player receives maximum share in at least 1 saturated resource
// due to subflows, compare with the maximum consumption and not the A matrix
Eigen::MatrixXd usage =
XBT_DEBUG("Saturated_j resources:\n%s", debug_eigen(saturated).c_str());
player_max_share.array().colwise() *= saturated.array();
+ // just check if it has received at least it's bound
+ for (int p = 0; p < rho.size(); p++) {
+ if (double_equals(rho[p], idx2Var_.at(p)->get_bound(), sg_maxmin_precision)) {
+ player_max_share(0, p) = 1; // it doesn't really matter, just to say that it's a bmf
+ saturated[0] = 1;
+ }
+ }
+
+ // 2) at least 1 resource is saturated
+ bmf = bmf && (saturated.array() == 1).any();
+
XBT_DEBUG("Player_ji usage of saturated resources:\n%s", debug_eigen(player_max_share).c_str());
// for all columns(players) it has to be the max at least in 1
bmf = bmf && (player_max_share.colwise().sum().all() >= 1);
if (not modified_)
return;
+ XBT_DEBUG("");
+ XBT_DEBUG("Starting BMF solver");
/* initialize players' weight and constraint matrices */
set_vector_C();
set_matrix_A();
/* BMF allocation for each player (current and last one) stop when are equal */
std::unordered_map<int, std::vector<int>> last_alloc;
- auto cur_alloc = get_alloc(fair_sharing);
+ auto cur_alloc = get_alloc(fair_sharing, true);
Eigen::VectorXd rho;
while (it < max_iteration_ && last_alloc != cur_alloc) {
last_alloc = cur_alloc;
XBT_DEBUG("Fair sharing vector (per resource):\n%s", debug_eigen(fair_sharing).c_str());
// get new allocation for players
- cur_alloc = get_alloc(fair_sharing);
+ cur_alloc = get_alloc(fair_sharing, false);
XBT_DEBUG("B (new allocation): %s", debug_alloc(cur_alloc).c_str());
it++;
}
REQUIRE(double_positive(rho_1->get_value(), sg_maxmin_precision));
}
+ SECTION("Bounded variable")
+ {
+ /*
+ * Assures a player receives the min(bound, share) if it's bounded
+ *
+ * o System: a1 * p1 * \rho1 + a2 * p2 * \rho2 < C
+ * o bounds: b1=0.1, b2=-1
+ * o consumption_weight: a1=1, a2=1
+ * o sharing_penalty: p1=1, p2=1
+ *
+ * Expectations
+ * o rho1 = .1
+ * o rho2 = .8
+ */
+
+ lmm::Constraint* sys_cnst = Sys.constraint_new(nullptr, 1);
+ lmm::Variable* rho_1 = Sys.variable_new(nullptr, 1, .1);
+ lmm::Variable* rho_2 = Sys.variable_new(nullptr, 1);
+
+ Sys.expand(sys_cnst, rho_1, 2);
+ Sys.expand(sys_cnst, rho_2, 1);
+ Sys.solve();
+ REQUIRE(double_equals(rho_1->get_value(), .1, sg_maxmin_precision));
+ REQUIRE(double_equals(rho_2->get_value(), .8, sg_maxmin_precision));
+ }
+
Sys.variable_free_all();
}
