1 /* Copyright (c) 2004-2022. The SimGrid Team. All rights reserved. */
3 /* This program is free software; you can redistribute it and/or modify it
4 * under the terms of the license (GNU LGPL) which comes with this package. */
9 #include "src/kernel/lmm/maxmin.hpp"
10 #include <boost/container_hash/hash.hpp>
11 #include <eigen3/Eigen/Dense>
12 #include <unordered_set>
18 /** @brief Generate all combinations of valid allocation */
19 class XBT_PUBLIC AllocationGenerator {
21 explicit AllocationGenerator(Eigen::MatrixXd A);
24 * @brief Get next valid allocation
26 * @param next_alloc Allocation (OUTPUT)
27 * @return true if there's an allocation not tested yet, false otherwise
29 bool next(std::vector<int>& next_alloc);
33 std::vector<int> alloc_;
40 * Despite the simplicity of BMF fairness definition, it's quite hard to
41 * find a BMF allocation in the general case.
43 * This solver implements one possible algorithm to find a BMF, as proposed
44 * at: https://hal.archives-ouvertes.fr/hal-01552739.
46 * The idea of this algorithm is that each player/flow "selects" a resource to
47 * saturate. Then, we calculate the rate each flow would have with this allocation.
48 * If the allocation is a valid BMF and no one needs to move, it's over. Otherwise,
49 * each player selects a new resource to saturate based on the minimim rate possible
50 * between all resources.
53 * 1) Given an initial allocation B_i
54 * 2) Build a matrix A'_ji and C'_ji which assures that the player receives the most
55 * share at selected resources
56 * 3) Solve: A'_ji * rho_i = C'_j
57 * 4) Calculate the minimum fair rate for each resource j: f_j. The f_j represents
58 * the maximum each flow can receive at the resource j.
59 * 5) Builds a new vector B'_i = arg min(f_j/A_ji).
60 * 6) Stop if B == B' (nobody needs to move), go to step 2 otherwise
62 * Despite the overall good performance of this algorithm, which converges in a few
63 * iterations, we don't have any assurance about its convergence. In the worst case,
64 * it may be needed to test all possible combination of allocations (which is exponential).
68 class XBT_PUBLIC BmfSolver {
71 * @brief Instantiate the BMF solver
73 * @param A A_ji: consumption of player i on resource j
74 * @param maxA maxA_ji: consumption of larger player i on resource j
75 * @param C Resource capacity
76 * @param shared Is resource shared between player or each player receives the full capacity (FATPIPE links)
77 * @param phi Bound for each player
79 BmfSolver(Eigen::MatrixXd A, Eigen::MatrixXd maxA, Eigen::VectorXd C, std::vector<bool> shared, Eigen::VectorXd phi);
80 /** @brief Solve equation system to find a fair-sharing of resources */
81 Eigen::VectorXd solve();
84 using allocation_map_t = std::unordered_map<int, std::unordered_set<int>>;
86 * @brief Get actual resource capacity considering bounded players
88 * Calculates the resource capacity considering that some players on it may be bounded by user,
89 * i.e. an explicit limit in speed was configured
91 * @param resource Internal index of resource in C_ vector
92 * @param bounded_players List of players that are externally bounded
93 * @return Actual resource capacity
95 double get_resource_capacity(int resource, const std::vector<int>& bounded_players) const;
98 * @brief Given an allocation calculates the speed/rho for each player
101 * Builds 2 auxiliares matrices A' and C' and solves the system: rho_i = inv(A'_ji) * C'_j
103 * All resources in A' and C' are saturated, i.e., sum(A'_j * rho_i) = C'_j.
105 * The matrix A' is built as follows:
106 * - For each resource j in alloc: copy row A_j to A'
107 * - If 2 players (i, k) share a same resource, assure fairness by adding a row in A' such as:
108 * - A_ji*rho_i - Ajk*rho_j = 0
110 * @param alloc for each resource, players that chose to saturate it
111 * @return Vector rho with "players' speed"
113 Eigen::VectorXd equilibrium(const allocation_map_t& alloc) const;
116 * @brief Given a fair_sharing vector, gets the allocation
118 * The allocation for player i is given by: min(bound, f_j/A_ji).
119 * The minimum between all fair-sharing and the external bound (if any)
121 * The algorithm dictates a random initial allocation. For simplicity, we opt to use the same
122 * logic with the fair_sharing vector.
124 * @param fair_sharing Fair sharing vector
125 * @param initial Is this the initial allocation?
126 * @return allocation vector
128 bool get_alloc(const Eigen::VectorXd& fair_sharing, const allocation_map_t& last_alloc, allocation_map_t& alloc,
131 bool disturb_allocation(allocation_map_t& alloc, std::vector<int>& alloc_by_player);
133 * @brief Calculates the fair sharing for each resource
135 * Basically 3 options:
136 * 1) resource in allocation: A_ji*rho_i since all players who selected this resource have the same share
137 * 2) resource not selected by saturated (fully used): divide it by the number of players C_/n_players
138 * 3) resource not selected and not-saturated: no limitation
140 * @param alloc Allocation map (resource-> players)
141 * @param rho Speed for each player i
142 * @param fair_sharing Output vector, fair sharing for each resource j
144 void set_fair_sharing(const allocation_map_t& alloc, const Eigen::VectorXd& rho, Eigen::VectorXd& fair_sharing) const;
147 * @brief Check if allocation is BMF
149 * To be a bmf allocation it must:
150 * - respect the capacity of all resources
151 * - saturate at least 1 resource
152 * - every player receives maximum share in at least 1 saturated resource
153 * @param rho Allocation
154 * @return true if BMF false otherwise
156 bool is_bmf(const Eigen::VectorXd& rho) const;
157 std::vector<int> alloc_map_to_vector(const allocation_map_t& alloc) const;
160 * @brief Set of debug functions to print the different objects
162 template <typename T> std::string debug_eigen(const T& obj) const;
163 template <typename C> std::string debug_vector(const C& container) const;
164 std::string debug_alloc(const allocation_map_t& alloc) const;
166 Eigen::MatrixXd A_; //!< A_ji: resource usage matrix, each row j represents a resource and col i a flow/player
167 Eigen::MatrixXd maxA_; //!< maxA_ji, similar as A_, but containing the maximum consumption of player i (if player a
168 //!< single flow it's equal to A_)
169 Eigen::VectorXd C_; //!< C_j Capacity of each resource
170 std::vector<bool> C_shared_; //!< shared_j Resource j is shared or not
171 Eigen::VectorXd phi_; //!< phi_i bound for each player
173 std::unordered_set<std::vector<int>, boost::hash<std::vector<int>>> allocations_;
174 AllocationGenerator gen_;
175 std::vector<int> allocations_age_;
176 static constexpr int NO_RESOURCE = -1; //!< flag to indicate player has selected no resource
177 int max_iteration_ = sg_bmf_max_iterations; //!< number maximum of iterations of BMF algorithm
183 * A BMF (bottleneck max fairness) solver to resolve inequation systems.
185 * Usually, SimGrid relies on a *max-min fairness* solver to share the resources.
186 * Max-min is great when sharing homogenous resources, however it cannot be used with heterogeneous resources.
188 * BMF is a natural alternative to max-min, providing a fair-sharing of heterogeneous resources (CPU, network, disk).
189 * It is specially relevant for the implementation of parallel tasks whose sharing involves different
190 * kinds of resources.
192 * BMF assures that every flow receives the maximum share possible in at least 1 bottleneck (fully used) resource.
194 * The BMF is characterized by:
195 * - A_ji: a matrix of requirement for flows/player. For each resource j, and flow i, A_ji represents the utilization
196 * of resource j for 1 unit of the flow i.
197 * - rho_i: the rate allocated for flow i (same among all resources)
198 * - C_j: the capacity of each resource (can be bytes/s, flops/s, etc)
200 * Therefore, these conditions need to satisfied to an allocation be considered a BMF:
201 * 1) All constraints are respected (flows cannot use more than the resource has available)
202 * - for all resource j and player i: A_ji * rho_i <= C_j
203 * 2) At least 1 resource is fully used (bottleneck).
204 * - for some resource j: A_ji * rho_i = C_j
205 * 3) Each flow (player) receives the maximum share in at least 1 bottleneck.
206 * - for all player i: exist a resource j: A_ji * rho_i >= A_jk * rho_k for all other player k
208 * Despite the prove of existence of a BMF allocation in the general case, it may not
209 * be unique, which leads to possible different rate for the applications.
211 * More details about BMF can be found at: https://hal.inria.fr/hal-01243985/document
216 * @brief Bottleneck max-fair system
218 class XBT_PUBLIC BmfSystem : public System {
220 using System::System;
221 /** @brief Implements the solve method to calculate a BMF allocation */
225 using allocation_map_t = std::unordered_map<int, std::unordered_set<int>>;
227 * @brief Solve equation system to find a fair-sharing of resources
229 * @param cnst_list Constraint list (modified for selective update or active)
231 template <class CnstList> void bmf_solve(const CnstList& cnst_list);
233 * @brief Iterates over system and build the consumption matrix A_ji and maxA_ji
235 * Each row j represents a resource and each col i a player/flow
237 * Considers only active variables to build the matrix.
239 * @param number_cnsts Number of constraints in the system
240 * @param A Consumption matrix (OUTPUT)
241 * @param maxA Max subflow consumption matrix (OUTPUT)
242 * @param phi Bounds for variables
244 void get_flows_data(int number_cnsts, Eigen::MatrixXd& A, Eigen::MatrixXd& maxA, Eigen::VectorXd& phi);
246 * @brief Builds the vector C_ with resource's capacity
248 * @param cnst_list Constraint list (modified for selective update or active)
249 * @param C Resource capacity vector
250 * @param shared Resource is shared or not (fatpipe links)
252 template <class CnstList>
253 void get_constraint_data(const CnstList& cnst_list, Eigen::VectorXd& C, std::vector<bool>& shared);
255 std::unordered_map<int, Variable*> idx2Var_; //!< Map player index (and position in matrices) to system's variable
256 std::unordered_map<const Constraint*, int> cnst2idx_; //!< Conversely map constraint to index
257 bool warned_nonlinear_ = false;
261 } // namespace kernel
262 } // namespace simgrid