1 /* Copyright (c) 2004-2021. 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. */
6 #ifndef SURF_MAXMIN_HPP
7 #define SURF_MAXMIN_HPP
9 #include "simgrid/kernel/resource/Action.hpp"
10 #include "simgrid/s4u/Link.hpp"
11 #include "src/surf/surf_interface.hpp"
12 #include "xbt/asserts.h"
14 #include "xbt/mallocator.h"
16 #include <boost/intrusive/list.hpp>
26 /** @addtogroup SURF_lmm
28 * A linear maxmin solver to resolve inequations systems.
30 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
31 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
32 * example and assume we have the variables \f$x_1\f$, \f$x_2\f$, \f$x_3\f$, and \f$x_4\f$ . Let's say that \f$x_1\f$
33 * and \f$x_2\f$ correspond to activities running and the same CPU \f$A\f$ whose capacity is \f$C_A\f$. In such a
34 * case, we need to enforce:
36 * \f[ x_1 + x_2 \leq C_A \f]
38 * Likewise, if \f$x_3\f$ (resp. \f$x_4\f$) corresponds to a network flow \f$F_3\f$ (resp. \f$F_4\f$) that goes through
39 * a set of links \f$L_1\f$ and \f$L_2\f$ (resp. \f$L_2\f$ and \f$L_3\f$), then we need to enforce:
41 * \f[ x_3 \leq C_{L_1} \f]
42 * \f[ x_3 + x_4 \leq C_{L_2} \f]
43 * \f[ x_4 \leq C_{L_3} \f]
45 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
46 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
47 * \f$x_i\f$ are positive and "as large as possible".
49 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
50 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
65 * A possible system could be:
66 * - three variables: `var1`, `var2`, `var3`
67 * - two constraints: `cons1`, `cons2`
68 * - four elements linking:
69 * - `elem1` linking `var1` and `cons1`
70 * - `elem2` linking `var2` and `cons1`
71 * - `elem3` linking `var2` and `cons2`
72 * - `elem4` linking `var3` and `cons2`
74 * And the corresponding inequations will be:
76 * var1.value <= var1.bound
77 * var2.value <= var2.bound
78 * var3.value <= var3.bound
79 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
80 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
82 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
84 * If a constraint is not shared, the sum is replaced by a max.
85 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
87 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
89 * This is useful for the sharing of resources for various models.
90 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
92 * Implementation details
94 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
95 * computation of constraints, and those who are part of the equations but are stuck to zero.
96 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
98 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
99 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
100 * than the conditions for it to be enabled.
101 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
102 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
103 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
104 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
105 * pausing of an action.
107 * Concurrency limit and maximum
109 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
110 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
112 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
114 * One may want to limit the concurrency of constraints for essentially three reasons:
115 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
117 * - Stay within parameters where the fluid model is accurate enough.
118 * - Model serialization effects
120 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
123 * Overall, each constraint contains three fields related to concurrency:
124 * - concurrency_limit which is the limit enforced by the solver
125 * - concurrency_current which is the current concurrency
126 * - concurrency_maximum which is the observed maximum concurrency
128 * Variables also have one field related to concurrency: concurrency_share.
129 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
130 * For example, cross-traffic is modeled using 2 elements per constraint.
131 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
135 /** @{ @ingroup SURF_lmm */
139 * Elements can be seen as glue between constraint objects and variable objects.
140 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
141 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
142 * vice-versa list all constraints for a given variable.
144 class XBT_PUBLIC Element {
146 // Use rule-of-three, and implicitely disable the move constructor which should be 'noexcept' according to C++ Core
149 Element(const Element&) = default;
150 ~Element() = default;
152 int get_concurrency() const;
153 void decrease_concurrency();
154 void increase_concurrency();
157 void make_inactive();
159 /* hookup to constraint */
160 boost::intrusive::list_member_hook<> enabled_element_set_hook;
161 boost::intrusive::list_member_hook<> disabled_element_set_hook;
162 boost::intrusive::list_member_hook<> active_element_set_hook;
164 Constraint* constraint;
167 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
168 // - if CPU, then probably 1.
169 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
170 double consumption_weight;
173 class ConstraintLight {
175 double remaining_over_usage;
180 * @brief LMM constraint
181 * Each constraint contains several partially overlapping logical sets of elements:
182 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
183 * the corresponding action will enable it (at least this is the idea).
184 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
185 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
186 * LMM_solve iterates over active elements during resolution, dynamically making them active or inactive.
188 class XBT_PUBLIC Constraint {
190 enum class SharingPolicy { SHARED = 1, FATPIPE = 0 };
191 Constraint() = delete;
192 Constraint(resource::Resource* id_value, double bound_value);
194 /** @brief Unshare a constraint. */
195 void unshare() { sharing_policy_ = SharingPolicy::FATPIPE; }
197 /** @brief Set how a constraint is shared */
198 void set_sharing_policy(SharingPolicy policy) { sharing_policy_ = policy; }
199 /** @brief Check how a constraint is shared */
200 SharingPolicy get_sharing_policy() const { return sharing_policy_; }
202 /** @brief Get the usage of the constraint after the last lmm solve */
203 double get_usage() const;
204 int get_variable_amount() const;
206 /** @brief Sets the concurrency limit for this constraint */
207 void set_concurrency_limit(int limit)
209 xbt_assert(limit < 0 || concurrency_maximum_ <= limit,
210 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
211 " concurrency_maximum_reset() to reset the maximum?");
212 concurrency_limit_ = limit;
215 /** @brief Gets the concurrency limit for this constraint */
216 int get_concurrency_limit() const { return concurrency_limit_; }
219 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
222 void reset_concurrency_maximum() { concurrency_maximum_ = 0; }
224 /** @brief Get the concurrency maximum for a given constraint (which reflects constraint evolution). */
225 int get_concurrency_maximum() const
227 xbt_assert(concurrency_limit_ < 0 || concurrency_maximum_ <= concurrency_limit_,
228 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
229 return concurrency_maximum_;
232 int get_concurrency_slack() const
234 return concurrency_limit_ < 0 ? std::numeric_limits<int>::max() : concurrency_limit_ - concurrency_current_;
238 * @brief Get a var associated to a constraint
239 * @details Get the first variable of the next variable of elem if elem is not NULL
240 * @param elem A element of constraint of the constraint or NULL
241 * @return A variable associated to a constraint
243 Variable* get_variable(const Element** elem) const;
246 * @brief Get a var associated to a constraint
247 * @details Get the first variable of the next variable of elem if elem is not NULL
248 * @param elem A element of constraint of the constraint or NULL
249 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
250 * @param numelem parameter representing the number of elements to go
251 * @return A variable associated to a constraint
253 Variable* get_variable_safe(const Element** elem, const Element** nextelem, size_t* numelem) const;
256 * @brief Get the data associated to a constraint
257 * @return The data associated to the constraint
259 resource::Resource* get_id() const { return id_; }
261 /* hookup to system */
262 boost::intrusive::list_member_hook<> constraint_set_hook_;
263 boost::intrusive::list_member_hook<> active_constraint_set_hook_;
264 boost::intrusive::list_member_hook<> modified_constraint_set_hook_;
265 boost::intrusive::list_member_hook<> saturated_constraint_set_hook_;
266 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
267 &Element::enabled_element_set_hook>>
268 enabled_element_set_;
269 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
270 &Element::disabled_element_set_hook>>
271 disabled_element_set_;
272 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
273 &Element::active_element_set_hook>>
275 double remaining_ = 0.0;
278 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
279 int concurrency_current_ = 0; /* The current concurrency */
280 int concurrency_maximum_ = 0; /* The maximum number of (enabled and disabled) variables associated to the constraint
281 * at any given time (essentially for tracing)*/
283 SharingPolicy sharing_policy_ = SharingPolicy::SHARED;
284 int rank_; // Only used in debug messages to identify the constraint
285 double lambda_ = 0.0;
286 double new_lambda_ = 0.0;
287 ConstraintLight* cnst_light_ = nullptr;
290 static int next_rank_; // To give a separate rank_ to each constraint
291 int concurrency_limit_ = sg_concurrency_limit; /* The maximum number of variables that may be enabled at any time
292 * (stage variables if necessary) */
293 resource::Resource* id_;
297 * @brief LMM variable
299 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
300 * soon as possible we enable the variable with desired weight
302 class XBT_PUBLIC Variable {
304 void initialize(resource::Action* id_value, double sharing_penalty, double bound_value, size_t number_of_constraints,
305 unsigned visited_value);
307 /** @brief Get the value of the variable after the last lmm solve */
308 double get_value() const { return value_; }
310 /** @brief Get the maximum value of the variable (-1.0 if no specified maximum) */
311 double get_bound() const { return bound_; }
314 * @brief Set the concurrent share of the variable
315 * @param value The new concurrency share
317 void set_concurrency_share(short int value) { concurrency_share_ = value; }
320 * @brief Get the numth constraint associated to the variable
321 * @param num The rank of constraint we want to get
322 * @return The numth constraint
324 Constraint* get_constraint(unsigned num) const { return num < cnsts_.size() ? cnsts_[num].constraint : nullptr; }
327 * @brief Get the weight of the numth constraint associated to the variable
328 * @param num The rank of constraint we want to get
329 * @return The numth constraint
331 double get_constraint_weight(unsigned num) const
333 return num < cnsts_.size() ? cnsts_[num].consumption_weight : 0.0;
336 /** @brief Get the number of constraint associated to a variable */
337 size_t get_number_of_constraint() const { return cnsts_.size(); }
339 /** @brief Get the data associated to a variable */
340 resource::Action* get_id() const { return id_; }
342 /** @brief Get the penalty of a variable */
343 double get_penalty() const { return sharing_penalty_; }
345 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
346 int get_min_concurrency_slack() const;
348 /** @brief Check if a variable can be enabled
349 * Make sure to set staged_penalty before, if your intent is only to check concurrency
351 bool can_enable() const { return staged_penalty_ > 0 && get_min_concurrency_slack() >= concurrency_share_; }
353 /* hookup to system */
354 boost::intrusive::list_member_hook<> variable_set_hook_;
355 boost::intrusive::list_member_hook<> saturated_variable_set_hook_;
357 std::vector<Element> cnsts_;
359 // sharing_penalty: variable's impact on the resource during the sharing
360 // if == 0, the variable is not considered by LMM
361 // on CPU, actions with N threads have a sharing of N
362 // on network, the actions with higher latency have a lesser sharing_penalty
363 double sharing_penalty_;
365 double staged_penalty_; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
369 short int concurrency_share_; /* The maximum number of elements that variable will add to a constraint */
370 resource::Action* id_;
371 int rank_; // Only used in debug messages to identify the variable
372 unsigned visited_; /* used by System::update_modified_set() */
376 static int next_rank_; // To give a separate rank_ to each variable
379 inline void Element::make_active()
381 constraint->active_element_set_.push_front(*this);
383 inline void Element::make_inactive()
385 if (active_element_set_hook.is_linked())
386 xbt::intrusive_erase(constraint->active_element_set_, *this);
392 class XBT_PUBLIC System {
395 * @brief Create a new Linear MaxMim system
396 * @param selective_update whether we should do lazy updates
398 explicit System(bool selective_update);
399 /** @brief Free an existing Linear MaxMin system */
403 * @brief Create a new Linear MaxMin constraint
404 * @param id Data associated to the constraint (e.g.: a network link)
405 * @param bound_value The bound value of the constraint
407 Constraint* constraint_new(resource::Resource* id, double bound_value);
410 * @brief Create a new Linear MaxMin variable
411 * @param id Data associated to the variable (e.g.: a network communication)
412 * @param sharing_penalty The weight of the variable (0.0 if not used)
413 * @param bound The maximum value of the variable (-1.0 if no maximum value)
414 * @param number_of_constraints The maximum number of constraints to associate to the variable
416 Variable* variable_new(resource::Action* id, double sharing_penalty, double bound = -1.0,
417 size_t number_of_constraints = 1);
420 * @brief Free a variable
421 * @param var The variable to free
423 void variable_free(Variable * var);
425 /** @brief Free all variables */
426 void variable_free_all();
429 * @brief Associate a variable to a constraint with a coefficient
430 * @param cnst A constraint
431 * @param var A variable
432 * @param value The coefficient associated to the variable in the constraint
434 void expand(Constraint * cnst, Variable * var, double value);
437 * @brief Add value to the coefficient between a constraint and a variable or create one
438 * @param cnst A constraint
439 * @param var A variable
440 * @param value The value to add to the coefficient associated to the variable in the constraint
442 void expand_add(Constraint * cnst, Variable * var, double value);
444 /** @brief Update the bound of a variable */
445 void update_variable_bound(Variable * var, double bound);
447 /** @brief Update the sharing penalty of a variable */
448 void update_variable_penalty(Variable* var, double penalty);
450 /** @brief Update a constraint bound */
451 void update_constraint_bound(Constraint * cnst, double bound);
453 int constraint_used(const Constraint* cnst) const { return cnst->active_constraint_set_hook_.is_linked(); }
455 /** @brief Print the lmm system */
458 /** @brief Solve the lmm system */
461 /** @brief Solve the lmm system. May be specialized in subclasses. */
462 virtual void solve() { lmm_solve(); }
465 static void* variable_mallocator_new_f();
466 static void variable_mallocator_free_f(void* var);
468 void var_free(Variable * var);
469 void cnst_free(Constraint * cnst);
470 Variable* extract_variable()
472 if (variable_set.empty())
474 Variable* res = &variable_set.front();
475 variable_set.pop_front();
478 Constraint* extract_constraint()
480 if (constraint_set.empty())
482 Constraint* res = &constraint_set.front();
483 constraint_set.pop_front();
486 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
487 void remove_variable(Variable * var)
489 if (var->variable_set_hook_.is_linked())
490 xbt::intrusive_erase(variable_set, *var);
491 if (var->saturated_variable_set_hook_.is_linked())
492 xbt::intrusive_erase(saturated_variable_set, *var);
494 void make_constraint_active(Constraint * cnst)
496 if (not cnst->active_constraint_set_hook_.is_linked())
497 active_constraint_set.push_back(*cnst);
499 void make_constraint_inactive(Constraint * cnst)
501 if (cnst->active_constraint_set_hook_.is_linked())
502 xbt::intrusive_erase(active_constraint_set, *cnst);
503 if (cnst->modified_constraint_set_hook_.is_linked())
504 xbt::intrusive_erase(modified_constraint_set, *cnst);
507 void enable_var(Variable * var);
508 void disable_var(Variable * var);
509 void on_disabled_var(Constraint * cnstr);
512 * @brief Update the value of element linking the constraint and the variable
513 * @param cnst A constraint
514 * @param var A variable
515 * @param value The new value
517 void update(Constraint * cnst, Variable * var, double value);
519 void update_modified_set(Constraint* cnst);
520 void update_modified_set_rec(const Constraint* cnst);
522 /** @brief Remove all constraints of the modified_constraint_set. */
523 void remove_all_modified_set();
524 void check_concurrency() const;
526 template <class CnstList> void lmm_solve(CnstList& cnst_list);
529 bool modified_ = false;
530 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
531 &Variable::variable_set_hook_>>
533 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
534 &Constraint::active_constraint_set_hook_>>
535 active_constraint_set;
536 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
537 &Variable::saturated_variable_set_hook_>>
538 saturated_variable_set;
539 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
540 &Constraint::saturated_constraint_set_hook_>>
541 saturated_constraint_set;
543 std::unique_ptr<resource::Action::ModifiedSet> modified_set_ = nullptr;
546 using dyn_light_t = std::vector<int>;
548 //Data used in lmm::solve
549 std::vector<ConstraintLight> cnst_light_vec;
550 dyn_light_t saturated_constraints;
552 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
553 unsigned visited_counter_ = 1; /* used by System::update_modified_set() and System::remove_all_modified_set() to
554 * cleverly (un-)flag the constraints (more details in these functions) */
555 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
556 &Constraint::constraint_set_hook_>>
558 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
559 &Constraint::modified_constraint_set_hook_>>
560 modified_constraint_set;
561 xbt_mallocator_t variable_mallocator_ =
562 xbt_mallocator_new(65536, System::variable_mallocator_new_f, System::variable_mallocator_free_f, nullptr);
565 class XBT_PUBLIC FairBottleneck : public System {
567 using System::System;
568 void solve() final { bottleneck_solve(); }
571 void bottleneck_solve();
576 } // namespace kernel
577 } // namespace simgrid