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 Constraint() = delete;
191 Constraint(resource::Resource* id_value, double bound_value);
193 /** @brief Unshare a constraint. */
194 void unshare() { sharing_policy_ = s4u::Link::SharingPolicy::FATPIPE; }
196 /** @brief Set how a constraint is shared */
197 void set_sharing_policy(s4u::Link::SharingPolicy policy) { sharing_policy_ = policy; }
198 /** @brief Check how a constraint is shared */
199 s4u::Link::SharingPolicy get_sharing_policy() const { return sharing_policy_; }
201 /** @brief Get the usage of the constraint after the last lmm solve */
202 double get_usage() const;
203 int get_variable_amount() const;
205 /** @brief Sets the concurrency limit for this constraint */
206 void set_concurrency_limit(int limit)
208 xbt_assert(limit < 0 || concurrency_maximum_ <= limit,
209 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
210 " concurrency_maximum_reset() to reset the maximum?");
211 concurrency_limit_ = limit;
214 /** @brief Gets the concurrency limit for this constraint */
215 int get_concurrency_limit() const { return concurrency_limit_; }
218 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
221 void reset_concurrency_maximum() { concurrency_maximum_ = 0; }
223 /** @brief Get the concurrency maximum for a given constraint (which reflects constraint evolution). */
224 int get_concurrency_maximum() const
226 xbt_assert(concurrency_limit_ < 0 || concurrency_maximum_ <= concurrency_limit_,
227 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
228 return concurrency_maximum_;
231 int get_concurrency_slack() const
233 return concurrency_limit_ < 0 ? std::numeric_limits<int>::max() : concurrency_limit_ - concurrency_current_;
237 * @brief Get a var associated to a constraint
238 * @details Get the first variable of the next variable of elem if elem is not NULL
239 * @param elem A element of constraint of the constraint or NULL
240 * @return A variable associated to a constraint
242 Variable* get_variable(const Element** elem) const;
245 * @brief Get a var associated to a constraint
246 * @details Get the first variable of the next variable of elem if elem is not NULL
247 * @param elem A element of constraint of the constraint or NULL
248 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
249 * @param numelem parameter representing the number of elements to go
250 * @return A variable associated to a constraint
252 Variable* get_variable_safe(const Element** elem, const Element** nextelem, int* numelem) const;
255 * @brief Get the data associated to a constraint
256 * @return The data associated to the constraint
258 resource::Resource* get_id() const { return id_; }
260 /* hookup to system */
261 boost::intrusive::list_member_hook<> constraint_set_hook_;
262 boost::intrusive::list_member_hook<> active_constraint_set_hook_;
263 boost::intrusive::list_member_hook<> modified_constraint_set_hook_;
264 boost::intrusive::list_member_hook<> saturated_constraint_set_hook_;
265 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
266 &Element::enabled_element_set_hook>>
267 enabled_element_set_;
268 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
269 &Element::disabled_element_set_hook>>
270 disabled_element_set_;
271 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
272 &Element::active_element_set_hook>>
274 double remaining_ = 0.0;
277 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
278 int concurrency_current_ = 0; /* The current concurrency */
279 int concurrency_maximum_ = 0; /* The maximum number of (enabled and disabled) variables associated to the constraint
280 * at any given time (essentially for tracing)*/
282 s4u::Link::SharingPolicy sharing_policy_ = s4u::Link::SharingPolicy::SHARED;
283 int rank_; // Only used in debug messages to identify the constraint
284 double lambda_ = 0.0;
285 double new_lambda_ = 0.0;
286 ConstraintLight* cnst_light_ = nullptr;
289 static int next_rank_; // To give a separate rank_ to each constraint
290 int concurrency_limit_ = sg_concurrency_limit; /* The maximum number of variables that may be enabled at any time
291 * (stage variables if necessary) */
292 resource::Resource* id_;
296 * @brief LMM variable
298 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
299 * soon as possible we enable the variable with desired weight
301 class XBT_PUBLIC Variable {
303 void initialize(resource::Action* id_value, double sharing_penalty, double bound_value, int number_of_constraints,
304 unsigned visited_value);
306 /** @brief Get the value of the variable after the last lmm solve */
307 double get_value() const { return value_; }
309 /** @brief Get the maximum value of the variable (-1.0 if no specified maximum) */
310 double get_bound() const { return bound_; }
313 * @brief Set the concurrent share of the variable
314 * @param value The new concurrency share
316 void set_concurrency_share(short int value) { concurrency_share_ = value; }
319 * @brief Get the numth constraint associated to the variable
320 * @param num The rank of constraint we want to get
321 * @return The numth constraint
323 Constraint* get_constraint(unsigned num) const { return num < cnsts_.size() ? cnsts_[num].constraint : nullptr; }
326 * @brief Get the weight of the numth constraint associated to the variable
327 * @param num The rank of constraint we want to get
328 * @return The numth constraint
330 double get_constraint_weight(unsigned num) const
332 return num < cnsts_.size() ? cnsts_[num].consumption_weight : 0.0;
335 /** @brief Get the number of constraint associated to a variable */
336 size_t get_number_of_constraint() const { return cnsts_.size(); }
338 /** @brief Get the data associated to a variable */
339 resource::Action* get_id() const { return id_; }
341 /** @brief Get the penalty of a variable */
342 double get_penalty() const { return sharing_penalty_; }
344 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
345 int get_min_concurrency_slack() const;
347 /** @brief Check if a variable can be enabled
348 * Make sure to set staged_penalty before, if your intent is only to check concurrency
350 bool can_enable() const { return staged_penalty_ > 0 && get_min_concurrency_slack() >= concurrency_share_; }
352 /* hookup to system */
353 boost::intrusive::list_member_hook<> variable_set_hook_;
354 boost::intrusive::list_member_hook<> saturated_variable_set_hook_;
356 std::vector<Element> cnsts_;
358 // sharing_penalty: variable's impact on the resource during the sharing
359 // if == 0, the variable is not considered by LMM
360 // on CPU, actions with N threads have a sharing of N
361 // on network, the actions with higher latency have a lesser sharing_penalty
362 double sharing_penalty_;
364 double staged_penalty_; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
368 short int concurrency_share_; /* The maximum number of elements that variable will add to a constraint */
369 resource::Action* id_;
370 int rank_; // Only used in debug messages to identify the variable
371 unsigned visited_; /* used by System::update_modified_set() */
375 static int next_rank_; // To give a separate rank_ to each variable
378 inline void Element::make_active()
380 constraint->active_element_set_.push_front(*this);
382 inline void Element::make_inactive()
384 if (active_element_set_hook.is_linked())
385 xbt::intrusive_erase(constraint->active_element_set_, *this);
391 class XBT_PUBLIC System {
394 * @brief Create a new Linear MaxMim system
395 * @param selective_update whether we should do lazy updates
397 explicit System(bool selective_update);
398 /** @brief Free an existing Linear MaxMin system */
402 * @brief Create a new Linear MaxMin constraint
403 * @param id Data associated to the constraint (e.g.: a network link)
404 * @param bound_value The bound value of the constraint
406 Constraint* constraint_new(resource::Resource* id, double bound_value);
409 * @brief Create a new Linear MaxMin variable
410 * @param id Data associated to the variable (e.g.: a network communication)
411 * @param sharing_penalty The weight of the variable (0.0 if not used)
412 * @param bound The maximum value of the variable (-1.0 if no maximum value)
413 * @param number_of_constraints The maximum number of constraints to associate to the variable
415 Variable* variable_new(resource::Action* id, double sharing_penalty, double bound = -1.0,
416 size_t number_of_constraints = 1);
419 * @brief Free a variable
420 * @param var The variable to free
422 void variable_free(Variable * var);
424 /** @brief Free all variables */
425 void variable_free_all();
428 * @brief Associate a variable to a constraint with a coefficient
429 * @param cnst A constraint
430 * @param var A variable
431 * @param value The coefficient associated to the variable in the constraint
433 void expand(Constraint * cnst, Variable * var, double value);
436 * @brief Add value to the coefficient between a constraint and a variable or create one
437 * @param cnst A constraint
438 * @param var A variable
439 * @param value The value to add to the coefficient associated to the variable in the constraint
441 void expand_add(Constraint * cnst, Variable * var, double value);
443 /** @brief Update the bound of a variable */
444 void update_variable_bound(Variable * var, double bound);
446 /** @brief Update the sharing penalty of a variable */
447 void update_variable_penalty(Variable* var, double penalty);
449 /** @brief Update a constraint bound */
450 void update_constraint_bound(Constraint * cnst, double bound);
452 int constraint_used(const Constraint* cnst) const { return cnst->active_constraint_set_hook_.is_linked(); }
454 /** @brief Print the lmm system */
457 /** @brief Solve the lmm system */
460 /** @brief Solve the lmm system. May be specialized in subclasses. */
461 virtual void solve() { lmm_solve(); }
464 static void* variable_mallocator_new_f();
465 static void variable_mallocator_free_f(void* var);
467 void var_free(Variable * var);
468 void cnst_free(Constraint * cnst);
469 Variable* extract_variable()
471 if (variable_set.empty())
473 Variable* res = &variable_set.front();
474 variable_set.pop_front();
477 Constraint* extract_constraint()
479 if (constraint_set.empty())
481 Constraint* res = &constraint_set.front();
482 constraint_set.pop_front();
485 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
486 void remove_variable(Variable * var)
488 if (var->variable_set_hook_.is_linked())
489 xbt::intrusive_erase(variable_set, *var);
490 if (var->saturated_variable_set_hook_.is_linked())
491 xbt::intrusive_erase(saturated_variable_set, *var);
493 void make_constraint_active(Constraint * cnst)
495 if (not cnst->active_constraint_set_hook_.is_linked())
496 active_constraint_set.push_back(*cnst);
498 void make_constraint_inactive(Constraint * cnst)
500 if (cnst->active_constraint_set_hook_.is_linked())
501 xbt::intrusive_erase(active_constraint_set, *cnst);
502 if (cnst->modified_constraint_set_hook_.is_linked())
503 xbt::intrusive_erase(modified_constraint_set, *cnst);
506 void enable_var(Variable * var);
507 void disable_var(Variable * var);
508 void on_disabled_var(Constraint * cnstr);
511 * @brief Update the value of element linking the constraint and the variable
512 * @param cnst A constraint
513 * @param var A variable
514 * @param value The new value
516 void update(Constraint * cnst, Variable * var, double value);
518 void update_modified_set(Constraint* cnst);
519 void update_modified_set_rec(const Constraint* cnst);
521 /** @brief Remove all constraints of the modified_constraint_set. */
522 void remove_all_modified_set();
523 void check_concurrency() const;
525 template <class CnstList> void lmm_solve(CnstList& cnst_list);
528 bool modified_ = false;
529 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
530 &Variable::variable_set_hook_>>
532 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
533 &Constraint::active_constraint_set_hook_>>
534 active_constraint_set;
535 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
536 &Variable::saturated_variable_set_hook_>>
537 saturated_variable_set;
538 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
539 &Constraint::saturated_constraint_set_hook_>>
540 saturated_constraint_set;
542 std::unique_ptr<resource::Action::ModifiedSet> modified_set_ = nullptr;
545 using dyn_light_t = std::vector<int>;
547 //Data used in lmm::solve
548 std::vector<ConstraintLight> cnst_light_vec;
549 dyn_light_t saturated_constraints;
551 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
552 unsigned visited_counter_ = 1; /* used by System::update_modified_set() and System::remove_all_modified_set() to
553 * cleverly (un-)flag the constraints (more details in these functions) */
554 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
555 &Constraint::constraint_set_hook_>>
557 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
558 &Constraint::modified_constraint_set_hook_>>
559 modified_constraint_set;
560 xbt_mallocator_t variable_mallocator_ =
561 xbt_mallocator_new(65536, System::variable_mallocator_new_f, System::variable_mallocator_free_f, nullptr);
564 class XBT_PUBLIC FairBottleneck : public System {
566 using System::System;
567 void solve() final { bottleneck_solve(); }
570 void bottleneck_solve();
575 } // namespace kernel
576 } // namespace simgrid