1 /* Copyright (c) 2004-2019. 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 "xbt/asserts.h"
12 #include "xbt/mallocator.h"
14 #include <boost/intrusive/list.hpp>
23 /** @addtogroup SURF_lmm
25 * A linear maxmin solver to resolve inequations systems.
27 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
28 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
29 * 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$x_1\f$
30 * 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
31 * case, we need to enforce:
33 * \f[ x_1 + x_2 \leq C_A \f]
35 * 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
36 * 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:
38 * \f[ x_3 \leq C_{L_1} \f]
39 * \f[ x_3 + x_4 \leq C_{L_2} \f]
40 * \f[ x_4 \leq C_{L_3} \f]
42 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
43 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
44 * \f$x_i\f$ are positive and "as large as possible".
46 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
47 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
62 * A possible system could be:
63 * - three variables: `var1`, `var2`, `var3`
64 * - two constraints: `cons1`, `cons2`
65 * - four elements linking:
66 * - `elem1` linking `var1` and `cons1`
67 * - `elem2` linking `var2` and `cons1`
68 * - `elem3` linking `var2` and `cons2`
69 * - `elem4` linking `var3` and `cons2`
71 * And the corresponding inequations will be:
73 * var1.value <= var1.bound
74 * var2.value <= var2.bound
75 * var3.value <= var3.bound
76 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
77 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
79 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
81 * If a constraint is not shared, the sum is replaced by a max.
82 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
84 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
86 * This is useful for the sharing of resources for various models.
87 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
89 * Implementation details
91 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
92 * computation of constraints, and those who are part of the equations but are stuck to zero.
93 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
95 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
96 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
97 * than the conditions for it to be enabled.
98 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
99 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
100 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
101 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
102 * pausing of an action.
104 * Concurrency limit and maximum
106 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
107 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
109 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
111 * One may want to limit the concurrency of constraints for essentially three reasons:
112 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
114 * - Stay within parameters where the fluid model is accurate enough.
115 * - Model serialization effects
117 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
120 * Overall, each constraint contains three fields related to concurrency:
121 * - concurrency_limit which is the limit enforced by the solver
122 * - concurrency_current which is the current concurrency
123 * - concurrency_maximum which is the observed maximum concurrency
125 * Variables also have one field related to concurrency: concurrency_share.
126 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
127 * For example, cross-traffic is modeled using 2 elements per constraint.
128 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
132 /** @{ @ingroup SURF_lmm */
136 * Elements can be seen as glue between constraint objects and variable objects.
137 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
138 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
139 * vice-versa list all constraints for a given variable.
141 class XBT_PUBLIC Element {
143 int get_concurrency() const;
144 void decrease_concurrency();
145 void increase_concurrency();
148 void make_inactive();
150 /* hookup to constraint */
151 boost::intrusive::list_member_hook<> enabled_element_set_hook;
152 boost::intrusive::list_member_hook<> disabled_element_set_hook;
153 boost::intrusive::list_member_hook<> active_element_set_hook;
155 Constraint* constraint;
158 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
159 // - if CPU, then probably 1.
160 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
161 double consumption_weight;
164 class ConstraintLight {
166 double remaining_over_usage;
171 * @brief LMM constraint
172 * Each constraint contains several partially overlapping logical sets of elements:
173 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
174 * the corresponding action will enable it (at least this is the idea).
175 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
176 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
177 * LMM_solve iterates over active elements during resolution, dynamically making them active or inactive.
179 class XBT_PUBLIC Constraint {
181 Constraint() = delete;
182 Constraint(resource::Resource* id_value, double bound_value);
184 /** @brief Unshare a constraint. */
185 void unshare() { sharing_policy_ = s4u::Link::SharingPolicy::FATPIPE; }
187 /** @brief Check how a constraint is shared */
188 s4u::Link::SharingPolicy get_sharing_policy() const { return sharing_policy_; }
190 /** @brief Get the usage of the constraint after the last lmm solve */
191 double get_usage() const;
192 int get_variable_amount() const;
194 /** @brief Sets the concurrency limit for this constraint */
195 void set_concurrency_limit(int limit)
197 xbt_assert(limit < 0 || concurrency_maximum_ <= limit,
198 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
199 " concurrency_maximum_reset() to reset the maximum?");
200 concurrency_limit_ = limit;
203 /** @brief Gets the concurrency limit for this constraint */
204 int get_concurrency_limit() const { return concurrency_limit_; }
207 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
210 void reset_concurrency_maximum() { concurrency_maximum_ = 0; }
212 /** @brief Get the concurrency maximum for a given constraint (which reflects constraint evolution). */
213 int get_concurrency_maximum() const
215 xbt_assert(concurrency_limit_ < 0 || concurrency_maximum_ <= concurrency_limit_,
216 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
217 return concurrency_maximum_;
220 int get_concurrency_slack() const
222 return concurrency_limit_ < 0 ? std::numeric_limits<int>::max() : concurrency_limit_ - concurrency_current_;
226 * @brief Get a var associated to a constraint
227 * @details Get the first variable of the next variable of elem if elem is not NULL
228 * @param elem A element of constraint of the constraint or NULL
229 * @return A variable associated to a constraint
231 Variable* get_variable(const Element** elem) const;
234 * @brief Get a var associated to a constraint
235 * @details Get the first variable of the next variable of elem if elem is not NULL
236 * @param elem A element of constraint of the constraint or NULL
237 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
238 * @param numelem parameter representing the number of elements to go
239 * @return A variable associated to a constraint
241 Variable* get_variable_safe(const Element** elem, const Element** nextelem, int* numelem) const;
244 * @brief Get the data associated to a constraint
245 * @return The data associated to the constraint
247 resource::Resource* get_id() const { return id_; }
249 /* hookup to system */
250 boost::intrusive::list_member_hook<> constraint_set_hook_;
251 boost::intrusive::list_member_hook<> active_constraint_set_hook_;
252 boost::intrusive::list_member_hook<> modified_constraint_set_hook_;
253 boost::intrusive::list_member_hook<> saturated_constraint_set_hook_;
254 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
255 &Element::enabled_element_set_hook>>
256 enabled_element_set_;
257 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
258 &Element::disabled_element_set_hook>>
259 disabled_element_set_;
260 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
261 &Element::active_element_set_hook>>
266 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
267 int concurrency_current_; /* The current concurrency */
268 int concurrency_maximum_; /* The maximum number of (enabled and disabled) variables associated to the constraint at
269 * any given time (essentially for tracing)*/
271 s4u::Link::SharingPolicy sharing_policy_;
272 int rank_; // Only used in debug messages to identify the constraint
275 ConstraintLight* cnst_light_;
278 static int next_rank_; // To give a separate rank_ to each constraint
279 int concurrency_limit_; /* The maximum number of variables that may be enabled at any time (stage variables if
281 resource::Resource* id_;
285 * @brief LMM variable
287 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
288 * soon as possible we enable the variable with desired weight
290 class XBT_PUBLIC Variable {
292 void initialize(resource::Action* id_value, double sharing_penalty, double bound_value, int number_of_constraints,
293 unsigned visited_value);
295 /** @brief Get the value of the variable after the last lmm solve */
296 double get_value() const { return value_; }
298 /** @brief Get the maximum value of the variable (-1.0 if no specified maximum) */
299 double get_bound() const { return bound_; }
302 * @brief Set the concurrent share of the variable
303 * @param value The new concurrency share
305 void set_concurrency_share(short int value) { concurrency_share_ = value; }
308 * @brief Get the numth constraint associated to the variable
309 * @param num The rank of constraint we want to get
310 * @return The numth constraint
312 Constraint* get_constraint(unsigned num) const { return num < cnsts_.size() ? cnsts_[num].constraint : nullptr; }
315 * @brief Get the weigth of the numth constraint associated to the variable
316 * @param num The rank of constraint we want to get
317 * @return The numth constraint
319 double get_constraint_weight(unsigned num) const
321 return num < cnsts_.size() ? cnsts_[num].consumption_weight : 0.0;
324 /** @brief Get the number of constraint associated to a variable */
325 size_t get_number_of_constraint() const { return cnsts_.size(); }
327 /** @brief Get the data associated to a variable */
328 resource::Action* get_id() const { return id_; }
330 /** @brief Get the penalty of a variable */
331 double get_penalty() const { return sharing_penalty_; }
333 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
334 int get_min_concurrency_slack() const;
336 /** @brief Check if a variable can be enabled
337 * Make sure to set staged_penalty before, if your intent is only to check concurrency
339 int can_enable() const { return staged_penalty_ > 0 && get_min_concurrency_slack() >= concurrency_share_; }
341 /* hookup to system */
342 boost::intrusive::list_member_hook<> variable_set_hook_;
343 boost::intrusive::list_member_hook<> saturated_variable_set_hook_;
345 std::vector<Element> cnsts_;
347 // sharing_penalty: variable's impact on the resource during the sharing
348 // if == 0, the variable is not considered by LMM
349 // on CPU, actions with N threads have a sharing of N
350 // on network, the actions with higher latency have a lesser sharing_penalty
351 double sharing_penalty_;
353 double staged_penalty_; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
357 short int concurrency_share_; /* The maximum number of elements that variable will add to a constraint */
358 resource::Action* id_;
359 int rank_; // Only used in debug messages to identify the variable
360 unsigned visited_; /* used by System::update_modified_set() */
364 static int next_rank_; // To give a separate rank_ to each variable
367 inline void Element::make_active()
369 constraint->active_element_set_.push_front(*this);
371 inline void Element::make_inactive()
373 if (active_element_set_hook.is_linked())
374 simgrid::xbt::intrusive_erase(constraint->active_element_set_, *this);
380 class XBT_PUBLIC System {
383 * @brief Create a new Linear MaxMim system
384 * @param selective_update whether we should do lazy updates
386 explicit System(bool selective_update);
387 /** @brief Free an existing Linear MaxMin system */
391 * @brief Create a new Linear MaxMin constraint
392 * @param id Data associated to the constraint (e.g.: a network link)
393 * @param bound_value The bound value of the constraint
395 Constraint* constraint_new(resource::Resource* id, double bound_value);
398 * @brief Create a new Linear MaxMin variable
399 * @param id Data associated to the variable (e.g.: a network communication)
400 * @param sharing_penalty The weight of the variable (0.0 if not used)
401 * @param bound The maximum value of the variable (-1.0 if no maximum value)
402 * @param number_of_constraints The maximum number of constraints to associate to the variable
404 Variable* variable_new(resource::Action* id, double sharing_penalty, double bound = -1.0,
405 size_t number_of_constraints = 1);
408 * @brief Free a variable
409 * @param var The variable to free
411 void variable_free(Variable * var);
413 /** @brief Free all variables */
414 void variable_free_all();
417 * @brief Associate a variable to a constraint with a coefficient
418 * @param cnst A constraint
419 * @param var A variable
420 * @param value The coefficient associated to the variable in the constraint
422 void expand(Constraint * cnst, Variable * var, double value);
425 * @brief Add value to the coefficient between a constraint and a variable or create one
426 * @param cnst A constraint
427 * @param var A variable
428 * @param value The value to add to the coefficient associated to the variable in the constraint
430 void expand_add(Constraint * cnst, Variable * var, double value);
432 /** @brief Update the bound of a variable */
433 void update_variable_bound(Variable * var, double bound);
435 /** @brief Update the sharing penalty of a variable */
436 void update_variable_penalty(Variable* var, double penalty);
438 /** @brief Update a constraint bound */
439 void update_constraint_bound(Constraint * cnst, double bound);
441 int constraint_used(Constraint* cnst) { return cnst->active_constraint_set_hook_.is_linked(); }
443 /** @brief Print the lmm system */
446 /** @brief Solve the lmm system */
449 /** @brief Solve the lmm system. May be specialized in subclasses. */
450 virtual void solve() { lmm_solve(); }
453 static void* variable_mallocator_new_f();
454 static void variable_mallocator_free_f(void* var);
456 void var_free(Variable * var);
457 void cnst_free(Constraint * cnst);
458 Variable* extract_variable()
460 if (variable_set.empty())
462 Variable* res = &variable_set.front();
463 variable_set.pop_front();
466 Constraint* extract_constraint()
468 if (constraint_set.empty())
470 Constraint* res = &constraint_set.front();
471 constraint_set.pop_front();
474 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
475 void remove_variable(Variable * var)
477 if (var->variable_set_hook_.is_linked())
478 simgrid::xbt::intrusive_erase(variable_set, *var);
479 if (var->saturated_variable_set_hook_.is_linked())
480 simgrid::xbt::intrusive_erase(saturated_variable_set, *var);
482 void make_constraint_active(Constraint * cnst)
484 if (not cnst->active_constraint_set_hook_.is_linked())
485 active_constraint_set.push_back(*cnst);
487 void make_constraint_inactive(Constraint * cnst)
489 if (cnst->active_constraint_set_hook_.is_linked())
490 simgrid::xbt::intrusive_erase(active_constraint_set, *cnst);
491 if (cnst->modified_constraint_set_hook_.is_linked())
492 simgrid::xbt::intrusive_erase(modified_constraint_set, *cnst);
495 void enable_var(Variable * var);
496 void disable_var(Variable * var);
497 void on_disabled_var(Constraint * cnstr);
500 * @brief Update the value of element linking the constraint and the variable
501 * @param cnst A constraint
502 * @param var A variable
503 * @param value The new value
505 void update(Constraint * cnst, Variable * var, double value);
507 void update_modified_set(Constraint * cnst);
508 void update_modified_set_rec(Constraint * cnst);
510 /** @brief Remove all constraints of the modified_constraint_set. */
511 void remove_all_modified_set();
512 void check_concurrency() const;
514 template <class CnstList> void lmm_solve(CnstList& cnst_list);
517 bool modified_ = false;
518 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
519 &Variable::variable_set_hook_>>
521 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
522 &Constraint::active_constraint_set_hook_>>
523 active_constraint_set;
524 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
525 &Variable::saturated_variable_set_hook_>>
526 saturated_variable_set;
527 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
528 &Constraint::saturated_constraint_set_hook_>>
529 saturated_constraint_set;
531 resource::Action::ModifiedSet* modified_set_ = nullptr;
535 typedef std::vector<int> dyn_light_t;
537 //Data used in lmm::solve
538 std::vector<ConstraintLight> cnst_light_vec;
539 dyn_light_t saturated_constraints;
541 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
542 unsigned visited_counter_ = 1; /* used by System::update_modified_set() and System::remove_all_modified_set() to
543 * cleverly (un-)flag the constraints (more details in these functions) */
544 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
545 &Constraint::constraint_set_hook_>>
547 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
548 &Constraint::modified_constraint_set_hook_>>
549 modified_constraint_set;
550 xbt_mallocator_t variable_mallocator_ =
551 xbt_mallocator_new(65536, System::variable_mallocator_new_f, System::variable_mallocator_free_f, nullptr);
554 class XBT_PUBLIC FairBottleneck : public System {
556 explicit FairBottleneck(bool selective_update) : System(selective_update) {}
557 void solve() final { bottleneck_solve(); }
560 void bottleneck_solve();
563 XBT_PUBLIC System* make_new_maxmin_system(bool selective_update);
564 XBT_PUBLIC System* make_new_fair_bottleneck_system(bool selective_update);