1 /* Copyright (c) 2004-2018. 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 "src/internal_config.h"
11 #include "src/surf/surf_interface.hpp"
12 #include "surf/surf.hpp"
13 #include "xbt/asserts.h"
14 #include "xbt/mallocator.h"
16 #include "xbt/utility.hpp"
18 #include <boost/intrusive/list.hpp>
27 /** @addtogroup SURF_lmm
29 * A linear maxmin solver to resolve inequations systems.
31 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
32 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
33 * 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$x_1\f$
34 * 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
35 * case, we need to enforce:
37 * \f[ x_1 + x_2 \leq C_A \f]
39 * 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
40 * 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:
42 * \f[ x_3 \leq C_{L_1} \f]
43 * \f[ x_3 + x_4 \leq C_{L_2} \f]
44 * \f[ x_4 \leq C_{L_3} \f]
46 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
47 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
48 * \f$x_i\f$ are positive and "as large as possible".
50 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
51 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
66 * A possible system could be:
67 * - three variables: `var1`, `var2`, `var3`
68 * - two constraints: `cons1`, `cons2`
69 * - four elements linking:
70 * - `elem1` linking `var1` and `cons1`
71 * - `elem2` linking `var2` and `cons1`
72 * - `elem3` linking `var2` and `cons2`
73 * - `elem4` linking `var3` and `cons2`
75 * And the corresponding inequations will be:
77 * var1.value <= var1.bound
78 * var2.value <= var2.bound
79 * var3.value <= var3.bound
80 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
81 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
83 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
85 * If a constraint is not shared, the sum is replaced by a max.
86 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
88 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
90 * This is useful for the sharing of resources for various models.
91 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
93 * Implementation details
95 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
96 * computation of constraints, and those who are part of the equations but are stuck to zero.
97 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
99 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
100 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
101 * than the conditions for it to be enabled.
102 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
103 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
104 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
105 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
106 * pausing of an action.
108 * Concurrency limit and maximum
110 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
111 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
113 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
115 * One may want to limit the concurrency of constraints for essentially three reasons:
116 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
118 * - Stay within parameters where the fluid model is accurate enough.
119 * - Model serialization effects
121 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
124 * Overall, each constraint contains three fields related to concurrency:
125 * - concurrency_limit which is the limit enforced by the solver
126 * - concurrency_current which is the current concurrency
127 * - concurrency_maximum which is the observed maximum concurrency
129 * Variables also have one field related to concurrency: concurrency_share.
130 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
131 * For example, cross-traffic is modeled using 2 elements per constraint.
132 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
136 /** @{ @ingroup SURF_lmm */
138 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
140 XBT_PUBLIC void set_default_protocol_function(double (*func_f)(const Variable& var, double x),
141 double (*func_fp)(const Variable& var, double x),
142 double (*func_fpi)(const Variable& var, double x));
144 XBT_PUBLIC double func_reno_f(const Variable& var, double x);
145 XBT_PUBLIC double func_reno_fp(const Variable& var, double x);
146 XBT_PUBLIC double func_reno_fpi(const Variable& var, double x);
148 XBT_PUBLIC double func_reno2_f(const Variable& var, double x);
149 XBT_PUBLIC double func_reno2_fp(const Variable& var, double x);
150 XBT_PUBLIC double func_reno2_fpi(const Variable& var, double x);
152 XBT_PUBLIC double func_vegas_f(const Variable& var, double x);
153 XBT_PUBLIC double func_vegas_fp(const Variable& var, double x);
154 XBT_PUBLIC double func_vegas_fpi(const Variable& var, double x);
158 * Elements can be seen as glue between constraint objects and variable objects.
159 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
160 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
161 * vice-versa list all constraints for a given variable.
163 class XBT_PUBLIC Element {
165 int get_concurrency() const;
166 void decrease_concurrency();
167 void increase_concurrency();
170 void make_inactive();
172 /* hookup to constraint */
173 boost::intrusive::list_member_hook<> enabled_element_set_hook;
174 boost::intrusive::list_member_hook<> disabled_element_set_hook;
175 boost::intrusive::list_member_hook<> active_element_set_hook;
177 Constraint* constraint;
180 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
181 // - if CPU, then probably 1.
182 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
183 double consumption_weight;
186 struct ConstraintLight {
187 double remaining_over_usage;
192 * @brief LMM constraint
193 * Each constraint contains several partially overlapping logical sets of elements:
194 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
195 * the corresponding action will enable it (at least this is the idea).
196 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
197 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
198 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
200 class XBT_PUBLIC Constraint {
202 Constraint() = delete;
203 Constraint(void* id_value, double bound_value);
205 /** @brief Unshare a constraint. */
206 void unshare() { sharing_policy = 0; }
209 * @brief Check if a constraint is shared (shared by default)
210 * @return 1 if shared, 0 otherwise
212 int get_sharing_policy() const { return sharing_policy; }
215 * @brief Get the usage of the constraint after the last lmm solve
216 * @return The usage of the constraint
218 double get_usage() const;
219 int get_variable_amount() const;
222 * @brief Sets the concurrency limit for this constraint
223 * @param limit The concurrency limit to use for this constraint
225 void set_concurrency_limit(int limit)
227 xbt_assert(limit < 0 || concurrency_maximum <= limit,
228 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
229 " concurrency_maximum_reset() to reset the maximum?");
230 concurrency_limit = limit;
234 * @brief Gets the concurrency limit for this constraint
235 * @return The concurrency limit used by this constraint
237 int get_concurrency_limit() const { return concurrency_limit; }
240 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
243 void reset_concurrency_maximum() { concurrency_maximum = 0; }
246 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
247 * @return the maximum concurrency of the constraint
249 int get_concurrency_maximum() const
251 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
252 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
253 return concurrency_maximum;
256 int get_concurrency_slack() const
258 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
262 * @brief Get a var associated to a constraint
263 * @details Get the first variable of the next variable of elem if elem is not NULL
264 * @param elem A element of constraint of the constraint or NULL
265 * @return A variable associated to a constraint
267 Variable* get_variable(const_lmm_element_t * elem) const;
270 * @brief Get a var associated to a constraint
271 * @details Get the first variable of the next variable of elem if elem is not NULL
272 * @param elem A element of constraint of the constraint or NULL
273 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
274 * @param numelem parameter representing the number of elements to go
275 * @return A variable associated to a constraint
277 Variable* get_variable_safe(const_lmm_element_t * elem, const_lmm_element_t * nextelem, int* numelem) const;
280 * @brief Get the data associated to a constraint
281 * @return The data associated to the constraint
283 void* get_id() const { return id; }
285 /* hookup to system */
286 boost::intrusive::list_member_hook<> constraint_set_hook;
287 boost::intrusive::list_member_hook<> active_constraint_set_hook;
288 boost::intrusive::list_member_hook<> modified_constraint_set_hook;
289 boost::intrusive::list_member_hook<> saturated_constraint_set_hook;
290 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
291 &Element::enabled_element_set_hook>>
293 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
294 &Element::disabled_element_set_hook>>
295 disabled_element_set;
296 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
297 &Element::active_element_set_hook>>
302 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
303 int concurrency_current; /* The current concurrency */
304 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
305 * given time (essentially for tracing)*/
307 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: SPLITDUPLEX) */
311 lmm_constraint_light_t cnst_light;
314 static int Global_debug_id;
315 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
321 * @brief LMM variable
323 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
324 * soon as possible we enable the variable with desired weight
326 class XBT_PUBLIC Variable {
328 void initialize(simgrid::kernel::resource::Action * id_value, double sharing_weight_value, double bound_value,
329 int number_of_constraints, unsigned visited_value);
332 * @brief Get the value of the variable after the last lmm solve
333 * @return The value of the variable
335 double get_value() const { return value; }
338 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
339 * @return The bound of the variable
341 double get_bound() const { return bound; }
344 * @brief Set the concurrent share of the variable
345 * @param value The new concurrency share
347 void set_concurrency_share(short int value) { concurrency_share = value; }
350 * @brief Get the numth constraint associated to the variable
351 * @param num The rank of constraint we want to get
352 * @return The numth constraint
354 Constraint* get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
357 * @brief Get the weigth of the numth constraint associated to the variable
358 * @param num The rank of constraint we want to get
359 * @return The numth constraint
361 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
364 * @brief Get the number of constraint associated to a variable
365 * @return The number of constraint associated to the variable
367 int get_number_of_constraint() const { return cnsts.size(); }
370 * @brief Get the data associated to a variable
371 * @return The data associated to the variable
373 simgrid::kernel::resource::Action* get_id() const { return id; }
376 * @brief Get the weight of a variable
377 * @return The weight of the variable
379 double get_weight() const { return sharing_weight; }
381 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
382 int get_min_concurrency_slack() const;
384 /** @brief Check if a variable can be enabled
385 * Make sure to set staged_weight before, if your intent is only to check concurrency
387 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
389 /* hookup to system */
390 boost::intrusive::list_member_hook<> variable_set_hook;
391 boost::intrusive::list_member_hook<> saturated_variable_set_hook;
393 std::vector<Element> cnsts;
395 // sharing_weight: variable's impact on the resource during the sharing
396 // if == 0, the variable is not considered by LMM
397 // on CPU, actions with N threads have a sharing of N
398 // on network, the actions with higher latency have a lesser sharing_weight
399 double sharing_weight;
401 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
405 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
406 simgrid::kernel::resource::Action* id;
408 unsigned visited; /* used by System::update_modified_set() */
409 /* \begin{For Lagrange only} */
412 double (*func_f)(const Variable& var, double x); /* (f) */
413 double (*func_fp)(const Variable& var, double x); /* (f') */
414 double (*func_fpi)(const Variable& var, double x); /* (f')^{-1} */
415 /* \end{For Lagrange only} */
418 static int Global_debug_id;
421 inline void Element::make_active()
423 constraint->active_element_set.push_front(*this);
425 inline void Element::make_inactive()
427 if (active_element_set_hook.is_linked())
428 simgrid::xbt::intrusive_erase(constraint->active_element_set, *this);
434 class XBT_PUBLIC System {
437 * @brief Create a new Linear MaxMim system
438 * @param selective_update whether we should do lazy updates
440 explicit System(bool selective_update);
441 /** @brief Free an existing Linear MaxMin system */
445 * @brief Create a new Linear MaxMin constraint
446 * @param id Data associated to the constraint (e.g.: a network link)
447 * @param bound_value The bound value of the constraint
449 Constraint* constraint_new(void* id, double bound_value);
452 * @brief Create a new Linear MaxMin variable
453 * @param id Data associated to the variable (e.g.: a network communication)
454 * @param weight_value The weight of the variable (0.0 if not used)
455 * @param bound The maximum value of the variable (-1.0 if no maximum value)
456 * @param number_of_constraints The maximum number of constraint to associate to the variable
458 Variable* variable_new(simgrid::kernel::resource::Action * id, double weight_value, double bound,
459 int number_of_constraints);
462 * @brief Free a variable
463 * @param var The variable to free
465 void variable_free(Variable * var);
468 * @brief Associate a variable to a constraint with a coefficient
469 * @param cnst A constraint
470 * @param var A variable
471 * @param value The coefficient associated to the variable in the constraint
473 void expand(Constraint * cnst, Variable * var, double value);
476 * @brief Add value to the coefficient between a constraint and a variable or create one
477 * @param cnst A constraint
478 * @param var A variable
479 * @param value The value to add to the coefficient associated to the variable in the constraint
481 void expand_add(Constraint * cnst, Variable * var, double value);
484 * @brief Update the bound of a variable
485 * @param var A constraint
486 * @param bound The new bound
488 void update_variable_bound(Variable * var, double bound);
491 * @brief Update the weight of a variable
492 * @param var A variable
493 * @param weight The new weight of the variable
495 void update_variable_weight(Variable * var, double weight);
498 * @brief Update a constraint bound
499 * @param cnst A constraint
500 * @param bound The new bound of the consrtaint
502 void update_constraint_bound(Constraint * cnst, double bound);
505 * @brief [brief description]
506 * @param cnst A constraint
507 * @return [description]
509 int constraint_used(Constraint * cnst) { return cnst->active_constraint_set_hook.is_linked(); }
511 /** @brief Print the lmm system */
514 /** @brief Solve the lmm system */
517 /** @brief Solve the lmm system. May be specialized in subclasses. */
518 virtual void solve() { lmm_solve(); }
521 static void* variable_mallocator_new_f();
522 static void variable_mallocator_free_f(void* var);
524 void var_free(Variable * var);
525 void cnst_free(Constraint * cnst);
526 Variable* extract_variable()
528 if (variable_set.empty())
530 Variable* res = &variable_set.front();
531 variable_set.pop_front();
534 Constraint* extract_constraint()
536 if (constraint_set.empty())
538 Constraint* res = &constraint_set.front();
539 constraint_set.pop_front();
542 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
543 void remove_variable(Variable * var)
545 if (var->variable_set_hook.is_linked())
546 simgrid::xbt::intrusive_erase(variable_set, *var);
547 if (var->saturated_variable_set_hook.is_linked())
548 simgrid::xbt::intrusive_erase(saturated_variable_set, *var);
550 void make_constraint_active(Constraint * cnst)
552 if (not cnst->active_constraint_set_hook.is_linked())
553 active_constraint_set.push_back(*cnst);
555 void make_constraint_inactive(Constraint * cnst)
557 if (cnst->active_constraint_set_hook.is_linked())
558 simgrid::xbt::intrusive_erase(active_constraint_set, *cnst);
559 if (cnst->modified_constraint_set_hook.is_linked())
560 simgrid::xbt::intrusive_erase(modified_constraint_set, *cnst);
563 void enable_var(Variable * var);
564 void disable_var(Variable * var);
565 void on_disabled_var(Constraint * cnstr);
568 * @brief Update the value of element linking the constraint and the variable
569 * @param cnst A constraint
570 * @param var A variable
571 * @param value The new value
573 void update(Constraint * cnst, Variable * var, double value);
575 void update_modified_set(Constraint * cnst);
576 void update_modified_set_rec(Constraint * cnst);
578 /** @brief Remove all constraints of the modified_constraint_set. */
579 void remove_all_modified_set();
580 void check_concurrency() const;
582 template <class CnstList> void lmm_solve(CnstList& cnst_list);
586 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
587 &Variable::variable_set_hook>>
589 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
590 &Constraint::active_constraint_set_hook>>
591 active_constraint_set;
592 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
593 &Variable::saturated_variable_set_hook>>
594 saturated_variable_set;
595 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
596 &Constraint::saturated_constraint_set_hook>>
597 saturated_constraint_set;
599 simgrid::kernel::resource::Action::ModifiedSet* modified_set_ = nullptr;
602 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
603 unsigned visited_counter; /* used by System::update_modified_set() and System::remove_all_modified_set() to
604 * cleverly (un-)flag the constraints (more details in these functions) */
605 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
606 &Constraint::constraint_set_hook>>
608 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
609 &Constraint::modified_constraint_set_hook>>
610 modified_constraint_set;
611 xbt_mallocator_t variable_mallocator;
614 class XBT_PUBLIC FairBottleneck : public System {
616 explicit FairBottleneck(bool selective_update) : System(selective_update) {}
617 void solve() final { bottleneck_solve(); }
620 void bottleneck_solve();
623 class XBT_PUBLIC Lagrange : public System {
625 explicit Lagrange(bool selective_update) : System(selective_update) {}
626 void solve() final { lagrange_solve(); }
629 void lagrange_solve();
631 bool check_feasible(bool warn);
632 double dual_objective();
635 XBT_PUBLIC System* make_new_maxmin_system(bool selective_update);
636 XBT_PUBLIC System* make_new_fair_bottleneck_system(bool selective_update);
637 XBT_PUBLIC System* make_new_lagrange_system(bool selective_update);
639 extern XBT_PRIVATE double (*func_f_def)(const Variable&, double);
640 extern XBT_PRIVATE double (*func_fp_def)(const Variable&, double);
641 extern XBT_PRIVATE double (*func_fpi_def)(const Variable&, double);