1 /* Copyright (c) 2004-2017. 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 "src/internal_config.h"
10 #include "src/surf/surf_interface.hpp"
11 #include "surf/surf.hpp"
12 #include "xbt/asserts.h"
13 #include "xbt/mallocator.h"
15 #include "xbt/utility.hpp"
16 #include <boost/intrusive/list.hpp>
25 /** @addtogroup SURF_lmm
27 * A linear maxmin solver to resolve inequations systems.
29 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
30 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
31 * 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$x_1\f$
32 * 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
33 * case, we need to enforce:
35 * \f[ x_1 + x_2 \leq C_A \f]
37 * 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
38 * 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:
40 * \f[ x_3 \leq C_{L_1} \f]
41 * \f[ x_3 + x_4 \leq C_{L_2} \f]
42 * \f[ x_4 \leq C_{L_3} \f]
44 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
45 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
46 * \f$x_i\f$ are positive and "as large as possible".
48 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
49 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
64 * A possible system could be:
65 * - three variables: `var1`, `var2`, `var3`
66 * - two constraints: `cons1`, `cons2`
67 * - four elements linking:
68 * - `elem1` linking `var1` and `cons1`
69 * - `elem2` linking `var2` and `cons1`
70 * - `elem3` linking `var2` and `cons2`
71 * - `elem4` linking `var3` and `cons2`
73 * And the corresponding inequations will be:
75 * var1.value <= var1.bound
76 * var2.value <= var2.bound
77 * var3.value <= var3.bound
78 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
79 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
81 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
83 * If a constraint is not shared, the sum is replaced by a max.
84 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
86 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
88 * This is usefull for the sharing of resources for various models.
89 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
91 * Implementation details
93 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
94 * computation of constraints, and those who are part of the equations but are stuck to zero.
95 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
97 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
98 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
99 * than the conditions for it to be enabled.
100 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
101 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
102 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
103 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
104 * pausing of an action.
106 * Concurrency limit and maximum
108 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
109 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
111 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
113 * One may want to limit the concurrency of constraints for essentially three reasons:
114 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
116 * - Stay within parameters where the fluid model is accurate enough.
117 * - Model serialization effects
119 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
122 * Overall, each constraint contains three fields related to concurrency:
123 * - concurrency_limit which is the limit enforced by the solver
124 * - concurrency_current which is the current concurrency
125 * - concurrency_maximum which is the observed maximum concurrency
127 * Variables also have one field related to concurrency: concurrency_share.
128 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
129 * For example, cross-traffic is modeled using 2 elements per constraint.
130 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
134 /** @{ @ingroup SURF_lmm */
137 * @brief Solve the lmm system
138 * @param sys The lmm system to solve
140 XBT_PUBLIC(void) lmm_solve(lmm_system_t sys);
142 XBT_PUBLIC(void) lagrange_solve(lmm_system_t sys);
143 XBT_PUBLIC(void) bottleneck_solve(lmm_system_t sys);
145 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
148 set_default_protocol_function(double (*func_f)(const Variable& var, double x),
149 double (*func_fp)(const Variable& var, double x),
150 double (*func_fpi)(const Variable& var, double x));
152 XBT_PUBLIC(double) func_reno_f(const Variable& var, double x);
153 XBT_PUBLIC(double) func_reno_fp(const Variable& var, double x);
154 XBT_PUBLIC(double) func_reno_fpi(const Variable& var, double x);
156 XBT_PUBLIC(double) func_reno2_f(const Variable& var, double x);
157 XBT_PUBLIC(double) func_reno2_fp(const Variable& var, double x);
158 XBT_PUBLIC(double) func_reno2_fpi(const Variable& var, double x);
160 XBT_PUBLIC(double) func_vegas_f(const Variable& var, double x);
161 XBT_PUBLIC(double) func_vegas_fp(const Variable& var, double x);
162 XBT_PUBLIC(double) func_vegas_fpi(const Variable& var, double x);
166 * Elements can be seen as glue between constraint objects and variable objects.
167 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
168 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
169 * vice-versa list all constraints for a given variable.
171 XBT_PUBLIC_CLASS Element
174 int get_concurrency() const;
175 void decrease_concurrency();
176 void increase_concurrency();
179 void make_inactive();
181 /* hookup to constraint */
182 boost::intrusive::list_member_hook<> enabled_element_set_hook;
183 boost::intrusive::list_member_hook<> disabled_element_set_hook;
184 boost::intrusive::list_member_hook<> active_element_set_hook;
186 lmm_constraint_t constraint;
187 lmm_variable_t variable;
189 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
190 // - if CPU, then probably 1.
191 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
192 double consumption_weight;
195 struct ConstraintLight {
196 double remaining_over_usage;
197 lmm_constraint_t cnst;
201 * @brief LMM constraint
202 * Each constraint contains several partially overlapping logical sets of elements:
203 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
204 * the corresponding action will enable it (at least this is the idea).
205 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
206 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
207 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
209 XBT_PUBLIC_CLASS Constraint
212 Constraint() = default;
213 Constraint(void* id_value, double bound_value);
215 /** @brief Unshare a constraint. */
216 void unshare() { sharing_policy = 0; }
219 * @brief Check if a constraint is shared (shared by default)
220 * @return 1 if shared, 0 otherwise
222 int get_sharing_policy() const { return sharing_policy; }
225 * @brief Get the usage of the constraint after the last lmm solve
226 * @return The usage of the constraint
228 double get_usage() const;
229 int get_variable_amount() const;
232 * @brief Sets the concurrency limit for this constraint
233 * @param concurrency_limit The concurrency limit to use for this constraint
235 void set_concurrency_limit(int limit)
237 xbt_assert(limit < 0 || concurrency_maximum <= limit,
238 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
239 " concurrency_maximum_reset() to reset the maximum?");
240 concurrency_limit = limit;
244 * @brief Gets the concurrency limit for this constraint
245 * @return The concurrency limit used by this constraint
247 int get_concurrency_limit() const { return concurrency_limit; }
250 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
253 void reset_concurrency_maximum() { concurrency_maximum = 0; }
256 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
257 * @return the maximum concurrency of the constraint
259 int get_concurrency_maximum() const
261 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
262 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
263 return concurrency_maximum;
266 int get_concurrency_slack() const
268 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
272 * @brief Get a var associated to a constraint
273 * @details Get the first variable of the next variable of elem if elem is not NULL
274 * @param elem A element of constraint of the constraint or NULL
275 * @return A variable associated to a constraint
277 lmm_variable_t get_variable(const_lmm_element_t* elem) const;
280 * @brief Get a var associated to a constraint
281 * @details Get the first variable of the next variable of elem if elem is not NULL
282 * @param elem A element of constraint of the constraint or NULL
283 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
284 * @param numelem parameter representing the number of elements to go
285 * @return A variable associated to a constraint
287 lmm_variable_t get_variable_safe(const_lmm_element_t* elem, const_lmm_element_t* nextelem, int* numelem) const;
290 * @brief Get the data associated to a constraint
291 * @return The data associated to the constraint
293 void* get_id() const { return id; }
295 /* hookup to system */
296 boost::intrusive::list_member_hook<> constraint_set_hook;
297 boost::intrusive::list_member_hook<> active_constraint_set_hook;
298 boost::intrusive::list_member_hook<> modified_constraint_set_hook;
299 boost::intrusive::list_member_hook<> saturated_constraint_set_hook;
300 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
301 &Element::enabled_element_set_hook>>
303 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
304 &Element::disabled_element_set_hook>>
305 disabled_element_set;
306 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
307 &Element::active_element_set_hook>>
312 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
313 int concurrency_current; /* The current concurrency */
314 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
315 * given time (essentially for tracing)*/
317 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: FULLDUPLEX) */
321 lmm_constraint_light_t cnst_light;
324 static int Global_debug_id;
325 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
331 * @brief LMM variable
333 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
334 * soon as possible we enable the variable with desired weight
336 XBT_PUBLIC_CLASS Variable
339 void initialize(simgrid::surf::Action* id_value, double sharing_weight_value, double bound_value,
340 int number_of_constraints, unsigned visited_value);
343 * @brief Get the value of the variable after the last lmm solve
344 * @return The value of the variable
346 double get_value() const { return value; }
349 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
350 * @return The bound of the variable
352 double get_bound() const { return bound; }
355 * @brief Set the concurrent share of the variable
356 * @param concurrency_share The new concurrency share
358 void set_concurrency_share(short int value) { concurrency_share = value; }
361 * @brief Get the numth constraint associated to the variable
362 * @param num The rank of constraint we want to get
363 * @return The numth constraint
365 lmm_constraint_t get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
368 * @brief Get the weigth of the numth constraint associated to the variable
369 * @param num The rank of constraint we want to get
370 * @return The numth constraint
372 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
375 * @brief Get the number of constraint associated to a variable
376 * @return The number of constraint associated to the variable
378 int get_number_of_constraint() const { return cnsts.size(); }
381 * @brief Get the data associated to a variable
382 * @return The data associated to the variable
384 simgrid::surf::Action* get_id() const { return id; }
387 * @brief Get the weight of a variable
388 * @return The weight of the variable
390 double get_weight() const { return sharing_weight; }
392 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
393 int get_min_concurrency_slack() const;
395 /** @brief Check if a variable can be enabled
396 * Make sure to set staged_weight before, if your intent is only to check concurrency
398 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
400 /* hookup to system */
401 boost::intrusive::list_member_hook<> variable_set_hook;
402 boost::intrusive::list_member_hook<> saturated_variable_set_hook;
404 std::vector<Element> cnsts;
406 // sharing_weight: variable's impact on the resource during the sharing
407 // if == 0, the variable is not considered by LMM
408 // on CPU, actions with N threads have a sharing of N
409 // on network, the actions with higher latency have a lesser sharing_weight
410 double sharing_weight;
412 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
416 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
417 simgrid::surf::Action* id;
419 unsigned visited; /* used by System::update_modified_set() */
420 /* \begin{For Lagrange only} */
423 double (*func_f)(const Variable& var, double x); /* (f) */
424 double (*func_fp)(const Variable& var, double x); /* (f') */
425 double (*func_fpi)(const Variable& var, double x); /* (f')^{-1} */
426 /* \end{For Lagrange only} */
429 static int Global_debug_id;
432 inline void Element::make_active()
434 constraint->active_element_set.push_front(*this);
436 inline void Element::make_inactive()
438 if (active_element_set_hook.is_linked())
439 simgrid::xbt::intrusive_erase(constraint->active_element_set, *this);
445 XBT_PUBLIC_CLASS System
449 * @brief Create a new Linear MaxMim system
450 * @param selective_update whether we should do lazy updates
452 explicit System(bool selective_update);
453 /** @brief Free an existing Linear MaxMin system */
457 * @brief Create a new Linear MaxMin constraint
458 * @param id Data associated to the constraint (e.g.: a network link)
459 * @param bound_value The bound value of the constraint
461 lmm_constraint_t constraint_new(void* id, double bound_value);
464 * @brief Create a new Linear MaxMin variable
465 * @param id Data associated to the variable (e.g.: a network communication)
466 * @param weight_value The weight of the variable (0.0 if not used)
467 * @param bound The maximum value of the variable (-1.0 if no maximum value)
468 * @param number_of_constraints The maximum number of constraint to associate to the variable
470 lmm_variable_t variable_new(simgrid::surf::Action* id, double weight_value, double bound, int number_of_constraints);
473 * @brief Free a variable
474 * @param var The variable to free
476 void variable_free(lmm_variable_t var);
479 * @brief Associate a variable to a constraint with a coefficient
480 * @param cnst A constraint
481 * @param var A variable
482 * @param value The coefficient associated to the variable in the constraint
484 void expand(lmm_constraint_t cnst, lmm_variable_t var, double value);
487 * @brief Add value to the coefficient between a constraint and a variable or create one
488 * @param cnst A constraint
489 * @param var A variable
490 * @param value The value to add to the coefficient associated to the variable in the constraint
492 void expand_add(lmm_constraint_t cnst, lmm_variable_t var, double value);
495 * @brief Update the bound of a variable
496 * @param var A constraint
497 * @param bound The new bound
499 void update_variable_bound(lmm_variable_t var, double bound);
502 * @brief Update the weight of a variable
503 * @param var A variable
504 * @param weight The new weight of the variable
506 void update_variable_weight(lmm_variable_t var, double weight);
509 * @brief Update a constraint bound
510 * @param cnst A constraint
511 * @param bound The new bound of the consrtaint
513 void update_constraint_bound(lmm_constraint_t cnst, double bound);
516 * @brief [brief description]
517 * @param cnst A constraint
518 * @return [description]
520 int constraint_used(lmm_constraint_t cnst) { return cnst->active_constraint_set_hook.is_linked(); }
522 /** @brief Print the lmm system */
525 /** @brief Solve the lmm system */
529 static void* variable_mallocator_new_f();
530 static void variable_mallocator_free_f(void* var);
532 void var_free(lmm_variable_t var);
533 void cnst_free(lmm_constraint_t cnst);
534 lmm_variable_t extract_variable()
536 if (variable_set.empty())
538 lmm_variable_t res = &variable_set.front();
539 variable_set.pop_front();
542 lmm_constraint_t extract_constraint()
544 if (constraint_set.empty())
546 lmm_constraint_t res = &constraint_set.front();
547 constraint_set.pop_front();
550 void insert_constraint(lmm_constraint_t cnst) { constraint_set.push_back(*cnst); }
551 void remove_variable(lmm_variable_t var)
553 if (var->variable_set_hook.is_linked())
554 simgrid::xbt::intrusive_erase(variable_set, *var);
555 if (var->saturated_variable_set_hook.is_linked())
556 simgrid::xbt::intrusive_erase(saturated_variable_set, *var);
558 void make_constraint_active(lmm_constraint_t cnst)
560 if (not cnst->active_constraint_set_hook.is_linked())
561 active_constraint_set.push_back(*cnst);
563 void make_constraint_inactive(lmm_constraint_t cnst)
565 if (cnst->active_constraint_set_hook.is_linked())
566 simgrid::xbt::intrusive_erase(active_constraint_set, *cnst);
567 if (cnst->modified_constraint_set_hook.is_linked())
568 simgrid::xbt::intrusive_erase(modified_constraint_set, *cnst);
571 void enable_var(lmm_variable_t var);
572 void disable_var(lmm_variable_t var);
573 void on_disabled_var(lmm_constraint_t cnstr);
576 * @brief Update the value of element linking the constraint and the variable
577 * @param cnst A constraint
578 * @param var A variable
579 * @param value The new value
581 void update(lmm_constraint_t cnst, lmm_variable_t var, double value);
583 void update_modified_set(lmm_constraint_t cnst);
584 void update_modified_set_rec(lmm_constraint_t cnst);
586 /** @brief Remove all constraints of the modified_constraint_set. */
587 void remove_all_modified_set();
588 void check_concurrency() const;
590 template <class CnstList> void solve(CnstList& cnst_list);
593 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
594 &Variable::variable_set_hook>>
596 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
597 &Constraint::active_constraint_set_hook>>
598 active_constraint_set;
599 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
600 &Variable::saturated_variable_set_hook>>
601 saturated_variable_set;
602 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
603 &Constraint::saturated_constraint_set_hook>>
604 saturated_constraint_set;
606 simgrid::surf::ActionLmmListPtr keep_track;
608 void (*solve_fun)(lmm_system_t self);
611 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
612 unsigned visited_counter; /* used by System::update_modified_set() and System::remove_all_modified_set() to
613 * cleverly (un-)flag the constraints (more details in these functions) */
614 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
615 &Constraint::constraint_set_hook>>
617 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
618 &Constraint::modified_constraint_set_hook>>
619 modified_constraint_set;
620 xbt_mallocator_t variable_mallocator;
623 extern XBT_PRIVATE double (*func_f_def)(const Variable&, double);
624 extern XBT_PRIVATE double (*func_fp_def)(const Variable&, double);
625 extern XBT_PRIVATE double (*func_fpi_def)(const Variable&, double);