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 "src/internal_config.h"
10 #include "src/kernel/resource/Action.hpp"
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"
17 #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 */
138 * @brief Solve the lmm system
139 * @param sys The lmm system to solve
141 XBT_PUBLIC(void) lmm_solve(lmm_system_t sys);
143 XBT_PUBLIC(void) lagrange_solve(lmm_system_t sys);
144 XBT_PUBLIC(void) bottleneck_solve(lmm_system_t sys);
146 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
149 set_default_protocol_function(double (*func_f)(const Variable& var, double x),
150 double (*func_fp)(const Variable& var, double x),
151 double (*func_fpi)(const Variable& var, double x));
153 XBT_PUBLIC(double) func_reno_f(const Variable& var, double x);
154 XBT_PUBLIC(double) func_reno_fp(const Variable& var, double x);
155 XBT_PUBLIC(double) func_reno_fpi(const Variable& var, double x);
157 XBT_PUBLIC(double) func_reno2_f(const Variable& var, double x);
158 XBT_PUBLIC(double) func_reno2_fp(const Variable& var, double x);
159 XBT_PUBLIC(double) func_reno2_fpi(const Variable& var, double x);
161 XBT_PUBLIC(double) func_vegas_f(const Variable& var, double x);
162 XBT_PUBLIC(double) func_vegas_fp(const Variable& var, double x);
163 XBT_PUBLIC(double) func_vegas_fpi(const Variable& var, double x);
167 * Elements can be seen as glue between constraint objects and variable objects.
168 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
169 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
170 * vice-versa list all constraints for a given variable.
172 XBT_PUBLIC_CLASS Element
175 int get_concurrency() const;
176 void decrease_concurrency();
177 void increase_concurrency();
180 void make_inactive();
182 /* hookup to constraint */
183 boost::intrusive::list_member_hook<> enabled_element_set_hook;
184 boost::intrusive::list_member_hook<> disabled_element_set_hook;
185 boost::intrusive::list_member_hook<> active_element_set_hook;
187 Constraint* constraint;
190 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
191 // - if CPU, then probably 1.
192 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
193 double consumption_weight;
196 struct ConstraintLight {
197 double remaining_over_usage;
202 * @brief LMM constraint
203 * Each constraint contains several partially overlapping logical sets of elements:
204 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
205 * the corresponding action will enable it (at least this is the idea).
206 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
207 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
208 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
210 XBT_PUBLIC_CLASS Constraint
213 Constraint() = delete;
214 Constraint(void* id_value, double bound_value);
216 /** @brief Unshare a constraint. */
217 void unshare() { sharing_policy = 0; }
220 * @brief Check if a constraint is shared (shared by default)
221 * @return 1 if shared, 0 otherwise
223 int get_sharing_policy() const { return sharing_policy; }
226 * @brief Get the usage of the constraint after the last lmm solve
227 * @return The usage of the constraint
229 double get_usage() const;
230 int get_variable_amount() const;
233 * @brief Sets the concurrency limit for this constraint
234 * @param limit The concurrency limit to use for this constraint
236 void set_concurrency_limit(int limit)
238 xbt_assert(limit < 0 || concurrency_maximum <= limit,
239 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
240 " concurrency_maximum_reset() to reset the maximum?");
241 concurrency_limit = limit;
245 * @brief Gets the concurrency limit for this constraint
246 * @return The concurrency limit used by this constraint
248 int get_concurrency_limit() const { return concurrency_limit; }
251 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
254 void reset_concurrency_maximum() { concurrency_maximum = 0; }
257 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
258 * @return the maximum concurrency of the constraint
260 int get_concurrency_maximum() const
262 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
263 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
264 return concurrency_maximum;
267 int get_concurrency_slack() const
269 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
273 * @brief Get a var associated to a constraint
274 * @details Get the first variable of the next variable of elem if elem is not NULL
275 * @param elem A element of constraint of the constraint or NULL
276 * @return A variable associated to a constraint
278 Variable* get_variable(const_lmm_element_t * elem) const;
281 * @brief Get a var associated to a constraint
282 * @details Get the first variable of the next variable of elem if elem is not NULL
283 * @param elem A element of constraint of the constraint or NULL
284 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
285 * @param numelem parameter representing the number of elements to go
286 * @return A variable associated to a constraint
288 Variable* get_variable_safe(const_lmm_element_t * elem, const_lmm_element_t * nextelem, int* numelem) const;
291 * @brief Get the data associated to a constraint
292 * @return The data associated to the constraint
294 void* get_id() const { return id; }
296 /* hookup to system */
297 boost::intrusive::list_member_hook<> constraint_set_hook;
298 boost::intrusive::list_member_hook<> active_constraint_set_hook;
299 boost::intrusive::list_member_hook<> modified_constraint_set_hook;
300 boost::intrusive::list_member_hook<> saturated_constraint_set_hook;
301 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
302 &Element::enabled_element_set_hook>>
304 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
305 &Element::disabled_element_set_hook>>
306 disabled_element_set;
307 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
308 &Element::active_element_set_hook>>
313 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
314 int concurrency_current; /* The current concurrency */
315 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
316 * given time (essentially for tracing)*/
318 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: SPLITDUPLEX) */
322 lmm_constraint_light_t cnst_light;
325 static int Global_debug_id;
326 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
332 * @brief LMM variable
334 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
335 * soon as possible we enable the variable with desired weight
337 XBT_PUBLIC_CLASS Variable
340 void initialize(simgrid::kernel::resource::Action * id_value, double sharing_weight_value, double bound_value,
341 int number_of_constraints, unsigned visited_value);
344 * @brief Get the value of the variable after the last lmm solve
345 * @return The value of the variable
347 double get_value() const { return value; }
350 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
351 * @return The bound of the variable
353 double get_bound() const { return bound; }
356 * @brief Set the concurrent share of the variable
357 * @param value The new concurrency share
359 void set_concurrency_share(short int value) { concurrency_share = value; }
362 * @brief Get the numth constraint associated to the variable
363 * @param num The rank of constraint we want to get
364 * @return The numth constraint
366 Constraint* get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
369 * @brief Get the weigth of the numth constraint associated to the variable
370 * @param num The rank of constraint we want to get
371 * @return The numth constraint
373 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
376 * @brief Get the number of constraint associated to a variable
377 * @return The number of constraint associated to the variable
379 int get_number_of_constraint() const { return cnsts.size(); }
382 * @brief Get the data associated to a variable
383 * @return The data associated to the variable
385 simgrid::kernel::resource::Action* get_id() const { return id; }
388 * @brief Get the weight of a variable
389 * @return The weight of the variable
391 double get_weight() const { return sharing_weight; }
393 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
394 int get_min_concurrency_slack() const;
396 /** @brief Check if a variable can be enabled
397 * Make sure to set staged_weight before, if your intent is only to check concurrency
399 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
401 /* hookup to system */
402 boost::intrusive::list_member_hook<> variable_set_hook;
403 boost::intrusive::list_member_hook<> saturated_variable_set_hook;
405 std::vector<Element> cnsts;
407 // sharing_weight: variable's impact on the resource during the sharing
408 // if == 0, the variable is not considered by LMM
409 // on CPU, actions with N threads have a sharing of N
410 // on network, the actions with higher latency have a lesser sharing_weight
411 double sharing_weight;
413 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
417 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
418 simgrid::kernel::resource::Action* id;
420 unsigned visited; /* used by System::update_modified_set() */
421 /* \begin{For Lagrange only} */
424 double (*func_f)(const Variable& var, double x); /* (f) */
425 double (*func_fp)(const Variable& var, double x); /* (f') */
426 double (*func_fpi)(const Variable& var, double x); /* (f')^{-1} */
427 /* \end{For Lagrange only} */
430 static int Global_debug_id;
433 inline void Element::make_active()
435 constraint->active_element_set.push_front(*this);
437 inline void Element::make_inactive()
439 if (active_element_set_hook.is_linked())
440 simgrid::xbt::intrusive_erase(constraint->active_element_set, *this);
446 XBT_PUBLIC_CLASS System
450 * @brief Create a new Linear MaxMim system
451 * @param selective_update whether we should do lazy updates
453 explicit System(bool selective_update);
454 /** @brief Free an existing Linear MaxMin system */
458 * @brief Create a new Linear MaxMin constraint
459 * @param id Data associated to the constraint (e.g.: a network link)
460 * @param bound_value The bound value of the constraint
462 Constraint* constraint_new(void* id, double bound_value);
465 * @brief Create a new Linear MaxMin variable
466 * @param id Data associated to the variable (e.g.: a network communication)
467 * @param weight_value The weight of the variable (0.0 if not used)
468 * @param bound The maximum value of the variable (-1.0 if no maximum value)
469 * @param number_of_constraints The maximum number of constraint to associate to the variable
471 Variable* variable_new(simgrid::kernel::resource::Action * id, double weight_value, double bound,
472 int number_of_constraints);
475 * @brief Free a variable
476 * @param var The variable to free
478 void variable_free(Variable * var);
481 * @brief Associate a variable to a constraint with a coefficient
482 * @param cnst A constraint
483 * @param var A variable
484 * @param value The coefficient associated to the variable in the constraint
486 void expand(Constraint * cnst, Variable * var, double value);
489 * @brief Add value to the coefficient between a constraint and a variable or create one
490 * @param cnst A constraint
491 * @param var A variable
492 * @param value The value to add to the coefficient associated to the variable in the constraint
494 void expand_add(Constraint * cnst, Variable * var, double value);
497 * @brief Update the bound of a variable
498 * @param var A constraint
499 * @param bound The new bound
501 void update_variable_bound(Variable * var, double bound);
504 * @brief Update the weight of a variable
505 * @param var A variable
506 * @param weight The new weight of the variable
508 void update_variable_weight(Variable * var, double weight);
511 * @brief Update a constraint bound
512 * @param cnst A constraint
513 * @param bound The new bound of the consrtaint
515 void update_constraint_bound(Constraint * cnst, double bound);
518 * @brief [brief description]
519 * @param cnst A constraint
520 * @return [description]
522 int constraint_used(Constraint * cnst) { return cnst->active_constraint_set_hook.is_linked(); }
524 /** @brief Print the lmm system */
527 /** @brief Solve the lmm system */
531 static void* variable_mallocator_new_f();
532 static void variable_mallocator_free_f(void* var);
534 void var_free(Variable * var);
535 void cnst_free(Constraint * cnst);
536 Variable* extract_variable()
538 if (variable_set.empty())
540 Variable* res = &variable_set.front();
541 variable_set.pop_front();
544 Constraint* extract_constraint()
546 if (constraint_set.empty())
548 Constraint* res = &constraint_set.front();
549 constraint_set.pop_front();
552 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
553 void remove_variable(Variable * var)
555 if (var->variable_set_hook.is_linked())
556 simgrid::xbt::intrusive_erase(variable_set, *var);
557 if (var->saturated_variable_set_hook.is_linked())
558 simgrid::xbt::intrusive_erase(saturated_variable_set, *var);
560 void make_constraint_active(Constraint * cnst)
562 if (not cnst->active_constraint_set_hook.is_linked())
563 active_constraint_set.push_back(*cnst);
565 void make_constraint_inactive(Constraint * cnst)
567 if (cnst->active_constraint_set_hook.is_linked())
568 simgrid::xbt::intrusive_erase(active_constraint_set, *cnst);
569 if (cnst->modified_constraint_set_hook.is_linked())
570 simgrid::xbt::intrusive_erase(modified_constraint_set, *cnst);
573 void enable_var(Variable * var);
574 void disable_var(Variable * var);
575 void on_disabled_var(Constraint * cnstr);
578 * @brief Update the value of element linking the constraint and the variable
579 * @param cnst A constraint
580 * @param var A variable
581 * @param value The new value
583 void update(Constraint * cnst, Variable * var, double value);
585 void update_modified_set(Constraint * cnst);
586 void update_modified_set_rec(Constraint * cnst);
588 /** @brief Remove all constraints of the modified_constraint_set. */
589 void remove_all_modified_set();
590 void check_concurrency() const;
592 template <class CnstList> void solve(CnstList& cnst_list);
595 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
596 &Variable::variable_set_hook>>
598 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
599 &Constraint::active_constraint_set_hook>>
600 active_constraint_set;
601 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
602 &Variable::saturated_variable_set_hook>>
603 saturated_variable_set;
604 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
605 &Constraint::saturated_constraint_set_hook>>
606 saturated_constraint_set;
608 simgrid::kernel::resource::ActionLmmListPtr keep_track;
610 void (*solve_fun)(lmm_system_t self);
613 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
614 unsigned visited_counter; /* used by System::update_modified_set() and System::remove_all_modified_set() to
615 * cleverly (un-)flag the constraints (more details in these functions) */
616 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
617 &Constraint::constraint_set_hook>>
619 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
620 &Constraint::modified_constraint_set_hook>>
621 modified_constraint_set;
622 xbt_mallocator_t variable_mallocator;
625 extern XBT_PRIVATE double (*func_f_def)(const Variable&, double);
626 extern XBT_PRIVATE double (*func_fp_def)(const Variable&, double);
627 extern XBT_PRIVATE double (*func_fpi_def)(const Variable&, double);