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 <boost/intrusive/list.hpp>
24 /** @addtogroup SURF_lmm
26 * A linear maxmin solver to resolve inequations systems.
28 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
29 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
30 * 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$x_1\f$
31 * 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
32 * case, we need to enforce:
34 * \f[ x_1 + x_2 \leq C_A \f]
36 * 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
37 * 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:
39 * \f[ x_3 \leq C_{L_1} \f]
40 * \f[ x_3 + x_4 \leq C_{L_2} \f]
41 * \f[ x_4 \leq C_{L_3} \f]
43 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
44 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
45 * \f$x_i\f$ are positive and "as large as possible".
47 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
48 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
63 * A possible system could be:
64 * - three variables: `var1`, `var2`, `var3`
65 * - two constraints: `cons1`, `cons2`
66 * - four elements linking:
67 * - `elem1` linking `var1` and `cons1`
68 * - `elem2` linking `var2` and `cons1`
69 * - `elem3` linking `var2` and `cons2`
70 * - `elem4` linking `var3` and `cons2`
72 * And the corresponding inequations will be:
74 * var1.value <= var1.bound
75 * var2.value <= var2.bound
76 * var3.value <= var3.bound
77 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
78 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
80 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
82 * If a constraint is not shared, the sum is replaced by a max.
83 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
85 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
87 * This is usefull for the sharing of resources for various models.
88 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
90 * Implementation details
92 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
93 * computation of constraints, and those who are part of the equations but are stuck to zero.
94 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
96 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
97 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
98 * than the conditions for it to be enabled.
99 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
100 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
101 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
102 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
103 * pausing of an action.
105 * Concurrency limit and maximum
107 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
108 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
110 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
112 * One may want to limit the concurrency of constraints for essentially three reasons:
113 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
115 * - Stay within parameters where the fluid model is accurate enough.
116 * - Model serialization effects
118 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
121 * Overall, each constraint contains three fields related to concurrency:
122 * - concurrency_limit which is the limit enforced by the solver
123 * - concurrency_current which is the current concurrency
124 * - concurrency_maximum which is the observed maximum concurrency
126 * Variables also have one field related to concurrency: concurrency_share.
127 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
128 * For example, cross-traffic is modeled using 2 elements per constraint.
129 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
133 /** @{ @ingroup SURF_lmm */
136 * @brief Solve the lmm system
137 * @param sys The lmm system to solve
139 XBT_PUBLIC(void) lmm_solve(lmm_system_t sys);
141 XBT_PUBLIC(void) lagrange_solve(lmm_system_t sys);
142 XBT_PUBLIC(void) bottleneck_solve(lmm_system_t sys);
144 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
147 lmm_set_default_protocol_function(double (*func_f)(const s_lmm_variable_t& var, double x),
148 double (*func_fp)(const s_lmm_variable_t& var, double x),
149 double (*func_fpi)(const s_lmm_variable_t& var, double x));
151 XBT_PUBLIC(double) func_reno_f(const s_lmm_variable_t& var, double x);
152 XBT_PUBLIC(double) func_reno_fp(const s_lmm_variable_t& var, double x);
153 XBT_PUBLIC(double) func_reno_fpi(const s_lmm_variable_t& var, double x);
155 XBT_PUBLIC(double) func_reno2_f(const s_lmm_variable_t& var, double x);
156 XBT_PUBLIC(double) func_reno2_fp(const s_lmm_variable_t& var, double x);
157 XBT_PUBLIC(double) func_reno2_fpi(const s_lmm_variable_t& var, double x);
159 XBT_PUBLIC(double) func_vegas_f(const s_lmm_variable_t& var, double x);
160 XBT_PUBLIC(double) func_vegas_fp(const s_lmm_variable_t& var, double x);
161 XBT_PUBLIC(double) func_vegas_fpi(const s_lmm_variable_t& var, double x);
165 * Elements can be seen as glue between constraint objects and variable objects.
166 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
167 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
168 * vice-versa list all constraints for a given variable.
170 XBT_PUBLIC_CLASS s_lmm_element_t
173 int get_concurrency() const;
174 void decrease_concurrency();
175 void increase_concurrency();
178 void make_inactive();
180 /* hookup to constraint */
181 boost::intrusive::list_member_hook<> enabled_element_set_hook;
182 boost::intrusive::list_member_hook<> disabled_element_set_hook;
183 boost::intrusive::list_member_hook<> active_element_set_hook;
185 lmm_constraint_t constraint;
186 lmm_variable_t variable;
188 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
189 // - if CPU, then probably 1.
190 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
191 double consumption_weight;
194 struct s_lmm_constraint_light_t {
195 double remaining_over_usage;
196 lmm_constraint_t cnst;
200 * @brief LMM constraint
201 * Each constraint contains several partially overlapping logical sets of elements:
202 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
203 * the corresponding action will enable it (at least this is the idea).
204 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
205 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
206 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
208 XBT_PUBLIC_CLASS s_lmm_constraint_t
211 s_lmm_constraint_t() = default;
212 s_lmm_constraint_t(void* id_value, double bound_value);
214 /** @brief Unshare a constraint. */
215 void unshare() { sharing_policy = 0; }
218 * @brief Check if a constraint is shared (shared by default)
219 * @return 1 if shared, 0 otherwise
221 int get_sharing_policy() const { return sharing_policy; }
224 * @brief Get the usage of the constraint after the last lmm solve
225 * @return The usage of the constraint
227 double get_usage() const;
228 int get_variable_amount() const;
231 * @brief Sets the concurrency limit for this constraint
232 * @param concurrency_limit The concurrency limit to use for this constraint
234 void set_concurrency_limit(int limit)
236 xbt_assert(limit < 0 || concurrency_maximum <= limit,
237 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
238 " concurrency_maximum_reset() to reset the maximum?");
239 concurrency_limit = limit;
243 * @brief Gets the concurrency limit for this constraint
244 * @return The concurrency limit used by this constraint
246 int get_concurrency_limit() const { return concurrency_limit; }
249 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
252 void reset_concurrency_maximum() { concurrency_maximum = 0; }
255 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
256 * @return the maximum concurrency of the constraint
258 int get_concurrency_maximum() const
260 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
261 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
262 return concurrency_maximum;
265 int get_concurrency_slack() const
267 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
271 * @brief Get a var associated to a constraint
272 * @details Get the first variable of the next variable of elem if elem is not NULL
273 * @param elem A element of constraint of the constraint or NULL
274 * @return A variable associated to a constraint
276 lmm_variable_t get_variable(const_lmm_element_t* elem) const;
279 * @brief Get a var associated to a constraint
280 * @details Get the first variable of the next variable of elem if elem is not NULL
281 * @param elem A element of constraint of the constraint or NULL
282 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
283 * @param numelem parameter representing the number of elements to go
284 * @return A variable associated to a constraint
286 lmm_variable_t get_variable_safe(const_lmm_element_t* elem, const_lmm_element_t* nextelem, int* numelem) const;
289 * @brief Get the data associated to a constraint
290 * @return The data associated to the constraint
292 void* get_id() const { return id; }
294 /* hookup to system */
295 boost::intrusive::list_member_hook<> constraint_set_hook;
296 boost::intrusive::list_member_hook<> active_constraint_set_hook;
297 boost::intrusive::list_member_hook<> modified_constraint_set_hook;
298 boost::intrusive::list_member_hook<> saturated_constraint_set_hook;
299 boost::intrusive::list<s_lmm_element_t,
300 boost::intrusive::member_hook<s_lmm_element_t, boost::intrusive::list_member_hook<>,
301 &s_lmm_element_t::enabled_element_set_hook>>
303 boost::intrusive::list<s_lmm_element_t,
304 boost::intrusive::member_hook<s_lmm_element_t, boost::intrusive::list_member_hook<>,
305 &s_lmm_element_t::disabled_element_set_hook>>
306 disabled_element_set;
307 boost::intrusive::list<s_lmm_element_t,
308 boost::intrusive::member_hook<s_lmm_element_t, boost::intrusive::list_member_hook<>,
309 &s_lmm_element_t::active_element_set_hook>>
314 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
315 int concurrency_current; /* The current concurrency */
316 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
317 * given time (essentially for tracing)*/
319 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: FULLDUPLEX) */
323 lmm_constraint_light_t cnst_light;
326 static int Global_debug_id;
327 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
333 * @brief LMM variable
335 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
336 * soon as possible we enable the variable with desired weight
338 XBT_PUBLIC_CLASS s_lmm_variable_t
341 void initialize(simgrid::surf::Action * id_value, double sharing_weight_value, double bound_value,
342 int number_of_constraints, unsigned visited_value);
345 * @brief Get the value of the variable after the last lmm solve
346 * @return The value of the variable
348 double get_value() const { return value; }
351 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
352 * @return The bound of the variable
354 double get_bound() const { return bound; }
357 * @brief Set the concurrent share of the variable
358 * @param concurrency_share The new concurrency share
360 void set_concurrency_share(short int value) { concurrency_share = value; }
363 * @brief Get the numth constraint associated to the variable
364 * @param num The rank of constraint we want to get
365 * @return The numth constraint
367 lmm_constraint_t get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
370 * @brief Get the weigth of the numth constraint associated to the variable
371 * @param num The rank of constraint we want to get
372 * @return The numth constraint
374 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
377 * @brief Get the number of constraint associated to a variable
378 * @return The number of constraint associated to the variable
380 int get_number_of_constraint() const { return cnsts.size(); }
383 * @brief Get the data associated to a variable
384 * @return The data associated to the variable
386 simgrid::surf::Action* get_id() const { return id; }
389 * @brief Get the weight of a variable
390 * @return The weight of the variable
392 double get_weight() const { return sharing_weight; }
394 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
395 int get_min_concurrency_slack() const;
397 /** @brief Check if a variable can be enabled
398 * Make sure to set staged_weight before, if your intent is only to check concurrency
400 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
402 /* hookup to system */
403 boost::intrusive::list_member_hook<> variable_set_hook;
404 boost::intrusive::list_member_hook<> saturated_variable_set_hook;
406 std::vector<s_lmm_element_t> cnsts;
408 // sharing_weight: variable's impact on the resource during the sharing
409 // if == 0, the variable is not considered by LMM
410 // on CPU, actions with N threads have a sharing of N
411 // on network, the actions with higher latency have a lesser sharing_weight
412 double sharing_weight;
414 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
418 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
419 simgrid::surf::Action* id;
421 unsigned visited; /* used by lmm_update_modified_set */
422 /* \begin{For Lagrange only} */
425 double (*func_f)(const s_lmm_variable_t& var, double x); /* (f) */
426 double (*func_fp)(const s_lmm_variable_t& var, double x); /* (f') */
427 double (*func_fpi)(const s_lmm_variable_t& var, double x); /* (f')^{-1} */
428 /* \end{For Lagrange only} */
431 static int Global_debug_id;
434 inline void s_lmm_element_t::make_active()
436 constraint->active_element_set.push_front(*this);
438 inline void s_lmm_element_t::make_inactive()
440 if (active_element_set_hook.is_linked()) {
441 auto& set = constraint->active_element_set;
442 set.erase(set.iterator_to(*this));
449 XBT_PUBLIC_CLASS s_lmm_system_t
453 * @brief Create a new Linear MaxMim system
454 * @param selective_update whether we should do lazy updates
456 explicit s_lmm_system_t(bool selective_update);
457 /** @brief Free an existing Linear MaxMin system */
461 * @brief Create a new Linear MaxMin constraint
462 * @param id Data associated to the constraint (e.g.: a network link)
463 * @param bound_value The bound value of the constraint
465 lmm_constraint_t constraint_new(void* id, double bound_value);
468 * @brief Create a new Linear MaxMin variable
469 * @param id Data associated to the variable (e.g.: a network communication)
470 * @param weight_value The weight of the variable (0.0 if not used)
471 * @param bound The maximum value of the variable (-1.0 if no maximum value)
472 * @param number_of_constraints The maximum number of constraint to associate to the variable
474 lmm_variable_t variable_new(simgrid::surf::Action * id, double weight_value, double bound, int number_of_constraints);
477 * @brief Free a variable
478 * @param var The variable to free
480 void variable_free(lmm_variable_t var);
483 * @brief Associate a variable to a constraint with a coefficient
484 * @param cnst A constraint
485 * @param var A variable
486 * @param value The coefficient associated to the variable in the constraint
488 void expand(lmm_constraint_t cnst, lmm_variable_t var, double value);
491 * @brief Add value to the coefficient between a constraint and a variable or create one
492 * @param cnst A constraint
493 * @param var A variable
494 * @param value The value to add to the coefficient associated to the variable in the constraint
496 void expand_add(lmm_constraint_t cnst, lmm_variable_t var, double value);
499 * @brief Update the bound of a variable
500 * @param var A constraint
501 * @param bound The new bound
503 void update_variable_bound(lmm_variable_t var, double bound);
506 * @brief Update the weight of a variable
507 * @param var A variable
508 * @param weight The new weight of the variable
510 void update_variable_weight(lmm_variable_t var, double weight);
513 * @brief Update a constraint bound
514 * @param cnst A constraint
515 * @param bound The new bound of the consrtaint
517 void update_constraint_bound(lmm_constraint_t cnst, double bound);
520 * @brief [brief description]
521 * @param cnst A constraint
522 * @return [description]
524 int constraint_used(lmm_constraint_t cnst) { return cnst->active_constraint_set_hook.is_linked(); }
526 /** @brief Print the lmm system */
529 /** @brief Solve the lmm system */
533 static void* variable_mallocator_new_f();
534 static void variable_mallocator_free_f(void* var);
536 void var_free(lmm_variable_t var);
537 void cnst_free(lmm_constraint_t cnst);
538 lmm_variable_t extract_variable()
540 if (variable_set.empty())
542 lmm_variable_t res = &variable_set.front();
543 variable_set.pop_front();
546 lmm_constraint_t extract_constraint()
548 if (constraint_set.empty())
550 lmm_constraint_t res = &constraint_set.front();
551 constraint_set.pop_front();
554 void insert_constraint(lmm_constraint_t cnst) { constraint_set.push_back(*cnst); }
555 void remove_variable(lmm_variable_t var)
557 if (var->variable_set_hook.is_linked())
558 variable_set.erase(variable_set.iterator_to(*var));
559 if (var->saturated_variable_set_hook.is_linked())
560 saturated_variable_set.erase(saturated_variable_set.iterator_to(*var));
562 void make_constraint_active(lmm_constraint_t cnst)
564 if (not cnst->active_constraint_set_hook.is_linked())
565 active_constraint_set.push_back(*cnst);
567 void make_constraint_inactive(lmm_constraint_t cnst)
569 if (cnst->active_constraint_set_hook.is_linked())
570 active_constraint_set.erase(active_constraint_set.iterator_to(*cnst));
571 if (cnst->modified_constraint_set_hook.is_linked())
572 modified_constraint_set.erase(modified_constraint_set.iterator_to(*cnst));
575 void enable_var(lmm_variable_t var);
576 void disable_var(lmm_variable_t var);
577 void on_disabled_var(lmm_constraint_t cnstr);
580 * @brief Update the value of element linking the constraint and the variable
581 * @param cnst A constraint
582 * @param var A variable
583 * @param value The new value
585 void update(lmm_constraint_t cnst, lmm_variable_t var, double value);
587 void update_modified_set(lmm_constraint_t cnst);
588 void update_modified_set_rec(lmm_constraint_t cnst);
590 /** @brief Remove all constraints of the modified_constraint_set. */
591 void remove_all_modified_set();
592 void check_concurrency() const;
594 template <class CnstList> void solve(CnstList& cnst_list);
597 boost::intrusive::list<s_lmm_variable_t,
598 boost::intrusive::member_hook<s_lmm_variable_t, boost::intrusive::list_member_hook<>,
599 &s_lmm_variable_t::variable_set_hook>>
601 boost::intrusive::list<s_lmm_constraint_t,
602 boost::intrusive::member_hook<s_lmm_constraint_t, boost::intrusive::list_member_hook<>,
603 &s_lmm_constraint_t::active_constraint_set_hook>>
604 active_constraint_set;
605 boost::intrusive::list<s_lmm_variable_t,
606 boost::intrusive::member_hook<s_lmm_variable_t, boost::intrusive::list_member_hook<>,
607 &s_lmm_variable_t::saturated_variable_set_hook>>
608 saturated_variable_set;
609 boost::intrusive::list<s_lmm_constraint_t,
610 boost::intrusive::member_hook<s_lmm_constraint_t, boost::intrusive::list_member_hook<>,
611 &s_lmm_constraint_t::saturated_constraint_set_hook>>
612 saturated_constraint_set;
614 simgrid::surf::ActionLmmListPtr keep_track;
616 void (*solve_fun)(lmm_system_t self);
619 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
620 unsigned visited_counter; /* used by lmm_update_modified_set and lmm_remove_modified_set to cleverly (un-)flag the
621 * constraints (more details in these functions) */
622 boost::intrusive::list<s_lmm_constraint_t,
623 boost::intrusive::member_hook<s_lmm_constraint_t, boost::intrusive::list_member_hook<>,
624 &s_lmm_constraint_t::constraint_set_hook>>
626 boost::intrusive::list<s_lmm_constraint_t,
627 boost::intrusive::member_hook<s_lmm_constraint_t, boost::intrusive::list_member_hook<>,
628 &s_lmm_constraint_t::modified_constraint_set_hook>>
629 modified_constraint_set;
630 xbt_mallocator_t variable_mallocator;
633 extern XBT_PRIVATE double (*func_f_def)(const s_lmm_variable_t&, double);
634 extern XBT_PRIVATE double (*func_fp_def)(const s_lmm_variable_t&, double);
635 extern XBT_PRIVATE double (*func_fpi_def)(const s_lmm_variable_t&, double);