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 "xbt/asserts.h"
11 #include "xbt/mallocator.h"
13 #include <boost/intrusive/list.hpp>
22 /** @addtogroup SURF_lmm
24 * A linear maxmin solver to resolve inequations systems.
26 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
27 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
28 * 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$x_1\f$
29 * 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
30 * case, we need to enforce:
32 * \f[ x_1 + x_2 \leq C_A \f]
34 * 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
35 * 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:
37 * \f[ x_3 \leq C_{L_1} \f]
38 * \f[ x_3 + x_4 \leq C_{L_2} \f]
39 * \f[ x_4 \leq C_{L_3} \f]
41 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
42 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
43 * \f$x_i\f$ are positive and "as large as possible".
45 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
46 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
61 * A possible system could be:
62 * - three variables: `var1`, `var2`, `var3`
63 * - two constraints: `cons1`, `cons2`
64 * - four elements linking:
65 * - `elem1` linking `var1` and `cons1`
66 * - `elem2` linking `var2` and `cons1`
67 * - `elem3` linking `var2` and `cons2`
68 * - `elem4` linking `var3` and `cons2`
70 * And the corresponding inequations will be:
72 * var1.value <= var1.bound
73 * var2.value <= var2.bound
74 * var3.value <= var3.bound
75 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
76 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
78 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
80 * If a constraint is not shared, the sum is replaced by a max.
81 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
83 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
85 * This is useful for the sharing of resources for various models.
86 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
88 * Implementation details
90 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
91 * computation of constraints, and those who are part of the equations but are stuck to zero.
92 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
94 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
95 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
96 * than the conditions for it to be enabled.
97 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
98 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
99 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
100 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
101 * pausing of an action.
103 * Concurrency limit and maximum
105 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
106 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
108 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
110 * One may want to limit the concurrency of constraints for essentially three reasons:
111 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
113 * - Stay within parameters where the fluid model is accurate enough.
114 * - Model serialization effects
116 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
119 * Overall, each constraint contains three fields related to concurrency:
120 * - concurrency_limit which is the limit enforced by the solver
121 * - concurrency_current which is the current concurrency
122 * - concurrency_maximum which is the observed maximum concurrency
124 * Variables also have one field related to concurrency: concurrency_share.
125 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
126 * For example, cross-traffic is modeled using 2 elements per constraint.
127 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
131 /** @{ @ingroup SURF_lmm */
133 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
135 XBT_PUBLIC double func_reno_f(const Variable& var, double x);
136 XBT_PUBLIC double func_reno_fp(const Variable& var, double x);
137 XBT_PUBLIC double func_reno_fpi(const Variable& var, double x);
139 XBT_PUBLIC double func_reno2_f(const Variable& var, double x);
140 XBT_PUBLIC double func_reno2_fp(const Variable& var, double x);
141 XBT_PUBLIC double func_reno2_fpi(const Variable& var, double x);
143 XBT_PUBLIC double func_vegas_f(const Variable& var, double x);
144 XBT_PUBLIC double func_vegas_fp(const Variable& var, double x);
145 XBT_PUBLIC double func_vegas_fpi(const Variable& var, double x);
149 * Elements can be seen as glue between constraint objects and variable objects.
150 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
151 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
152 * vice-versa list all constraints for a given variable.
154 class XBT_PUBLIC Element {
156 int get_concurrency() const;
157 void decrease_concurrency();
158 void increase_concurrency();
161 void make_inactive();
163 /* hookup to constraint */
164 boost::intrusive::list_member_hook<> enabled_element_set_hook;
165 boost::intrusive::list_member_hook<> disabled_element_set_hook;
166 boost::intrusive::list_member_hook<> active_element_set_hook;
168 Constraint* constraint;
171 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
172 // - if CPU, then probably 1.
173 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
174 double consumption_weight;
177 struct ConstraintLight {
178 double remaining_over_usage;
183 * @brief LMM constraint
184 * Each constraint contains several partially overlapping logical sets of elements:
185 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
186 * the corresponding action will enable it (at least this is the idea).
187 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
188 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
189 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
191 class XBT_PUBLIC Constraint {
193 Constraint() = delete;
194 Constraint(void* id_value, double bound_value);
196 /** @brief Unshare a constraint. */
197 void unshare() { sharing_policy = 0; }
200 * @brief Check if a constraint is shared (shared by default)
201 * @return 1 if shared, 0 otherwise
203 int get_sharing_policy() const { return sharing_policy; }
206 * @brief Get the usage of the constraint after the last lmm solve
207 * @return The usage of the constraint
209 double get_usage() const;
210 int get_variable_amount() const;
213 * @brief Sets the concurrency limit for this constraint
214 * @param limit The concurrency limit to use for this constraint
216 void set_concurrency_limit(int limit)
218 xbt_assert(limit < 0 || concurrency_maximum <= limit,
219 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
220 " concurrency_maximum_reset() to reset the maximum?");
221 concurrency_limit = limit;
225 * @brief Gets the concurrency limit for this constraint
226 * @return The concurrency limit used by this constraint
228 int get_concurrency_limit() const { return concurrency_limit; }
231 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
234 void reset_concurrency_maximum() { concurrency_maximum = 0; }
237 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
238 * @return the maximum concurrency of the constraint
240 int get_concurrency_maximum() const
242 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
243 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
244 return concurrency_maximum;
247 int get_concurrency_slack() const
249 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
253 * @brief Get a var associated to a constraint
254 * @details Get the first variable of the next variable of elem if elem is not NULL
255 * @param elem A element of constraint of the constraint or NULL
256 * @return A variable associated to a constraint
258 Variable* get_variable(const Element** elem) const;
261 * @brief Get a var associated to a constraint
262 * @details Get the first variable of the next variable of elem if elem is not NULL
263 * @param elem A element of constraint of the constraint or NULL
264 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
265 * @param numelem parameter representing the number of elements to go
266 * @return A variable associated to a constraint
268 Variable* get_variable_safe(const Element** elem, const Element** nextelem, int* numelem) const;
271 * @brief Get the data associated to a constraint
272 * @return The data associated to the constraint
274 void* get_id() const { return id; }
276 /* hookup to system */
277 boost::intrusive::list_member_hook<> constraint_set_hook;
278 boost::intrusive::list_member_hook<> active_constraint_set_hook;
279 boost::intrusive::list_member_hook<> modified_constraint_set_hook;
280 boost::intrusive::list_member_hook<> saturated_constraint_set_hook;
281 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
282 &Element::enabled_element_set_hook>>
284 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
285 &Element::disabled_element_set_hook>>
286 disabled_element_set;
287 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
288 &Element::active_element_set_hook>>
293 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
294 int concurrency_current; /* The current concurrency */
295 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
296 * given time (essentially for tracing)*/
298 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: SPLITDUPLEX) */
302 ConstraintLight* cnst_light;
305 static int Global_debug_id;
306 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
312 * @brief LMM variable
314 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
315 * soon as possible we enable the variable with desired weight
317 class XBT_PUBLIC Variable {
319 void initialize(resource::Action* id_value, double sharing_weight_value, double bound_value,
320 int number_of_constraints, unsigned visited_value);
323 * @brief Get the value of the variable after the last lmm solve
324 * @return The value of the variable
326 double get_value() const { return value; }
329 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
330 * @return The bound of the variable
332 double get_bound() const { return bound; }
335 * @brief Set the concurrent share of the variable
336 * @param value The new concurrency share
338 void set_concurrency_share(short int value) { concurrency_share = value; }
341 * @brief Get the numth constraint associated to the variable
342 * @param num The rank of constraint we want to get
343 * @return The numth constraint
345 Constraint* get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
348 * @brief Get the weigth of the numth constraint associated to the variable
349 * @param num The rank of constraint we want to get
350 * @return The numth constraint
352 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
355 * @brief Get the number of constraint associated to a variable
356 * @return The number of constraint associated to the variable
358 int get_number_of_constraint() const { return cnsts.size(); }
361 * @brief Get the data associated to a variable
362 * @return The data associated to the variable
364 resource::Action* get_id() const { return id; }
367 * @brief Get the weight of a variable
368 * @return The weight of the variable
370 double get_weight() const { return sharing_weight; }
372 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
373 int get_min_concurrency_slack() const;
375 /** @brief Check if a variable can be enabled
376 * Make sure to set staged_weight before, if your intent is only to check concurrency
378 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
380 /* hookup to system */
381 boost::intrusive::list_member_hook<> variable_set_hook;
382 boost::intrusive::list_member_hook<> saturated_variable_set_hook;
384 std::vector<Element> cnsts;
386 // sharing_weight: variable's impact on the resource during the sharing
387 // if == 0, the variable is not considered by LMM
388 // on CPU, actions with N threads have a sharing of N
389 // on network, the actions with higher latency have a lesser sharing_weight
390 double sharing_weight;
392 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
396 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
397 resource::Action* id;
399 unsigned visited; /* used by System::update_modified_set() */
400 /* \begin{For Lagrange only} */
403 /* \end{For Lagrange only} */
406 static int Global_debug_id;
409 inline void Element::make_active()
411 constraint->active_element_set.push_front(*this);
413 inline void Element::make_inactive()
415 if (active_element_set_hook.is_linked())
416 simgrid::xbt::intrusive_erase(constraint->active_element_set, *this);
422 class XBT_PUBLIC System {
425 * @brief Create a new Linear MaxMim system
426 * @param selective_update whether we should do lazy updates
428 explicit System(bool selective_update);
429 /** @brief Free an existing Linear MaxMin system */
433 * @brief Create a new Linear MaxMin constraint
434 * @param id Data associated to the constraint (e.g.: a network link)
435 * @param bound_value The bound value of the constraint
437 Constraint* constraint_new(void* id, double bound_value);
440 * @brief Create a new Linear MaxMin variable
441 * @param id Data associated to the variable (e.g.: a network communication)
442 * @param weight_value The weight of the variable (0.0 if not used)
443 * @param bound The maximum value of the variable (-1.0 if no maximum value)
444 * @param number_of_constraints The maximum number of constraint to associate to the variable
446 Variable* variable_new(resource::Action* id, double weight_value, double bound, int number_of_constraints);
449 * @brief Free a variable
450 * @param var The variable to free
452 void variable_free(Variable * var);
455 * @brief Associate a variable to a constraint with a coefficient
456 * @param cnst A constraint
457 * @param var A variable
458 * @param value The coefficient associated to the variable in the constraint
460 void expand(Constraint * cnst, Variable * var, double value);
463 * @brief Add value to the coefficient between a constraint and a variable or create one
464 * @param cnst A constraint
465 * @param var A variable
466 * @param value The value to add to the coefficient associated to the variable in the constraint
468 void expand_add(Constraint * cnst, Variable * var, double value);
471 * @brief Update the bound of a variable
472 * @param var A constraint
473 * @param bound The new bound
475 void update_variable_bound(Variable * var, double bound);
478 * @brief Update the weight of a variable
479 * @param var A variable
480 * @param weight The new weight of the variable
482 void update_variable_weight(Variable * var, double weight);
485 * @brief Update a constraint bound
486 * @param cnst A constraint
487 * @param bound The new bound of the consrtaint
489 void update_constraint_bound(Constraint * cnst, double bound);
492 * @brief [brief description]
493 * @param cnst A constraint
494 * @return [description]
496 int constraint_used(Constraint * cnst) { return cnst->active_constraint_set_hook.is_linked(); }
498 /** @brief Print the lmm system */
501 /** @brief Solve the lmm system */
504 /** @brief Solve the lmm system. May be specialized in subclasses. */
505 virtual void solve() { lmm_solve(); }
508 static void* variable_mallocator_new_f();
509 static void variable_mallocator_free_f(void* var);
511 void var_free(Variable * var);
512 void cnst_free(Constraint * cnst);
513 Variable* extract_variable()
515 if (variable_set.empty())
517 Variable* res = &variable_set.front();
518 variable_set.pop_front();
521 Constraint* extract_constraint()
523 if (constraint_set.empty())
525 Constraint* res = &constraint_set.front();
526 constraint_set.pop_front();
529 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
530 void remove_variable(Variable * var)
532 if (var->variable_set_hook.is_linked())
533 simgrid::xbt::intrusive_erase(variable_set, *var);
534 if (var->saturated_variable_set_hook.is_linked())
535 simgrid::xbt::intrusive_erase(saturated_variable_set, *var);
537 void make_constraint_active(Constraint * cnst)
539 if (not cnst->active_constraint_set_hook.is_linked())
540 active_constraint_set.push_back(*cnst);
542 void make_constraint_inactive(Constraint * cnst)
544 if (cnst->active_constraint_set_hook.is_linked())
545 simgrid::xbt::intrusive_erase(active_constraint_set, *cnst);
546 if (cnst->modified_constraint_set_hook.is_linked())
547 simgrid::xbt::intrusive_erase(modified_constraint_set, *cnst);
550 void enable_var(Variable * var);
551 void disable_var(Variable * var);
552 void on_disabled_var(Constraint * cnstr);
555 * @brief Update the value of element linking the constraint and the variable
556 * @param cnst A constraint
557 * @param var A variable
558 * @param value The new value
560 void update(Constraint * cnst, Variable * var, double value);
562 void update_modified_set(Constraint * cnst);
563 void update_modified_set_rec(Constraint * cnst);
565 /** @brief Remove all constraints of the modified_constraint_set. */
566 void remove_all_modified_set();
567 void check_concurrency() const;
569 template <class CnstList> void lmm_solve(CnstList& cnst_list);
572 bool modified_ = false;
573 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
574 &Variable::variable_set_hook>>
576 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
577 &Constraint::active_constraint_set_hook>>
578 active_constraint_set;
579 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
580 &Variable::saturated_variable_set_hook>>
581 saturated_variable_set;
582 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
583 &Constraint::saturated_constraint_set_hook>>
584 saturated_constraint_set;
586 resource::Action::ModifiedSet* modified_set_ = nullptr;
589 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
590 unsigned visited_counter_ = 1; /* used by System::update_modified_set() and System::remove_all_modified_set() to
591 * cleverly (un-)flag the constraints (more details in these functions) */
592 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
593 &Constraint::constraint_set_hook>>
595 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
596 &Constraint::modified_constraint_set_hook>>
597 modified_constraint_set;
598 xbt_mallocator_t variable_mallocator_ =
599 xbt_mallocator_new(65536, System::variable_mallocator_new_f, System::variable_mallocator_free_f, nullptr);
603 class XBT_PUBLIC FairBottleneck : public System {
605 explicit FairBottleneck(bool selective_update) : System(selective_update) {}
606 void solve() final { bottleneck_solve(); }
609 void bottleneck_solve();
612 class XBT_PUBLIC Lagrange : public System {
614 explicit Lagrange(bool selective_update) : System(selective_update) {}
615 void solve() final { lagrange_solve(); }
617 static void set_default_protocol_function(double (*func_f)(const Variable& var, double x),
618 double (*func_fp)(const Variable& var, double x),
619 double (*func_fpi)(const Variable& var, double x));
622 void lagrange_solve();
624 bool check_feasible(bool warn);
625 double dual_objective();
627 static double (*func_f)(const Variable& var, double x); /* (f) */
628 static double (*func_fp)(const Variable& var, double x); /* (f') */
629 static double (*func_fpi)(const Variable& var, double x); /* (f')^{-1} */
632 * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
634 // computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
635 static double dichotomy(double init, double diff(double, const Constraint&), const Constraint& cnst,
637 // computes the value of the differential of constraint cnst applied to lambda
638 static double partial_diff_lambda(double lambda, const Constraint& cnst);
640 static double new_value(const Variable& var);
641 static double new_mu(const Variable& var);
644 XBT_PUBLIC System* make_new_maxmin_system(bool selective_update);
645 XBT_PUBLIC System* make_new_fair_bottleneck_system(bool selective_update);
646 XBT_PUBLIC System* make_new_lagrange_system(bool selective_update);