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 "simgrid/s4u/Link.hpp"
11 #include "xbt/asserts.h"
12 #include "xbt/mallocator.h"
14 #include <boost/intrusive/list.hpp>
23 /** @addtogroup SURF_lmm
25 * A linear maxmin solver to resolve inequations systems.
27 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
28 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
29 * 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$x_1\f$
30 * 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
31 * case, we need to enforce:
33 * \f[ x_1 + x_2 \leq C_A \f]
35 * 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
36 * 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:
38 * \f[ x_3 \leq C_{L_1} \f]
39 * \f[ x_3 + x_4 \leq C_{L_2} \f]
40 * \f[ x_4 \leq C_{L_3} \f]
42 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
43 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
44 * \f$x_i\f$ are positive and "as large as possible".
46 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
47 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
62 * A possible system could be:
63 * - three variables: `var1`, `var2`, `var3`
64 * - two constraints: `cons1`, `cons2`
65 * - four elements linking:
66 * - `elem1` linking `var1` and `cons1`
67 * - `elem2` linking `var2` and `cons1`
68 * - `elem3` linking `var2` and `cons2`
69 * - `elem4` linking `var3` and `cons2`
71 * And the corresponding inequations will be:
73 * var1.value <= var1.bound
74 * var2.value <= var2.bound
75 * var3.value <= var3.bound
76 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
77 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
79 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
81 * If a constraint is not shared, the sum is replaced by a max.
82 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
84 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
86 * This is useful for the sharing of resources for various models.
87 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
89 * Implementation details
91 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
92 * computation of constraints, and those who are part of the equations but are stuck to zero.
93 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
95 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
96 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
97 * than the conditions for it to be enabled.
98 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
99 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
100 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
101 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
102 * pausing of an action.
104 * Concurrency limit and maximum
106 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
107 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
109 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
111 * One may want to limit the concurrency of constraints for essentially three reasons:
112 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
114 * - Stay within parameters where the fluid model is accurate enough.
115 * - Model serialization effects
117 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
120 * Overall, each constraint contains three fields related to concurrency:
121 * - concurrency_limit which is the limit enforced by the solver
122 * - concurrency_current which is the current concurrency
123 * - concurrency_maximum which is the observed maximum concurrency
125 * Variables also have one field related to concurrency: concurrency_share.
126 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
127 * For example, cross-traffic is modeled using 2 elements per constraint.
128 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
132 /** @{ @ingroup SURF_lmm */
134 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
136 XBT_PUBLIC double func_reno_f(const Variable& var, double x);
137 XBT_PUBLIC double func_reno_fp(const Variable& var, double x);
138 XBT_PUBLIC double func_reno_fpi(const Variable& var, double x);
140 XBT_PUBLIC double func_reno2_f(const Variable& var, double x);
141 XBT_PUBLIC double func_reno2_fp(const Variable& var, double x);
142 XBT_PUBLIC double func_reno2_fpi(const Variable& var, double x);
144 XBT_PUBLIC double func_vegas_f(const Variable& var, double x);
145 XBT_PUBLIC double func_vegas_fp(const Variable& var, double x);
146 XBT_PUBLIC double func_vegas_fpi(const Variable& var, double x);
150 * Elements can be seen as glue between constraint objects and variable objects.
151 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
152 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
153 * vice-versa list all constraints for a given variable.
155 class XBT_PUBLIC Element {
157 int get_concurrency() const;
158 void decrease_concurrency();
159 void increase_concurrency();
162 void make_inactive();
164 /* hookup to constraint */
165 boost::intrusive::list_member_hook<> enabled_element_set_hook;
166 boost::intrusive::list_member_hook<> disabled_element_set_hook;
167 boost::intrusive::list_member_hook<> active_element_set_hook;
169 Constraint* constraint;
172 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
173 // - if CPU, then probably 1.
174 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
175 double consumption_weight;
178 struct ConstraintLight {
179 double remaining_over_usage;
184 * @brief LMM constraint
185 * Each constraint contains several partially overlapping logical sets of elements:
186 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
187 * the corresponding action will enable it (at least this is the idea).
188 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
189 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
190 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
192 class XBT_PUBLIC Constraint {
194 Constraint() = delete;
195 Constraint(void* id_value, double bound_value);
197 /** @brief Unshare a constraint. */
198 void unshare() { sharing_policy = s4u::Link::SharingPolicy::FATPIPE; }
201 * @brief Check if a constraint is shared (shared by default)
202 * @return 1 if shared, 0 otherwise
204 s4u::Link::SharingPolicy get_sharing_policy() const { return sharing_policy; }
207 * @brief Get the usage of the constraint after the last lmm solve
208 * @return The usage of the constraint
210 double get_usage() const;
211 int get_variable_amount() const;
214 * @brief Sets the concurrency limit for this constraint
215 * @param limit The concurrency limit to use for this constraint
217 void set_concurrency_limit(int limit)
219 xbt_assert(limit < 0 || concurrency_maximum <= limit,
220 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
221 " concurrency_maximum_reset() to reset the maximum?");
222 concurrency_limit = limit;
226 * @brief Gets the concurrency limit for this constraint
227 * @return The concurrency limit used by this constraint
229 int get_concurrency_limit() const { return concurrency_limit; }
232 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
235 void reset_concurrency_maximum() { concurrency_maximum = 0; }
238 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
239 * @return the maximum concurrency of the constraint
241 int get_concurrency_maximum() const
243 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
244 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
245 return concurrency_maximum;
248 int get_concurrency_slack() const
250 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
254 * @brief Get a var associated to a constraint
255 * @details Get the first variable of the next variable of elem if elem is not NULL
256 * @param elem A element of constraint of the constraint or NULL
257 * @return A variable associated to a constraint
259 Variable* get_variable(const Element** elem) const;
262 * @brief Get a var associated to a constraint
263 * @details Get the first variable of the next variable of elem if elem is not NULL
264 * @param elem A element of constraint of the constraint or NULL
265 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
266 * @param numelem parameter representing the number of elements to go
267 * @return A variable associated to a constraint
269 Variable* get_variable_safe(const Element** elem, const Element** nextelem, int* numelem) const;
272 * @brief Get the data associated to a constraint
273 * @return The data associated to the constraint
275 void* get_id() const { return id; }
277 /* hookup to system */
278 boost::intrusive::list_member_hook<> constraint_set_hook;
279 boost::intrusive::list_member_hook<> active_constraint_set_hook;
280 boost::intrusive::list_member_hook<> modified_constraint_set_hook;
281 boost::intrusive::list_member_hook<> saturated_constraint_set_hook;
282 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
283 &Element::enabled_element_set_hook>>
285 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
286 &Element::disabled_element_set_hook>>
287 disabled_element_set;
288 boost::intrusive::list<Element, boost::intrusive::member_hook<Element, boost::intrusive::list_member_hook<>,
289 &Element::active_element_set_hook>>
294 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
295 int concurrency_current; /* The current concurrency */
296 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
297 * given time (essentially for tracing)*/
299 s4u::Link::SharingPolicy sharing_policy;
303 ConstraintLight* cnst_light;
306 static int Global_debug_id;
307 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
313 * @brief LMM variable
315 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
316 * soon as possible we enable the variable with desired weight
318 class XBT_PUBLIC Variable {
320 void initialize(resource::Action* id_value, double sharing_weight_value, double bound_value,
321 int number_of_constraints, unsigned visited_value);
324 * @brief Get the value of the variable after the last lmm solve
325 * @return The value of the variable
327 double get_value() const { return value; }
330 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
331 * @return The bound of the variable
333 double get_bound() const { return bound; }
336 * @brief Set the concurrent share of the variable
337 * @param value The new concurrency share
339 void set_concurrency_share(short int value) { concurrency_share = value; }
342 * @brief Get the numth constraint associated to the variable
343 * @param num The rank of constraint we want to get
344 * @return The numth constraint
346 Constraint* get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
349 * @brief Get the weigth of the numth constraint associated to the variable
350 * @param num The rank of constraint we want to get
351 * @return The numth constraint
353 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
356 * @brief Get the number of constraint associated to a variable
357 * @return The number of constraint associated to the variable
359 int get_number_of_constraint() const { return cnsts.size(); }
362 * @brief Get the data associated to a variable
363 * @return The data associated to the variable
365 resource::Action* get_id() const { return id; }
368 * @brief Get the weight of a variable
369 * @return The weight of the variable
371 double get_weight() const { return sharing_weight; }
373 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
374 int get_min_concurrency_slack() const;
376 /** @brief Check if a variable can be enabled
377 * Make sure to set staged_weight before, if your intent is only to check concurrency
379 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
381 /* hookup to system */
382 boost::intrusive::list_member_hook<> variable_set_hook;
383 boost::intrusive::list_member_hook<> saturated_variable_set_hook;
385 std::vector<Element> cnsts;
387 // sharing_weight: variable's impact on the resource during the sharing
388 // if == 0, the variable is not considered by LMM
389 // on CPU, actions with N threads have a sharing of N
390 // on network, the actions with higher latency have a lesser sharing_weight
391 double sharing_weight;
393 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
397 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
398 resource::Action* id;
400 unsigned visited; /* used by System::update_modified_set() */
401 /* \begin{For Lagrange only} */
404 /* \end{For Lagrange only} */
407 static int Global_debug_id;
410 inline void Element::make_active()
412 constraint->active_element_set.push_front(*this);
414 inline void Element::make_inactive()
416 if (active_element_set_hook.is_linked())
417 simgrid::xbt::intrusive_erase(constraint->active_element_set, *this);
423 class XBT_PUBLIC System {
426 * @brief Create a new Linear MaxMim system
427 * @param selective_update whether we should do lazy updates
429 explicit System(bool selective_update);
430 /** @brief Free an existing Linear MaxMin system */
434 * @brief Create a new Linear MaxMin constraint
435 * @param id Data associated to the constraint (e.g.: a network link)
436 * @param bound_value The bound value of the constraint
438 Constraint* constraint_new(void* id, double bound_value);
441 * @brief Create a new Linear MaxMin variable
442 * @param id Data associated to the variable (e.g.: a network communication)
443 * @param weight_value The weight of the variable (0.0 if not used)
444 * @param bound The maximum value of the variable (-1.0 if no maximum value)
445 * @param number_of_constraints The maximum number of constraint to associate to the variable
447 Variable* variable_new(resource::Action* id, double weight_value, double bound, int number_of_constraints);
450 * @brief Free a variable
451 * @param var The variable to free
453 void variable_free(Variable * var);
456 * @brief Associate a variable to a constraint with a coefficient
457 * @param cnst A constraint
458 * @param var A variable
459 * @param value The coefficient associated to the variable in the constraint
461 void expand(Constraint * cnst, Variable * var, double value);
464 * @brief Add value to the coefficient between a constraint and a variable or create one
465 * @param cnst A constraint
466 * @param var A variable
467 * @param value The value to add to the coefficient associated to the variable in the constraint
469 void expand_add(Constraint * cnst, Variable * var, double value);
472 * @brief Update the bound of a variable
473 * @param var A constraint
474 * @param bound The new bound
476 void update_variable_bound(Variable * var, double bound);
479 * @brief Update the weight of a variable
480 * @param var A variable
481 * @param weight The new weight of the variable
483 void update_variable_weight(Variable * var, double weight);
486 * @brief Update a constraint bound
487 * @param cnst A constraint
488 * @param bound The new bound of the consrtaint
490 void update_constraint_bound(Constraint * cnst, double bound);
493 * @brief [brief description]
494 * @param cnst A constraint
495 * @return [description]
497 int constraint_used(Constraint * cnst) { return cnst->active_constraint_set_hook.is_linked(); }
499 /** @brief Print the lmm system */
502 /** @brief Solve the lmm system */
505 /** @brief Solve the lmm system. May be specialized in subclasses. */
506 virtual void solve() { lmm_solve(); }
509 static void* variable_mallocator_new_f();
510 static void variable_mallocator_free_f(void* var);
512 void var_free(Variable * var);
513 void cnst_free(Constraint * cnst);
514 Variable* extract_variable()
516 if (variable_set.empty())
518 Variable* res = &variable_set.front();
519 variable_set.pop_front();
522 Constraint* extract_constraint()
524 if (constraint_set.empty())
526 Constraint* res = &constraint_set.front();
527 constraint_set.pop_front();
530 void insert_constraint(Constraint * cnst) { constraint_set.push_back(*cnst); }
531 void remove_variable(Variable * var)
533 if (var->variable_set_hook.is_linked())
534 simgrid::xbt::intrusive_erase(variable_set, *var);
535 if (var->saturated_variable_set_hook.is_linked())
536 simgrid::xbt::intrusive_erase(saturated_variable_set, *var);
538 void make_constraint_active(Constraint * cnst)
540 if (not cnst->active_constraint_set_hook.is_linked())
541 active_constraint_set.push_back(*cnst);
543 void make_constraint_inactive(Constraint * cnst)
545 if (cnst->active_constraint_set_hook.is_linked())
546 simgrid::xbt::intrusive_erase(active_constraint_set, *cnst);
547 if (cnst->modified_constraint_set_hook.is_linked())
548 simgrid::xbt::intrusive_erase(modified_constraint_set, *cnst);
551 void enable_var(Variable * var);
552 void disable_var(Variable * var);
553 void on_disabled_var(Constraint * cnstr);
556 * @brief Update the value of element linking the constraint and the variable
557 * @param cnst A constraint
558 * @param var A variable
559 * @param value The new value
561 void update(Constraint * cnst, Variable * var, double value);
563 void update_modified_set(Constraint * cnst);
564 void update_modified_set_rec(Constraint * cnst);
566 /** @brief Remove all constraints of the modified_constraint_set. */
567 void remove_all_modified_set();
568 void check_concurrency() const;
570 template <class CnstList> void lmm_solve(CnstList& cnst_list);
573 bool modified_ = false;
574 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
575 &Variable::variable_set_hook>>
577 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
578 &Constraint::active_constraint_set_hook>>
579 active_constraint_set;
580 boost::intrusive::list<Variable, boost::intrusive::member_hook<Variable, boost::intrusive::list_member_hook<>,
581 &Variable::saturated_variable_set_hook>>
582 saturated_variable_set;
583 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
584 &Constraint::saturated_constraint_set_hook>>
585 saturated_constraint_set;
587 resource::Action::ModifiedSet* modified_set_ = nullptr;
590 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
591 unsigned visited_counter_ = 1; /* used by System::update_modified_set() and System::remove_all_modified_set() to
592 * cleverly (un-)flag the constraints (more details in these functions) */
593 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
594 &Constraint::constraint_set_hook>>
596 boost::intrusive::list<Constraint, boost::intrusive::member_hook<Constraint, boost::intrusive::list_member_hook<>,
597 &Constraint::modified_constraint_set_hook>>
598 modified_constraint_set;
599 xbt_mallocator_t variable_mallocator_ =
600 xbt_mallocator_new(65536, System::variable_mallocator_new_f, System::variable_mallocator_free_f, nullptr);
604 class XBT_PUBLIC FairBottleneck : public System {
606 explicit FairBottleneck(bool selective_update) : System(selective_update) {}
607 void solve() final { bottleneck_solve(); }
610 void bottleneck_solve();
613 class XBT_PUBLIC Lagrange : public System {
615 explicit Lagrange(bool selective_update) : System(selective_update) {}
616 void solve() final { lagrange_solve(); }
618 static void set_default_protocol_function(double (*func_f)(const Variable& var, double x),
619 double (*func_fp)(const Variable& var, double x),
620 double (*func_fpi)(const Variable& var, double x));
623 void lagrange_solve();
625 bool check_feasible(bool warn);
626 double dual_objective();
628 static double (*func_f)(const Variable& var, double x); /* (f) */
629 static double (*func_fp)(const Variable& var, double x); /* (f') */
630 static double (*func_fpi)(const Variable& var, double x); /* (f')^{-1} */
633 * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
635 // computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
636 static double dichotomy(double init, double diff(double, const Constraint&), const Constraint& cnst,
638 // computes the value of the differential of constraint cnst applied to lambda
639 static double partial_diff_lambda(double lambda, const Constraint& cnst);
641 static double new_value(const Variable& var);
642 static double new_mu(const Variable& var);
645 XBT_PUBLIC System* make_new_maxmin_system(bool selective_update);
646 XBT_PUBLIC System* make_new_fair_bottleneck_system(bool selective_update);
647 XBT_PUBLIC System* make_new_lagrange_system(bool selective_update);