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"
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 usefull 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 */
135 * @brief Solve the lmm system
136 * @param sys The lmm system to solve
138 XBT_PUBLIC(void) lmm_solve(lmm_system_t sys);
140 XBT_PUBLIC(void) lagrange_solve(lmm_system_t sys);
141 XBT_PUBLIC(void) bottleneck_solve(lmm_system_t sys);
143 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
146 lmm_set_default_protocol_function(double (*func_f)(lmm_variable_t var, double x),
147 double (*func_fp)(lmm_variable_t var, double x),
148 double (*func_fpi)(lmm_variable_t var, double x));
150 XBT_PUBLIC(double) func_reno_f(lmm_variable_t var, double x);
151 XBT_PUBLIC(double) func_reno_fp(lmm_variable_t var, double x);
152 XBT_PUBLIC(double) func_reno_fpi(lmm_variable_t var, double x);
154 XBT_PUBLIC(double) func_reno2_f(lmm_variable_t var, double x);
155 XBT_PUBLIC(double) func_reno2_fp(lmm_variable_t var, double x);
156 XBT_PUBLIC(double) func_reno2_fpi(lmm_variable_t var, double x);
158 XBT_PUBLIC(double) func_vegas_f(lmm_variable_t var, double x);
159 XBT_PUBLIC(double) func_vegas_fp(lmm_variable_t var, double x);
160 XBT_PUBLIC(double) func_vegas_fpi(lmm_variable_t var, double x);
164 * Elements can be seen as glue between constraint objects and variable objects.
165 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
166 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
167 * vice-versa list all constraints for a given variable.
169 XBT_PUBLIC_CLASS s_lmm_element_t {
171 int get_concurrency() const;
172 void decrease_concurrency();
173 void increase_concurrency();
176 void make_inactive();
178 /* hookup to constraint */
179 s_xbt_swag_hookup_t enabled_element_set_hookup;
180 s_xbt_swag_hookup_t disabled_element_set_hookup;
181 s_xbt_swag_hookup_t active_element_set_hookup;
183 lmm_constraint_t constraint;
184 lmm_variable_t variable;
186 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
187 // - if CPU, then probably 1.
188 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
189 double consumption_weight;
192 struct s_lmm_constraint_light_t {
193 double remaining_over_usage;
194 lmm_constraint_t cnst;
198 * @brief LMM constraint
199 * Each constraint contains several partially overlapping logical sets of elements:
200 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
201 * the corresponding action will enable it (at least this is the idea).
202 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
203 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
204 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
206 XBT_PUBLIC_CLASS s_lmm_constraint_t {
208 s_lmm_constraint_t() = default;
209 s_lmm_constraint_t(void* id_value, double bound_value);
211 /** @brief Unshare a constraint. */
212 void unshare() { sharing_policy = 0; }
215 * @brief Check if a constraint is shared (shared by default)
216 * @return 1 if shared, 0 otherwise
218 int get_sharing_policy() const { return sharing_policy; }
221 * @brief Get the usage of the constraint after the last lmm solve
222 * @return The usage of the constraint
224 double get_usage() const;
225 int get_variable_amount() const;
228 * @brief Sets the concurrency limit for this constraint
229 * @param concurrency_limit The concurrency limit to use for this constraint
231 void set_concurrency_limit(int limit)
233 xbt_assert(limit < 0 || concurrency_maximum <= limit,
234 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
235 " concurrency_maximum_reset() to reset the maximum?");
236 concurrency_limit = limit;
240 * @brief Gets the concurrency limit for this constraint
241 * @return The concurrency limit used by this constraint
243 int get_concurrency_limit() const { return concurrency_limit; }
246 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
249 void reset_concurrency_maximum() { concurrency_maximum = 0; }
252 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
253 * @return the maximum concurrency of the constraint
255 int get_concurrency_maximum() const
257 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
258 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
259 return concurrency_maximum;
262 int get_concurrency_slack() const
264 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
268 * @brief Get a var associated to a constraint
269 * @details Get the first variable of the next variable of elem if elem is not NULL
270 * @param elem A element of constraint of the constraint or NULL
271 * @return A variable associated to a constraint
273 lmm_variable_t get_variable(lmm_element_t* elem) const;
276 * @brief Get a var associated to a constraint
277 * @details Get the first variable of the next variable of elem if elem is not NULL
278 * @param elem A element of constraint of the constraint or NULL
279 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
280 * @param numelem parameter representing the number of elements to go
281 * @return A variable associated to a constraint
283 lmm_variable_t get_variable_safe(lmm_element_t* elem, lmm_element_t* nextelem, int* numelem) const;
286 * @brief Get the data associated to a constraint
287 * @return The data associated to the constraint
289 void* get_id() const { return id; }
291 /* hookup to system */
292 s_xbt_swag_hookup_t constraint_set_hookup = {nullptr, nullptr};
293 s_xbt_swag_hookup_t active_constraint_set_hookup = {nullptr, nullptr};
294 s_xbt_swag_hookup_t modified_constraint_set_hookup = {nullptr, nullptr};
295 s_xbt_swag_hookup_t saturated_constraint_set_hookup = {nullptr, nullptr};
296 s_xbt_swag_t enabled_element_set; /* a list of lmm_element_t */
297 s_xbt_swag_t disabled_element_set; /* a list of lmm_element_t */
298 s_xbt_swag_t active_element_set; /* a list of lmm_element_t */
302 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
303 int concurrency_current; /* The current concurrency */
304 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
305 * given time (essentially for tracing)*/
307 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: FULLDUPLEX) */
311 lmm_constraint_light_t cnst_light;
314 static int Global_debug_id;
315 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
321 * @brief LMM variable
323 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
324 * soon as possible we enable the variable with desired weight
326 XBT_PUBLIC_CLASS s_lmm_variable_t {
328 void initialize(simgrid::surf::Action* id_value, double sharing_weight_value, double bound_value,
329 int number_of_constraints, unsigned visited_value);
332 * @brief Get the value of the variable after the last lmm solve
333 * @return The value of the variable
335 double get_value() const { return value; }
338 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
339 * @return The bound of the variable
341 double get_bound() const { return bound; }
344 * @brief Set the concurrent share of the variable
345 * @param concurrency_share The new concurrency share
347 void set_concurrency_share(short int value) { concurrency_share = value; }
350 * @brief Get the numth constraint associated to the variable
351 * @param num The rank of constraint we want to get
352 * @return The numth constraint
354 lmm_constraint_t get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
357 * @brief Get the weigth of the numth constraint associated to the variable
358 * @param num The rank of constraint we want to get
359 * @return The numth constraint
361 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
364 * @brief Get the number of constraint associated to a variable
365 * @return The number of constraint associated to the variable
367 int get_number_of_constraint() const { return cnsts.size(); }
370 * @brief Get the data associated to a variable
371 * @return The data associated to the variable
373 simgrid::surf::Action* get_id() const { return id; }
376 * @brief Get the weight of a variable
377 * @return The weight of the variable
379 double get_weight() const { return sharing_weight; }
381 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
382 int get_min_concurrency_slack() const;
384 /** @brief Check if a variable can be enabled
385 * Make sure to set staged_weight before, if your intent is only to check concurrency
387 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
389 /* hookup to system */
390 s_xbt_swag_hookup_t variable_set_hookup = {nullptr, nullptr};
391 s_xbt_swag_hookup_t saturated_variable_set_hookup = {nullptr, nullptr};
393 std::vector<s_lmm_element_t> cnsts;
395 // sharing_weight: variable's impact on the resource during the sharing
396 // if == 0, the variable is not considered by LMM
397 // on CPU, actions with N threads have a sharing of N
398 // on network, the actions with higher latency have a lesser sharing_weight
399 double sharing_weight;
401 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
405 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
406 simgrid::surf::Action* id;
408 unsigned visited; /* used by lmm_update_modified_set */
409 /* \begin{For Lagrange only} */
412 double (*func_f)(s_lmm_variable_t* var, double x); /* (f) */
413 double (*func_fp)(s_lmm_variable_t* var, double x); /* (f') */
414 double (*func_fpi)(s_lmm_variable_t* var, double x); /* (f')^{-1} */
415 /* \end{For Lagrange only} */
418 static int Global_debug_id;
421 inline void s_lmm_element_t::make_active()
423 xbt_swag_insert_at_head(this, &constraint->active_element_set);
425 inline void s_lmm_element_t::make_inactive()
427 xbt_swag_remove(this, &constraint->active_element_set);
433 XBT_PUBLIC_CLASS s_lmm_system_t {
436 * @brief Create a new Linear MaxMim system
437 * @param selective_update whether we should do lazy updates
439 explicit s_lmm_system_t(bool selective_update);
440 /** @brief Free an existing Linear MaxMin system */
444 * @brief Create a new Linear MaxMin constraint
445 * @param id Data associated to the constraint (e.g.: a network link)
446 * @param bound_value The bound value of the constraint
448 lmm_constraint_t constraint_new(void* id, double bound_value);
451 * @brief Create a new Linear MaxMin variable
452 * @param id Data associated to the variable (e.g.: a network communication)
453 * @param weight_value The weight of the variable (0.0 if not used)
454 * @param bound The maximum value of the variable (-1.0 if no maximum value)
455 * @param number_of_constraints The maximum number of constraint to associate to the variable
457 lmm_variable_t variable_new(simgrid::surf::Action* id, double weight_value, double bound, int number_of_constraints);
460 * @brief Free a variable
461 * @param var The variable to free
463 void variable_free(lmm_variable_t var);
466 * @brief Associate a variable to a constraint with a coefficient
467 * @param cnst A constraint
468 * @param var A variable
469 * @param value The coefficient associated to the variable in the constraint
471 void expand(lmm_constraint_t cnst, lmm_variable_t var, double value);
474 * @brief Add value to the coefficient between a constraint and a variable or create one
475 * @param cnst A constraint
476 * @param var A variable
477 * @param value The value to add to the coefficient associated to the variable in the constraint
479 void expand_add(lmm_constraint_t cnst, lmm_variable_t var, double value);
482 * @brief Update the bound of a variable
483 * @param var A constraint
484 * @param bound The new bound
486 void update_variable_bound(lmm_variable_t var, double bound);
489 * @brief Update the weight of a variable
490 * @param var A variable
491 * @param weight The new weight of the variable
493 void update_variable_weight(lmm_variable_t var, double weight);
496 * @brief Update a constraint bound
497 * @param cnst A constraint
498 * @param bound The new bound of the consrtaint
500 void update_constraint_bound(lmm_constraint_t cnst, double bound);
503 * @brief [brief description]
504 * @param cnst A constraint
505 * @return [description]
507 int constraint_used(lmm_constraint_t cnst) { return xbt_swag_belongs(cnst, &active_constraint_set); }
509 /** @brief Print the lmm system */
512 /** @brief Solve the lmm system */
516 static void* variable_mallocator_new_f();
517 static void variable_mallocator_free_f(void* var);
519 void var_free(lmm_variable_t var);
520 void cnst_free(lmm_constraint_t cnst);
521 lmm_variable_t extract_variable() { return static_cast<lmm_variable_t>(xbt_swag_extract(&variable_set)); }
522 lmm_constraint_t extract_constraint() { return static_cast<lmm_constraint_t>(xbt_swag_extract(&constraint_set)); }
523 void insert_constraint(lmm_constraint_t cnst) { xbt_swag_insert(cnst, &constraint_set); }
524 void remove_variable(lmm_variable_t var)
526 xbt_swag_remove(var, &variable_set);
527 xbt_swag_remove(var, &saturated_variable_set);
529 void make_constraint_active(lmm_constraint_t cnst) { xbt_swag_insert(cnst, &active_constraint_set); }
530 void make_constraint_inactive(lmm_constraint_t cnst)
532 xbt_swag_remove(cnst, &active_constraint_set);
533 xbt_swag_remove(cnst, &modified_constraint_set);
536 void enable_var(lmm_variable_t var);
537 void disable_var(lmm_variable_t var);
538 void on_disabled_var(lmm_constraint_t cnstr);
541 * @brief Update the value of element linking the constraint and the variable
542 * @param cnst A constraint
543 * @param var A variable
544 * @param value The new value
546 void update(lmm_constraint_t cnst, lmm_variable_t var, double value);
548 void update_modified_set(lmm_constraint_t cnst);
549 void update_modified_set_rec(lmm_constraint_t cnst);
551 /** @brief Remove all constraints of the modified_constraint_set. */
552 void remove_all_modified_set();
553 void check_concurrency();
557 s_xbt_swag_t variable_set; /* a list of lmm_variable_t */
558 s_xbt_swag_t active_constraint_set; /* a list of lmm_constraint_t */
559 s_xbt_swag_t saturated_variable_set; /* a list of lmm_variable_t */
560 s_xbt_swag_t saturated_constraint_set; /* a list of lmm_constraint_t */
562 simgrid::surf::ActionLmmListPtr keep_track;
564 void (*solve_fun)(lmm_system_t self);
567 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
568 unsigned visited_counter; /* used by lmm_update_modified_set and lmm_remove_modified_set to cleverly (un-)flag the
569 * constraints (more details in these functions) */
570 s_xbt_swag_t constraint_set; /* a list of lmm_constraint_t */
571 s_xbt_swag_t modified_constraint_set; /* a list of modified lmm_constraint_t */
572 xbt_mallocator_t variable_mallocator;
575 extern XBT_PRIVATE double (*func_f_def)(lmm_variable_t, double);
576 extern XBT_PRIVATE double (*func_fp_def)(lmm_variable_t, double);
577 extern XBT_PRIVATE double (*func_fpi_def)(lmm_variable_t, double);