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"
20 /** @addtogroup SURF_lmm
22 * A linear maxmin solver to resolve inequations systems.
24 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
25 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
26 * 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$x_1\f$
27 * 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
28 * case, we need to enforce:
30 * \f[ x_1 + x_2 \leq C_A \f]
32 * 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
33 * 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:
35 * \f[ x_3 \leq C_{L_1} \f]
36 * \f[ x_3 + x_4 \leq C_{L_2} \f]
37 * \f[ x_4 \leq C_{L_3} \f]
39 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
40 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
41 * \f$x_i\f$ are positive and "as large as possible".
43 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
44 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
59 * A possible system could be:
60 * - three variables: `var1`, `var2`, `var3`
61 * - two constraints: `cons1`, `cons2`
62 * - four elements linking:
63 * - `elem1` linking `var1` and `cons1`
64 * - `elem2` linking `var2` and `cons1`
65 * - `elem3` linking `var2` and `cons2`
66 * - `elem4` linking `var3` and `cons2`
68 * And the corresponding inequations will be:
70 * var1.value <= var1.bound
71 * var2.value <= var2.bound
72 * var3.value <= var3.bound
73 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
74 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
76 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
78 * If a constraint is not shared, the sum is replaced by a max.
79 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
81 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
83 * This is usefull for the sharing of resources for various models.
84 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
86 * Implementation details
88 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
89 * computation of constraints, and those who are part of the equations but are stuck to zero.
90 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
92 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
93 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
94 * than the conditions for it to be enabled.
95 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
96 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
97 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
98 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
99 * pausing of an action.
101 * Concurrency limit and maximum
103 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
104 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
106 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
108 * One may want to limit the concurrency of constraints for essentially three reasons:
109 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
111 * - Stay within parameters where the fluid model is accurate enough.
112 * - Model serialization effects
114 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
117 * Overall, each constraint contains three fields related to concurrency:
118 * - concurrency_limit which is the limit enforced by the solver
119 * - concurrency_current which is the current concurrency
120 * - concurrency_maximum which is the observed maximum concurrency
122 * Variables also have one field related to concurrency: concurrency_share.
123 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
124 * For example, cross-traffic is modeled using 2 elements per constraint.
125 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
129 /** @{ @ingroup SURF_lmm */
132 * @brief Solve the lmm system
133 * @param sys The lmm system to solve
135 XBT_PUBLIC(void) lmm_solve(lmm_system_t sys);
137 XBT_PUBLIC(void) lagrange_solve(lmm_system_t sys);
138 XBT_PUBLIC(void) bottleneck_solve(lmm_system_t sys);
140 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
143 lmm_set_default_protocol_function(double (*func_f)(lmm_variable_t var, double x),
144 double (*func_fp)(lmm_variable_t var, double x),
145 double (*func_fpi)(lmm_variable_t var, double x));
147 XBT_PUBLIC(double) func_reno_f(lmm_variable_t var, double x);
148 XBT_PUBLIC(double) func_reno_fp(lmm_variable_t var, double x);
149 XBT_PUBLIC(double) func_reno_fpi(lmm_variable_t var, double x);
151 XBT_PUBLIC(double) func_reno2_f(lmm_variable_t var, double x);
152 XBT_PUBLIC(double) func_reno2_fp(lmm_variable_t var, double x);
153 XBT_PUBLIC(double) func_reno2_fpi(lmm_variable_t var, double x);
155 XBT_PUBLIC(double) func_vegas_f(lmm_variable_t var, double x);
156 XBT_PUBLIC(double) func_vegas_fp(lmm_variable_t var, double x);
157 XBT_PUBLIC(double) func_vegas_fpi(lmm_variable_t var, double x);
161 * Elements can be seen as glue between constraint objects and variable objects.
162 * Basically, each variable will have a set of elements, one for each constraint where it is involved.
163 * Then, it is used to list all variables involved in constraint through constraint's xxx_element_set lists, or
164 * vice-versa list all constraints for a given variable.
166 class s_lmm_element_t {
168 int get_concurrency() const;
169 void decrease_concurrency();
170 void increase_concurrency();
173 void make_inactive();
175 /* hookup to constraint */
176 s_xbt_swag_hookup_t enabled_element_set_hookup;
177 s_xbt_swag_hookup_t disabled_element_set_hookup;
178 s_xbt_swag_hookup_t active_element_set_hookup;
180 lmm_constraint_t constraint;
181 lmm_variable_t variable;
183 // consumption_weight: impact of 1 byte or flop of your application onto the resource (in byte or flop)
184 // - if CPU, then probably 1.
185 // - If network, then 1 in forward direction and 0.05 backward for the ACKs
186 double consumption_weight;
189 struct s_lmm_constraint_light_t {
190 double remaining_over_usage;
191 lmm_constraint_t cnst;
195 * @brief LMM constraint
196 * Each constraint contains several partially overlapping logical sets of elements:
197 * \li Disabled elements which variable's weight is zero. This variables are not at all processed by LMM, but eventually
198 * the corresponding action will enable it (at least this is the idea).
199 * \li Enabled elements which variable's weight is non-zero. They are utilized in some LMM functions.
200 * \li Active elements which variable's weight is non-zero (i.e. it is enabled) AND its element value is non-zero.
201 * LMM_solve iterates over active elements during resolution, dynamically making them active or unactive.
203 class s_lmm_constraint_t {
205 s_lmm_constraint_t() = default;
206 s_lmm_constraint_t(void* id_value, double bound_value);
208 /** @brief Share a constraint. FIXME: name is misleading */
209 void shared() { sharing_policy = 0; }
212 * @brief Check if a constraint is shared (shared by default)
213 * @return 1 if shared, 0 otherwise
215 int get_sharing_policy() const { return sharing_policy; }
218 * @brief Get the usage of the constraint after the last lmm solve
219 * @return The usage of the constraint
221 double get_usage() const;
222 int get_variable_amount() const;
225 * @brief Sets the concurrency limit for this constraint
226 * @param concurrency_limit The concurrency limit to use for this constraint
228 void set_concurrency_limit(int limit)
230 xbt_assert(limit < 0 || concurrency_maximum <= limit,
231 "New concurrency limit should be larger than observed concurrency maximum. Maybe you want to call"
232 " concurrency_maximum_reset() to reset the maximum?");
233 concurrency_limit = limit;
237 * @brief Gets the concurrency limit for this constraint
238 * @return The concurrency limit used by this constraint
240 int get_concurrency_limit() const { return concurrency_limit; }
243 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
246 void reset_concurrency_maximum() { concurrency_maximum = 0; }
249 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
250 * @return the maximum concurrency of the constraint
252 int get_concurrency_maximum() const
254 xbt_assert(concurrency_limit < 0 || concurrency_maximum <= concurrency_limit,
255 "Very bad: maximum observed concurrency is higher than limit. This is a bug of SURF, please report it.");
256 return concurrency_maximum;
259 int get_concurrency_slack() const
261 return concurrency_limit < 0 ? std::numeric_limits<int>::max() : concurrency_limit - concurrency_current;
265 * @brief Get a var associated to a constraint
266 * @details Get the first variable of the next variable of elem if elem is not NULL
267 * @param elem A element of constraint of the constraint or NULL
268 * @return A variable associated to a constraint
270 lmm_variable_t get_variable(lmm_element_t* elem) const;
273 * @brief Get a var associated to a constraint
274 * @details Get the first variable of the next variable of elem if elem is not NULL
275 * @param elem A element of constraint of the constraint or NULL
276 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
277 * @param numelem parameter representing the number of elements to go
278 * @return A variable associated to a constraint
280 lmm_variable_t get_variable_safe(lmm_element_t* elem, lmm_element_t* nextelem, int* numelem) const;
283 * @brief Get the data associated to a constraint
284 * @return The data associated to the constraint
286 void* get_id() const { return id; }
288 /* hookup to system */
289 s_xbt_swag_hookup_t constraint_set_hookup = {nullptr, nullptr};
290 s_xbt_swag_hookup_t active_constraint_set_hookup = {nullptr, nullptr};
291 s_xbt_swag_hookup_t modified_constraint_set_hookup = {nullptr, nullptr};
292 s_xbt_swag_hookup_t saturated_constraint_set_hookup = {nullptr, nullptr};
293 s_xbt_swag_t enabled_element_set; /* a list of lmm_element_t */
294 s_xbt_swag_t disabled_element_set; /* a list of lmm_element_t */
295 s_xbt_swag_t active_element_set; /* a list of lmm_element_t */
299 // TODO MARTIN Check maximum value across resources at the end of simulation and give a warning is more than e.g. 500
300 int concurrency_current; /* The current concurrency */
301 int concurrency_maximum; /* The maximum number of (enabled and disabled) variables associated to the constraint at any
302 * given time (essentially for tracing)*/
304 int sharing_policy; /* see @e_surf_link_sharing_policy_t (0: FATPIPE, 1: SHARED, 2: FULLDUPLEX) */
308 lmm_constraint_light_t cnst_light;
311 static int Global_debug_id;
312 int concurrency_limit; /* The maximum number of variables that may be enabled at any time (stage variables if
318 * @brief LMM variable
320 * When something prevents us from enabling a variable, we "stage" the weight that we would have like to set, so that as
321 * soon as possible we enable the variable with desired weight
323 class s_lmm_variable_t {
325 void initialize(simgrid::surf::Action* id_value, double sharing_weight_value, double bound_value,
326 int number_of_constraints, unsigned visited_value);
329 * @brief Get the value of the variable after the last lmm solve
330 * @return The value of the variable
332 double get_value() const { return value; }
335 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
336 * @return The bound of the variable
338 double get_bound() const { return bound; }
341 * @brief Set the concurrent share of the variable
342 * @param concurrency_share The new concurrency share
344 void set_concurrency_share(short int value) { concurrency_share = value; }
347 * @brief Get the numth constraint associated to the variable
348 * @param num The rank of constraint we want to get
349 * @return The numth constraint
351 lmm_constraint_t get_constraint(unsigned num) const { return num < cnsts.size() ? cnsts[num].constraint : nullptr; }
354 * @brief Get the weigth of the numth constraint associated to the variable
355 * @param num The rank of constraint we want to get
356 * @return The numth constraint
358 double get_constraint_weight(unsigned num) const { return num < cnsts.size() ? cnsts[num].consumption_weight : 0.0; }
361 * @brief Get the number of constraint associated to a variable
362 * @return The number of constraint associated to the variable
364 int get_number_of_constraint() const { return cnsts.size(); }
367 * @brief Get the data associated to a variable
368 * @return The data associated to the variable
370 simgrid::surf::Action* get_id() const { return id; }
373 * @brief Get the weight of a variable
374 * @return The weight of the variable
376 double get_weight() const { return sharing_weight; }
378 /** @brief Measure the minimum concurrency slack across all constraints where the given var is involved */
379 int get_min_concurrency_slack() const;
381 /** @brief Check if a variable can be enabled
382 * Make sure to set staged_weight before, if your intent is only to check concurrency
384 int can_enable() const { return staged_weight > 0 && get_min_concurrency_slack() >= concurrency_share; }
386 /* hookup to system */
387 s_xbt_swag_hookup_t variable_set_hookup = {nullptr, nullptr};
388 s_xbt_swag_hookup_t saturated_variable_set_hookup = {nullptr, nullptr};
390 std::vector<s_lmm_element_t> cnsts;
392 // sharing_weight: variable's impact on the resource during the sharing
393 // if == 0, the variable is not considered by LMM
394 // on CPU, actions with N threads have a sharing of N
395 // on network, the actions with higher latency have a lesser sharing_weight
396 double sharing_weight;
398 double staged_weight; /* If non-zero, variable is staged for addition as soon as maxconcurrency constraints will be
402 short int concurrency_share; /* The maximum number of elements that variable will add to a constraint */
403 simgrid::surf::Action* id;
405 unsigned visited; /* used by lmm_update_modified_set */
406 /* \begin{For Lagrange only} */
409 double (*func_f)(s_lmm_variable_t* var, double x); /* (f) */
410 double (*func_fp)(s_lmm_variable_t* var, double x); /* (f') */
411 double (*func_fpi)(s_lmm_variable_t* var, double x); /* (f')^{-1} */
412 /* \end{For Lagrange only} */
415 static int Global_debug_id;
418 inline void s_lmm_element_t::make_active()
420 xbt_swag_insert_at_head(this, &constraint->active_element_set);
422 inline void s_lmm_element_t::make_inactive()
424 xbt_swag_remove(this, &constraint->active_element_set);
430 class s_lmm_system_t {
433 * @brief Create a new Linear MaxMim system
434 * @param selective_update whether we should do lazy updates
436 s_lmm_system_t(bool selective_update);
437 /** @brief Free an existing Linear MaxMin system */
441 * @brief Create a new Linear MaxMin constraint
442 * @param id Data associated to the constraint (e.g.: a network link)
443 * @param bound_value The bound value of the constraint
445 lmm_constraint_t constraint_new(void* id, double bound_value);
448 * @brief Create a new Linear MaxMin variable
449 * @param id Data associated to the variable (e.g.: a network communication)
450 * @param weight_value The weight of the variable (0.0 if not used)
451 * @param bound The maximum value of the variable (-1.0 if no maximum value)
452 * @param number_of_constraints The maximum number of constraint to associate to the variable
454 lmm_variable_t variable_new(simgrid::surf::Action* id, double weight_value, double bound, int number_of_constraints);
457 * @brief Free a variable
458 * @param var The variable to free
460 void variable_free(lmm_variable_t var);
463 * @brief Associate a variable to a constraint with a coefficient
464 * @param cnst A constraint
465 * @param var A variable
466 * @param value The coefficient associated to the variable in the constraint
468 void expand(lmm_constraint_t cnst, lmm_variable_t var, double value);
471 * @brief Add value to the coefficient between a constraint and a variable or create one
472 * @param cnst A constraint
473 * @param var A variable
474 * @param value The value to add to the coefficient associated to the variable in the constraint
476 void expand_add(lmm_constraint_t cnst, lmm_variable_t var, double value);
479 * @brief Update the bound of a variable
480 * @param var A constraint
481 * @param bound The new bound
483 void update_variable_bound(lmm_variable_t var, double bound);
486 * @brief Update the weight of a variable
487 * @param var A variable
488 * @param weight The new weight of the variable
490 void update_variable_weight(lmm_variable_t var, double weight);
493 * @brief Update a constraint bound
494 * @param cnst A constraint
495 * @param bound The new bound of the consrtaint
497 void update_constraint_bound(lmm_constraint_t cnst, double bound);
500 * @brief [brief description]
501 * @param cnst A constraint
502 * @return [description]
504 int constraint_used(lmm_constraint_t cnst) { return xbt_swag_belongs(cnst, &active_constraint_set); }
506 /** @brief Print the lmm system */
509 /** @brief Solve the lmm system */
513 static void* variable_mallocator_new_f();
514 static void variable_mallocator_free_f(void* var);
516 void var_free(lmm_variable_t var);
517 void cnst_free(lmm_constraint_t cnst);
518 lmm_variable_t extract_variable() { return static_cast<lmm_variable_t>(xbt_swag_extract(&variable_set)); }
519 lmm_constraint_t extract_constraint() { return static_cast<lmm_constraint_t>(xbt_swag_extract(&constraint_set)); }
520 void insert_constraint(lmm_constraint_t cnst) { xbt_swag_insert(cnst, &constraint_set); }
521 void remove_variable(lmm_variable_t var)
523 xbt_swag_remove(var, &variable_set);
524 xbt_swag_remove(var, &saturated_variable_set);
526 void remove_constraint(lmm_constraint_t cnst) // FIXME: unused
528 xbt_swag_remove(cnst, &constraint_set);
529 xbt_swag_remove(cnst, &saturated_constraint_set);
531 void make_constraint_active(lmm_constraint_t cnst) { xbt_swag_insert(cnst, &active_constraint_set); }
532 void make_constraint_inactive(lmm_constraint_t cnst)
534 xbt_swag_remove(cnst, &active_constraint_set);
535 xbt_swag_remove(cnst, &modified_constraint_set);
538 void enable_var(lmm_variable_t var);
539 void disable_var(lmm_variable_t var);
540 void on_disabled_var(lmm_constraint_t cnstr);
543 * @brief Update the value of element linking the constraint and the variable
544 * @param cnst A constraint
545 * @param var A variable
546 * @param value The new value
548 void update(lmm_constraint_t cnst, lmm_variable_t var, double value);
550 void update_modified_set(lmm_constraint_t cnst);
551 void update_modified_set_rec(lmm_constraint_t cnst);
553 /** @brief Remove all constraints of the modified_constraint_set. */
554 void remove_all_modified_set();
555 void check_concurrency();
559 s_xbt_swag_t variable_set; /* a list of lmm_variable_t */
560 s_xbt_swag_t active_constraint_set; /* a list of lmm_constraint_t */
561 s_xbt_swag_t saturated_variable_set; /* a list of lmm_variable_t */
562 s_xbt_swag_t saturated_constraint_set; /* a list of lmm_constraint_t */
564 simgrid::surf::ActionLmmListPtr keep_track;
566 void (*solve_fun)(lmm_system_t self);
569 bool selective_update_active; /* flag to update partially the system only selecting changed portions */
570 unsigned visited_counter; /* used by lmm_update_modified_set and lmm_remove_modified_set to cleverly (un-)flag the
571 * constraints (more details in these functions) */
572 s_xbt_swag_t constraint_set; /* a list of lmm_constraint_t */
573 s_xbt_swag_t modified_constraint_set; /* a list of modified lmm_constraint_t */
574 xbt_mallocator_t variable_mallocator;
577 extern XBT_PRIVATE double (*func_f_def)(lmm_variable_t, double);
578 extern XBT_PRIVATE double (*func_fp_def)(lmm_variable_t, double);
579 extern XBT_PRIVATE double (*func_fpi_def)(lmm_variable_t, double);