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 "surf/datatypes.h"
11 #include "xbt/asserts.h"
21 /** @addtogroup SURF_lmm
23 * A linear maxmin solver to resolve inequations systems.
25 * Most SimGrid model rely on a "fluid/steady-state" modeling that simulate the sharing of resources between actions at
26 * relatively coarse-grain. Such sharing is generally done by solving a set of linear inequations. Let's take an
27 * 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$x_1\f$
28 * 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
29 * case, we need to enforce:
31 * \f[ x_1 + x_2 \leq C_A \f]
33 * 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
34 * 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:
36 * \f[ x_3 \leq C_{L_1} \f]
37 * \f[ x_3 + x_4 \leq C_{L_2} \f]
38 * \f[ x_4 \leq C_{L_3} \f]
40 * One could set every variable to 0 to make sure the constraints are satisfied but this would obviously not be very
41 * realistic. A possible objective is to try to maximize the minimum of the \f$x_i\f$ . This ensures that all the
42 * \f$x_i\f$ are positive and "as large as possible".
44 * This is called *max-min fairness* and is the most commonly used objective in SimGrid. Another possibility is to
45 * maximize \f$\sum_if(x_i)\f$, where \f$f\f$ is a strictly increasing concave function.
60 * A possible system could be:
61 * - three variables: `var1`, `var2`, `var3`
62 * - two constraints: `cons1`, `cons2`
63 * - four elements linking:
64 * - `elem1` linking `var1` and `cons1`
65 * - `elem2` linking `var2` and `cons1`
66 * - `elem3` linking `var2` and `cons2`
67 * - `elem4` linking `var3` and `cons2`
69 * And the corresponding inequations will be:
71 * var1.value <= var1.bound
72 * var2.value <= var2.bound
73 * var3.value <= var3.bound
74 * var1.weight * var1.value * elem1.value + var2.weight * var2.value * elem2.value <= cons1.bound
75 * var2.weight * var2.value * elem3.value + var3.weight * var3.value * elem4.value <= cons2.bound
77 * where `var1.value`, `var2.value` and `var3.value` are the unknown values.
79 * If a constraint is not shared, the sum is replaced by a max.
80 * For example, a third non-shared constraint `cons3` and the associated elements `elem5` and `elem6` could write as:
82 * max( var1.weight * var1.value * elem5.value , var3.weight * var3.value * elem6.value ) <= cons3.bound
84 * This is usefull for the sharing of resources for various models.
85 * For instance, for the network model, each link is associated to a constraint and each communication to a variable.
87 * Implementation details
89 * For implementation reasons, we are interested in distinguishing variables that actually participate to the
90 * computation of constraints, and those who are part of the equations but are stuck to zero.
91 * We call enabled variables, those which var.weight is strictly positive. Zero-weight variables are called disabled
93 * Unfortunately this concept of enabled/disabled variables intersects with active/inactive variable.
94 * Semantically, the intent is similar, but the conditions under which a variable is active is slightly more strict
95 * than the conditions for it to be enabled.
96 * A variable is active only if its var.value is non-zero (and, by construction, its var.weight is non-zero).
97 * In general, variables remain disabled after their creation, which often models an initialization phase (e.g. first
98 * packet propagating in the network). Then, it is enabled by the corresponding model. Afterwards, the max-min solver
99 * (lmm_solve()) activates it when appropriate. It is possible that the variable is again disabled, e.g. to model the
100 * pausing of an action.
102 * Concurrency limit and maximum
104 * We call concurrency, the number of variables that can be enabled at any time for each constraint.
105 * From a model perspective, this "concurrency" often represents the number of actions that actually compete for one
107 * The LMM solver is able to limit the concurrency for each constraint, and to monitor its maximum value.
109 * One may want to limit the concurrency of constraints for essentially three reasons:
110 * - Keep LMM system in a size that can be solved (it does not react very well with tens of thousands of variables per
112 * - Stay within parameters where the fluid model is accurate enough.
113 * - Model serialization effects
115 * The concurrency limit can also be set to a negative value to disable concurrency limit. This can improve performance
118 * Overall, each constraint contains three fields related to concurrency:
119 * - concurrency_limit which is the limit enforced by the solver
120 * - concurrency_current which is the current concurrency
121 * - concurrency_maximum which is the observed maximum concurrency
123 * Variables also have one field related to concurrency: concurrency_share.
124 * In effect, in some cases, one variable is involved multiple times (i.e. two elements) in a constraint.
125 * For example, cross-traffic is modeled using 2 elements per constraint.
126 * concurrency_share formally corresponds to the maximum number of elements that associate the variable and any given
130 XBT_PUBLIC_DATA(double) sg_maxmin_precision;
131 XBT_PUBLIC_DATA(double) sg_surf_precision;
132 XBT_PUBLIC_DATA(int) sg_concurrency_limit;
134 static inline void double_update(double *variable, double value, double precision)
136 //printf("Updating %g -= %g +- %g\n",*variable,value,precision);
137 //xbt_assert(value==0 || value>precision);
138 //Check that precision is higher than the machine-dependent size of the mantissa. If not, brutal rounding may happen,
139 //and the precision mechanism is not active...
140 //xbt_assert(*variable< (2<<DBL_MANT_DIG)*precision && FLT_RADIX==2);
142 if (*variable < precision)
146 static inline int double_positive(double value, double precision)
148 return (value > precision);
151 static inline int double_equals(double value1, double value2, double precision)
153 return (fabs(value1 - value2) < precision);
158 /** @{ @ingroup SURF_lmm */
160 * @brief Create a new Linear MaxMim system
161 * @param selective_update whether we should do lazy updates
163 XBT_PUBLIC(lmm_system_t) lmm_system_new(bool selective_update);
166 * @brief Free an existing Linear MaxMin system
167 * @param sys The lmm system to free
169 XBT_PUBLIC(void) lmm_system_free(lmm_system_t sys);
172 * @brief Create a new Linear MaxMin constraint
173 * @param sys The system in which we add a constraint
174 * @param id Data associated to the constraint (e.g.: a network link)
175 * @param bound_value The bound value of the constraint
177 XBT_PUBLIC(lmm_constraint_t) lmm_constraint_new(lmm_system_t sys, void *id,double bound_value);
180 * @brief Share a constraint
181 * @param cnst The constraint to share
183 XBT_PUBLIC(void) lmm_constraint_shared(lmm_constraint_t cnst);
186 * @brief Check if a constraint is shared (shared by default)
187 * @param cnst The constraint to share
188 * @return 1 if shared, 0 otherwise
190 XBT_PUBLIC(int) lmm_constraint_sharing_policy(lmm_constraint_t cnst);
193 * @brief Free a constraint
194 * @param sys The system associated to the constraint
195 * @param cnst The constraint to free
197 XBT_PUBLIC(void) lmm_constraint_free(lmm_system_t sys, lmm_constraint_t cnst);
200 * @brief Get the usage of the constraint after the last lmm solve
201 * @param cnst A constraint
202 * @return The usage of the constraint
204 XBT_PUBLIC(double) lmm_constraint_get_usage(lmm_constraint_t cnst);
206 XBT_PUBLIC(int) lmm_constraint_get_variable_amount(lmm_constraint_t cnst);
209 * @brief Sets the concurrency limit for this constraint
210 * @param cnst A constraint
211 * @param concurrency_limit The concurrency limit to use for this constraint
213 XBT_PUBLIC(void) lmm_constraint_concurrency_limit_set(lmm_constraint_t cnst, int concurrency_limit);
216 * @brief Gets the concurrency limit for this constraint
217 * @param cnst A constraint
218 * @return The concurrency limit used by this constraint
220 XBT_PUBLIC(int) lmm_constraint_concurrency_limit_get(lmm_constraint_t cnst);
223 * @brief Reset the concurrency maximum for a given variable (we will update the maximum to reflect constraint
225 * @param cnst A constraint
227 XBT_PUBLIC(void) lmm_constraint_concurrency_maximum_reset(lmm_constraint_t cnst);
230 * @brief Get the concurrency maximum for a given variable (which reflects constraint evolution).
231 * @param cnst A constraint
232 * @return the maximum concurrency of the constraint
234 XBT_PUBLIC(int) lmm_constraint_concurrency_maximum_get(lmm_constraint_t cnst);
237 * @brief Create a new Linear MaxMin variable
238 * @param sys The system in which we add a constaint
239 * @param id Data associated to the variable (e.g.: a network communication)
240 * @param weight_value The weight of the variable (0.0 if not used)
241 * @param bound The maximum value of the variable (-1.0 if no maximum value)
242 * @param number_of_constraints The maximum number of constraint to associate to the variable
244 XBT_PUBLIC(lmm_variable_t)
245 lmm_variable_new(lmm_system_t sys, simgrid::surf::Action* id, double weight_value, double bound,
246 int number_of_constraints);
248 * @brief Free a variable
249 * @param sys The system associated to the variable
250 * @param var The variable to free
252 XBT_PUBLIC(void) lmm_variable_free(lmm_system_t sys, lmm_variable_t var);
255 * @brief Get the value of the variable after the last lmm solve
256 * @param var A variable
257 * @return The value of the variable
259 XBT_PUBLIC(double) lmm_variable_getvalue(lmm_variable_t var);
262 * @brief Get the maximum value of the variable (-1.0 if no maximum value)
263 * @param var A variable
264 * @return The bound of the variable
266 XBT_PUBLIC(double) lmm_variable_getbound(lmm_variable_t var);
269 * @brief Set the concurrent share of the variable
270 * @param var A variable
271 * @param concurrency_share The new concurrency share
273 XBT_PUBLIC(void) lmm_variable_concurrency_share_set(lmm_variable_t var, short int concurrency_share);
276 * @brief Remove a variable from a constraint
277 * @param sys A system
278 * @param cnst A constraint
279 * @param var The variable to remove
281 XBT_PUBLIC(void) lmm_shrink(lmm_system_t sys, lmm_constraint_t cnst, lmm_variable_t var);
284 * @brief Associate a variable to a constraint with a coefficient
285 * @param sys A system
286 * @param cnst A constraint
287 * @param var A variable
288 * @param value The coefficient associated to the variable in the constraint
290 XBT_PUBLIC(void) lmm_expand(lmm_system_t sys, lmm_constraint_t cnst, lmm_variable_t var, double value);
293 * @brief Add value to the coefficient between a constraint and a variable or create one
294 * @param sys A system
295 * @param cnst A constraint
296 * @param var A variable
297 * @param value The value to add to the coefficient associated to the variable in the constraint
299 XBT_PUBLIC(void) lmm_expand_add(lmm_system_t sys, lmm_constraint_t cnst, lmm_variable_t var, double value);
302 * @brief Get the numth constraint associated to the variable
303 * @param sys The system associated to the variable (not used)
304 * @param var A variable
305 * @param num The rank of constraint we want to get
306 * @return The numth constraint
308 XBT_PUBLIC(lmm_constraint_t) lmm_get_cnst_from_var(lmm_system_t sys, lmm_variable_t var, int num);
311 * @brief Get the weigth of the numth constraint associated to the variable
312 * @param sys The system associated to the variable (not used)
313 * @param var A variable
314 * @param num The rank of constraint we want to get
315 * @return The numth constraint
317 XBT_PUBLIC(double) lmm_get_cnst_weight_from_var(lmm_system_t sys, lmm_variable_t var, int num);
320 * @brief Get the number of constraint associated to a variable
321 * @param sys The system associated to the variable (not used)
322 * @param var A variable
323 * @return The number of constraint associated to the variable
325 XBT_PUBLIC(int) lmm_get_number_of_cnst_from_var(lmm_system_t sys, lmm_variable_t var);
328 * @brief Get a var associated to a constraint
329 * @details Get the first variable of the next variable of elem if elem is not NULL
330 * @param sys The system associated to the variable (not used)
331 * @param cnst A constraint
332 * @param elem A element of constraint of the constraint or NULL
333 * @return A variable associated to a constraint
335 XBT_PUBLIC(lmm_variable_t) lmm_get_var_from_cnst(lmm_system_t sys, lmm_constraint_t cnst, lmm_element_t * elem);
338 * @brief Get a var associated to a constraint
339 * @details Get the first variable of the next variable of elem if elem is not NULL
340 * @param cnst A constraint
341 * @param elem A element of constraint of the constraint or NULL
342 * @param nextelem A element of constraint of the constraint or NULL, the one after elem
343 * @param numelem parameter representing the number of elements to go
345 * @return A variable associated to a constraint
347 XBT_PUBLIC(lmm_variable_t) lmm_get_var_from_cnst_safe(lmm_system_t sys, lmm_constraint_t cnst,
348 lmm_element_t * elem, lmm_element_t * nextelem, int * numelem);
351 * @brief Get the first active constraint of a system
352 * @param sys A system
353 * @return The first active constraint
355 XBT_PUBLIC(lmm_constraint_t) lmm_get_first_active_constraint(lmm_system_t sys);
358 * @brief Get the next active constraint of a constraint in a system
359 * @param sys A system
360 * @param cnst An active constraint of the system
362 * @return The next active constraint
364 XBT_PUBLIC(lmm_constraint_t) lmm_get_next_active_constraint(lmm_system_t sys, lmm_constraint_t cnst);
367 * @brief Get the data associated to a constraint
368 * @param cnst A constraint
369 * @return The data associated to the constraint
371 XBT_PUBLIC(void *) lmm_constraint_id(lmm_constraint_t cnst);
374 * @brief Get the data associated to a variable
375 * @param var A variable
376 * @return The data associated to the variable
378 XBT_PUBLIC(void *) lmm_variable_id(lmm_variable_t var);
381 * @brief Update the value of element linking the constraint and the variable
382 * @param sys A system
383 * @param cnst A constraint
384 * @param var A variable
385 * @param value The new value
387 XBT_PUBLIC(void) lmm_update(lmm_system_t sys, lmm_constraint_t cnst, lmm_variable_t var, double value);
390 * @brief Update the bound of a variable
391 * @param sys A system
392 * @param var A constraint
393 * @param bound The new bound
395 XBT_PUBLIC(void) lmm_update_variable_bound(lmm_system_t sys, lmm_variable_t var, double bound);
398 * @brief Update the weight of a variable
399 * @param sys A system
400 * @param var A variable
401 * @param weight The new weight of the variable
403 XBT_PUBLIC(void) lmm_update_variable_weight(lmm_system_t sys, lmm_variable_t var, double weight);
406 * @brief Get the weight of a variable
407 * @param var A variable
408 * @return The weight of the variable
410 XBT_PUBLIC(double) lmm_get_variable_weight(lmm_variable_t var);
413 * @brief Update a constraint bound
414 * @param sys A system
415 * @param cnst A constraint
416 * @param bound The new bound of the consrtaint
418 XBT_PUBLIC(void) lmm_update_constraint_bound(lmm_system_t sys, lmm_constraint_t cnst, double bound);
421 * @brief [brief description]
422 * @param sys A system
423 * @param cnst A constraint
424 * @return [description]
426 XBT_PUBLIC(int) lmm_constraint_used(lmm_system_t sys, lmm_constraint_t cnst);
429 * @brief Print the lmm system
430 * @param sys The lmm system to print
432 XBT_PUBLIC(void) lmm_print(lmm_system_t sys);
435 * @brief Solve the lmm system
436 * @param sys The lmm system to solve
438 XBT_PUBLIC(void) lmm_solve(lmm_system_t sys);
440 XBT_PUBLIC(void) lagrange_solve(lmm_system_t sys);
441 XBT_PUBLIC(void) bottleneck_solve(lmm_system_t sys);
443 /** Default functions associated to the chosen protocol. When using the lagrangian approach. */
445 XBT_PUBLIC(void) lmm_set_default_protocol_function(double (*func_f)(lmm_variable_t var,double x),
446 double (*func_fp)(lmm_variable_t var,double x),
447 double (*func_fpi)(lmm_variable_t var,double x));
449 XBT_PUBLIC(double func_reno_f) (lmm_variable_t var, double x);
450 XBT_PUBLIC(double func_reno_fp) (lmm_variable_t var, double x);
451 XBT_PUBLIC(double func_reno_fpi) (lmm_variable_t var, double x);
453 XBT_PUBLIC(double func_reno2_f) (lmm_variable_t var, double x);
454 XBT_PUBLIC(double func_reno2_fp) (lmm_variable_t var, double x);
455 XBT_PUBLIC(double func_reno2_fpi) (lmm_variable_t var, double x);
457 XBT_PUBLIC(double func_vegas_f) (lmm_variable_t var, double x);
458 XBT_PUBLIC(double func_vegas_fp) (lmm_variable_t var, double x);
459 XBT_PUBLIC(double func_vegas_fpi) (lmm_variable_t var, double x);