Messages in this thread Patch in this message | | | Date | Wed, 24 Oct 2012 02:58:38 -0700 | From | tip-bot for Peter Zijlstra <> | Subject | [tip:sched/core] sched: Describe CFS load-balancer |
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Commit-ID: e9c84cb8d5f1b1ea6fcbe6190d51dc84b6975938 Gitweb: http://git.kernel.org/tip/e9c84cb8d5f1b1ea6fcbe6190d51dc84b6975938 Author: Peter Zijlstra <peterz@infradead.org> AuthorDate: Tue, 3 Jul 2012 13:53:26 +0200 Committer: Ingo Molnar <mingo@kernel.org> CommitDate: Wed, 24 Oct 2012 10:27:33 +0200
sched: Describe CFS load-balancer
Add some scribbles on how and why the load-balancer works..
Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl> Link: http://lkml.kernel.org/r/1341316406.23484.64.camel@twins Signed-off-by: Ingo Molnar <mingo@kernel.org> --- kernel/sched/fair.c | 118 ++++++++++++++++++++++++++++++++++++++++++++++++++- 1 files changed, 116 insertions(+), 2 deletions(-)
diff --git a/kernel/sched/fair.c b/kernel/sched/fair.c index 3e6a353..a319d56c 100644 --- a/kernel/sched/fair.c +++ b/kernel/sched/fair.c @@ -3456,8 +3456,122 @@ static bool yield_to_task_fair(struct rq *rq, struct task_struct *p, bool preemp #ifdef CONFIG_SMP /************************************************** - * Fair scheduling class load-balancing methods: - */ + * Fair scheduling class load-balancing methods. + * + * BASICS + * + * The purpose of load-balancing is to achieve the same basic fairness the + * per-cpu scheduler provides, namely provide a proportional amount of compute + * time to each task. This is expressed in the following equation: + * + * W_i,n/P_i == W_j,n/P_j for all i,j (1) + * + * Where W_i,n is the n-th weight average for cpu i. The instantaneous weight + * W_i,0 is defined as: + * + * W_i,0 = \Sum_j w_i,j (2) + * + * Where w_i,j is the weight of the j-th runnable task on cpu i. This weight + * is derived from the nice value as per prio_to_weight[]. + * + * The weight average is an exponential decay average of the instantaneous + * weight: + * + * W'_i,n = (2^n - 1) / 2^n * W_i,n + 1 / 2^n * W_i,0 (3) + * + * P_i is the cpu power (or compute capacity) of cpu i, typically it is the + * fraction of 'recent' time available for SCHED_OTHER task execution. But it + * can also include other factors [XXX]. + * + * To achieve this balance we define a measure of imbalance which follows + * directly from (1): + * + * imb_i,j = max{ avg(W/P), W_i/P_i } - min{ avg(W/P), W_j/P_j } (4) + * + * We them move tasks around to minimize the imbalance. In the continuous + * function space it is obvious this converges, in the discrete case we get + * a few fun cases generally called infeasible weight scenarios. + * + * [XXX expand on: + * - infeasible weights; + * - local vs global optima in the discrete case. ] + * + * + * SCHED DOMAINS + * + * In order to solve the imbalance equation (4), and avoid the obvious O(n^2) + * for all i,j solution, we create a tree of cpus that follows the hardware + * topology where each level pairs two lower groups (or better). This results + * in O(log n) layers. Furthermore we reduce the number of cpus going up the + * tree to only the first of the previous level and we decrease the frequency + * of load-balance at each level inv. proportional to the number of cpus in + * the groups. + * + * This yields: + * + * log_2 n 1 n + * \Sum { --- * --- * 2^i } = O(n) (5) + * i = 0 2^i 2^i + * `- size of each group + * | | `- number of cpus doing load-balance + * | `- freq + * `- sum over all levels + * + * Coupled with a limit on how many tasks we can migrate every balance pass, + * this makes (5) the runtime complexity of the balancer. + * + * An important property here is that each CPU is still (indirectly) connected + * to every other cpu in at most O(log n) steps: + * + * The adjacency matrix of the resulting graph is given by: + * + * log_2 n + * A_i,j = \Union (i % 2^k == 0) && i / 2^(k+1) == j / 2^(k+1) (6) + * k = 0 + * + * And you'll find that: + * + * A^(log_2 n)_i,j != 0 for all i,j (7) + * + * Showing there's indeed a path between every cpu in at most O(log n) steps. + * The task movement gives a factor of O(m), giving a convergence complexity + * of: + * + * O(nm log n), n := nr_cpus, m := nr_tasks (8) + * + * + * WORK CONSERVING + * + * In order to avoid CPUs going idle while there's still work to do, new idle + * balancing is more aggressive and has the newly idle cpu iterate up the domain + * tree itself instead of relying on other CPUs to bring it work. + * + * This adds some complexity to both (5) and (8) but it reduces the total idle + * time. + * + * [XXX more?] + * + * + * CGROUPS + * + * Cgroups make a horror show out of (2), instead of a simple sum we get: + * + * s_k,i + * W_i,0 = \Sum_j \Prod_k w_k * ----- (9) + * S_k + * + * Where + * + * s_k,i = \Sum_j w_i,j,k and S_k = \Sum_i s_k,i (10) + * + * w_i,j,k is the weight of the j-th runnable task in the k-th cgroup on cpu i. + * + * The big problem is S_k, its a global sum needed to compute a local (W_i) + * property. + * + * [XXX write more on how we solve this.. _after_ merging pjt's patches that + * rewrite all of this once again.] + */ static unsigned long __read_mostly max_load_balance_interval = HZ/10;
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