Add write-up about load-balancing

doc/Load_Balancing.md

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+I have conducted a quick study of different methods to load-balance data over different Garage nodes using consistent hashing.
+
+### Requirements
+
+- good balancing: two nodes that have the same announced capacity should receive close to the same number of items
+- multi-datacenter: the replicas of a partition should be distributed over as many datacenters as possible
+- minimal disruption: when adding or removing a node, as few partitions as possible should have to move around
+
+### Methods
+
+#### Naive multi-DC ring walking strategy
+
+This strategy can be used with any ring-linke algorithm to make it aware of the *multi-datacenter* requirement:
+
+- the ring is a list of positions, each associated with a single node in the cluster
+- look up position of item on ring
+- select the node for that position
+- go clockwise, skipping nodes that:
+  - we halve already selected
+  - are in a datacenter of a node we have selected, except if we already have nodes from all available datacenters
+
+In this way the selected nodes will always be distributed over
+`min(n_datacenters, n_replicas)` different datacenters, which is the best we
+can do.
+
+This method was implemented in the first iteration of Garage, with the basic
+ring construction that consists in associating `n_token` random positions to
+each node.
+
+#### Better rings
+
+The ring construction that selects `n_token` random positions for each nodes gives a ring of positions that
+is not well-balanced: the space between the tokens varies a lot, and some partitions are thus bigger than others.
+This problem was demonstrated in the original Dynamo DB paper.
+
+To solve this, we want to apply a second method for partitionning our dataset:
+
+1. fix an initially large number of partitions (say 1024) with evenly-spaced delimiters, 
+
+2. attribute each partition randomly to a node, with a probability
+   proportionnal to its capacity (which `n_tokens` represented in the first
+   method)
+
+I have studied two ways to do the attribution, in a way that is deterministic:
+
+- Custom: take `argmin_node(hash(node, partition_number))`
+- MagLev: see [here](https://blog.acolyer.org/2016/03/21/maglev-a-fast-and-reliable-software-network-load-balancer/)
+
+MagLev provided significantly better balancing, as it guarantees that the exact
+same number of partitions is attributed to all nodes that have the same
+capacity (and that this number is proportionnal to the node's capacity, except
+for large values), however in both cases:
+
+- the distribution is still bad, because we use the naive multi-DC ring walking
+  that behaves strangely due to interactions between consecutive positions on
+  the ring
+
+- the disruption in case of adding/removing a node is not as low as it can be,
+  as we show with the following method.
+
+A quick description of MagLev:
+
+> The basic idea of Maglev hashing is to assign a preference list of all the
+> lookup table positions to each backend. Then all the backends take turns
+> filling their most-preferred table positions that are still empty, until the
+> lookup table is completely filled in. Hence, Maglev hashing gives an almost
+> equal share of the lookup table to each of the backends. Heterogeneous
+> backend weights can be achieved by altering the relative frequency of the
+> backends’ turns…
+
+Here are some stats (run `scripts/simulate_ring.py` to reproduce):
+
+```
+##### Custom-ring (min-hash) #####
+
+#partitions per node (capacity in parenthesis):
+- datura (8) :  227
+- digitale (8) :  351
+- drosera (8) :  259
+- geant (16) :  476
+- gipsie (16) :  410
+- io (16) :  495
+- isou (8) :  231
+- mini (4) :  149
+- mixi (4) :  188
+- modi (4) :  127
+- moxi (4) :  159
+
+Variance of load distribution for load normalized to intra-class mean
+(a class being the set of nodes with the same announced capacity): 2.18%     <-- REALLY BAD
+
+Disruption when removing nodes (partitions moved on 0/1/2/3 nodes):
+removing atuin digitale : 63.09% 30.18% 6.64% 0.10%
+removing atuin drosera : 72.36% 23.44% 4.10% 0.10%
+removing atuin datura : 73.24% 21.48% 5.18% 0.10%
+removing jupiter io : 48.34% 38.48% 12.30% 0.88%
+removing jupiter isou : 74.12% 19.73% 6.05% 0.10%
+removing grog mini : 84.47% 12.40% 2.93% 0.20%
+removing grog mixi : 80.76% 16.60% 2.64% 0.00%
+removing grog moxi : 83.59% 14.06% 2.34% 0.00%
+removing grog modi : 87.01% 11.43% 1.46% 0.10%
+removing grisou geant : 48.24% 37.40% 13.67% 0.68%
+removing grisou gipsie : 53.03% 33.59% 13.09% 0.29%
+on average:  69.84% 23.53% 6.40% 0.23%                  <-- COULD BE BETTER
+
+--------
+
+##### MagLev #####
+
+#partitions per node:
+- datura (8) :  273
+- digitale (8) :  256
+- drosera (8) :  267
+- geant (16) :  452
+- gipsie (16) :  427
+- io (16) :  483
+- isou (8) :  272
+- mini (4) :  184
+- mixi (4) :  160
+- modi (4) :  144
+- moxi (4) :  154
+
+Variance of load distribution: 0.37%                <-- Already much better, but not optimal
+
+Disruption when removing nodes (partitions moved on 0/1/2/3 nodes):
+removing atuin digitale : 62.60% 29.20% 7.91% 0.29%
+removing atuin drosera : 65.92% 26.56% 7.23% 0.29%
+removing atuin datura : 63.96% 27.83% 7.71% 0.49%
+removing jupiter io : 44.63% 40.33% 14.06% 0.98%
+removing jupiter isou : 63.38% 27.25% 8.98% 0.39%
+removing grog mini : 72.46% 21.00% 6.35% 0.20%
+removing grog mixi : 72.95% 22.46% 4.39% 0.20%
+removing grog moxi : 74.22% 20.61% 4.98% 0.20%
+removing grog modi : 75.98% 18.36% 5.27% 0.39%
+removing grisou geant : 46.97% 36.62% 15.04% 1.37%
+removing grisou gipsie : 49.22% 36.52% 12.79% 1.46%
+on average:  62.94% 27.89% 8.61% 0.57%                  <-- Worse than custom method
+```
+
+#### The magical solution: multi-DC aware MagLev
+
+(insert algorithm description here, in the meantime refer to `method4` in the simulation script)
+
+```
+##### Multi-DC aware MagLev #####
+
+#partitions per node:
+- datura (8) :  268                 <-- NODES WITH THE SAME CAPACITY
+- digitale (8) :  267                   HAVE THE SAME NUM OF PARTITIONS
+- drosera (8) :  267                    (+- 1)
+- geant (16) :  470
+- gipsie (16) :  472
+- io (16) :  516
+- isou (8) :  268
+- mini (4) :  136
+- mixi (4) :  136
+- modi (4) :  136
+- moxi (4) :  136
+
+Variance of load distribution: 0.06%                <-- CAN'T DO BETTER THAN THIS
+
+Disruption when removing nodes (partitions moved on 0/1/2/3 nodes):
+removing atuin digitale : 65.72% 33.01% 1.27% 0.00%
+removing atuin drosera : 64.65% 33.89% 1.37% 0.10%
+removing atuin datura : 66.11% 32.62% 1.27% 0.00%
+removing jupiter io : 42.97% 53.42% 3.61% 0.00%
+removing jupiter isou : 66.11% 32.32% 1.56% 0.00%
+removing grog mini : 80.47% 18.85% 0.68% 0.00%
+removing grog mixi : 80.27% 18.85% 0.88% 0.00%
+removing grog moxi : 80.18% 19.04% 0.78% 0.00%
+removing grog modi : 79.69% 19.92% 0.39% 0.00%
+removing grisou geant : 44.63% 52.15% 3.22% 0.00%
+removing grisou gipsie : 43.55% 52.54% 3.91% 0.00%
+on average:  64.94% 33.33% 1.72% 0.01%                  <-- VERY GOOD
+```