-*- mode: org; -*-
#+TITLE: Machi cluster-of-clusters "name game" sketch
#+AUTHOR: Scott
#+STARTUP: lognotedone hidestars indent showall inlineimages
#+SEQ_TODO: TODO WORKING WAITING DONE
#+COMMENT: M-x visual-line-mode
#+COMMENT: Also, disable auto-fill-mode

* 1. "Name Games" with random-slicing style consistent hashing

Our goal: to distribute lots of files very evenly across a cluster of
Machi clusters (hereafter called a "cluster of clusters" or "CoC").

* 2. Assumptions

** Basic familiarity with Machi high level design and Machi's "projection"

The [[https://github.com/basho/machi/blob/master/doc/high-level-machi.pdf][Machi high level design document]] contains all of the basic
background assumed by the rest of this document.

** Familiarity with the Machi cluster-of-clusters/CoC concept

This isn't yet well-defined (April 2015).  However, it's clear from
the [[https://github.com/basho/machi/blob/master/doc/high-level-machi.pdf][Machi high level design document]] that Machi alone does not support
any kind of file partitioning/distribution/sharding across multiple
small Machi clusters.  There must be another layer above a Machi cluster to
provide such partitioning services.

The name "cluster of clusters" orignated within Basho to avoid
conflicting use of the word "cluster".  A Machi cluster is usually
synonymous with a single Chain Replication chain and a single set of
machines (e.g. 2-5 machines).  However, in the not-so-far future, we
expect much more complicated patterns of Chain Replication to be used
in real-world deployments.

"Cluster of clusters" is clunky and long, but we haven't found a good
substitute yet.  If you have a good suggestion, please contact us!
~^_^~

Using the [[https://github.com/basho/machi/tree/master/prototype/demo-day-hack][cluster-of-clusters quick-and-dirty prototype]] as an
architecture sketch, let's now assume that we have ~N~ independent Machi
clusters.  We wish to provide partitioned/distributed file storage
across all ~N~ clusters.  We call the entire collection of ~N~ Machi
clusters a "cluster of clusters", or abbreviated "CoC".

** Continue CoC prototype's assumption: a Machi cluster is unaware of CoC

Let's continue with an assumption that an individual Machi cluster
inside of the cluster-of-clusters is completely unaware of the
cluster-of-clusters layer.

We may need to break this assumption sometime in the future?  It isn't
quite clear yet, sorry.

** Analogy: "neighborhood : city :: Machi : cluster-of-clusters"

Analogy: The word "machi" in Japanese means small town or
neighborhood.  As the Tokyo Metropolitan Area is built from many
machis and smaller cities, therefore a big, partitioned file store can
be built out of many small Machi clusters.

** The reader is familiar with the random slicing technique

I'd done something very-very-nearly-identical for the Hibari database
6 years ago.  But the Hibari technique was based on stuff I did at
Sendmail, Inc, so it felt old news to me.  {shrug}

The Hibari documentation has a brief photo illustration of how random
slicing works, see [[http://hibari.github.io/hibari-doc/hibari-sysadmin-guide.en.html#chain-migration][Hibari Sysadmin Guide, chain migration]]

For a comprehensive description, please see these two papers:

#+BEGIN_QUOTE
Reliable and Randomized Data Distribution Strategies for Large Scale Storage Systems
Alberto Miranda et al.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.226.5609
                                                  (short version, HIPC'11)

Random Slicing: Efficient and Scalable Data Placement for Large-Scale
    Storage Systems 
Alberto Miranda et al.
DOI: http://dx.doi.org/10.1145/2632230 (long version, ACM Transactions
                              on Storage, Vol. 10, No. 3, Article 9, 2014)
#+END_QUOTE

** We use random slicing to map CoC file names -> Machi cluster ID/name

We will use a single random slicing map.  This map (called ~Map~ in
the descriptions below), together with the random slicing hash
function (called ~rs_hash()~ below), will be used to map:

#+BEGIN_QUOTE
    CoC client-visible file name -> Machi cluster ID/name/thingie
#+END_QUOTE

** Machi cluster ID/name management: TBD, but, really, should be simple

The mapping from:

#+BEGIN_QUOTE
    Machi CoC member ID/name/thingie -> ???
#+END_QUOTE

... remains To Be Determined.  But, really, this is going to be pretty
simple.  The ID/name/thingie will probably be a human-friendly,
printable ASCII string, and the "???" will probably be a single Machi
cluster projection data structure.

The Machi projection is enough information to contact any member of
that cluster and, if necessary, request the most up-to-date projection
information required to use that cluster.

It's likely that the projection given by this map will be out-of-date,
so the client must be ready to use the standard Machi procedure to
request the cluster's current projection, in any case.

* 3. A simple illustration

I'm borrowing an illustration from the HibariDB documentation here,
but it fits my purposes quite well.  (And I originally created that
image, and the use license is OK.)

#+CAPTION: Illustration of 'Map', using four Machi clusters

[[./migration-4.png]]

Assume that we have a random slicing map called ~Map~.  This particular
~Map~ maps the unit interval onto 4 Machi clusters:

| Hash range  | Cluster ID |
|-------------+------------|
| 0.00 - 0.25 | Cluster1   |
| 0.25 - 0.33 | Cluster4   |
| 0.33 - 0.58 | Cluster2   |
| 0.58 - 0.66 | Cluster4   |
| 0.66 - 0.91 | Cluster3   |
| 0.91 - 1.00 | Cluster4   |

Then, if we had CoC file name "~foo~", the hash ~SHA("foo")~ maps to about
0.05 on the unit interval.  So, according to ~Map~, the value of
~rs_hash("foo",Map) = Cluster1~.  Similarly, ~SHA("hello")~ is about
0.67 on the unit interval, so ~rs_hash("hello",Map) = Cluster3~.

* 4. An additional assumption: clients will want some control over file placement

We will continue to use the 4-cluster diagram from the previous
section.

When a client wishes to append data to a Machi file, the Machi server
chooses the file name & byte offset for storing that data.  This
feature is why Machi's eventual consistency operating mode is so
nifty: it allows us to merge together files safely at any time because
any two client append operations will always write to different files
& different offsets.

** Our new assumption: client control over initial file placement

The CoC management scheme may decide that files need to migrate to
other clusters.  The reason could be for storage load or I/O load
balancing reasons.  It could be because a cluster is being
decomissioned by its owners.  There are many legitimate reasons why a
file that is initially created on cluster ID X has been moved to
cluster ID Y.

However, there are also legitimate reasons for why the client would want
control over the choice of Machi cluster when the data is first
written.  The single biggest reason is load balancing.  Assuming that
the client (or the CoC management layer acting on behalf of the CoC
client) knows the current utilization across the participating Machi
clusters, then it may be very helpful to send new append() requests to
under-utilized clusters.

** Cool!  Except for a couple of problems...

If the client wants to store some data
on Cluster2 and therefore sends an ~append("foo",CoolData)~ request to
the head of Cluster2 (which the client magically knows how to
contact), then the result will look something like
~{ok,"foo.s923.z47",ByteOffset}~.

Therefore, the file name "~foo.s923.z47~" must be used by any Machi
CoC client in order to retrieve the CoolData bytes.

*** Problem #1: "foo.s923.z47" doesn't always map via random slicing to Cluster2

... if we ignore the problem of "CoC files may be redistributed in the
future", then we still have a problem.

In fact, the value of ~ps_hash("foo.s923.z47",Map)~ is Cluster1.

*** Problem #2: We want CoC files to move around automatically

If the CoC client stores two pieces of information, the file name
"~foo.s923.z47~" and the Cluster ID Cluster2, then what happens when the
cluster-of-clusters system decides to rebalance files across all
machines?  The CoC manager may decide to move our file to Cluster66.

How will a future CoC client wishes to retrieve CoolData when Cluster2
no longer stores the required file?

**** When migrating the file, we could put a "pointer" on Cluster2 that points to the new location, Cluster66.

This scheme is a bit brittle, even if all of the pointers are always
created 100% correctly.  Also, if Cluster2 is ever unavailable, then
we cannot fetch our CoolData, even though the file moved away from
Cluster2 several years ago.

The scheme would also introduce extra round-trips to the servers
whenever we try to read a file where we do not know the most
up-to-date cluster ID for.

**** We could store a pointer to file "foo.s923.z47"'s location in an LDAP database!

Or we could store it in Riak.  Or in another, external database.  We'd
rather not create such an external dependency, however.  Furthermore,
we would also have the same problem of updating this external database
each time that a file is moved/rebalanced across the CoC.

* 5. Proposal: Break the opacity of Machi file names, slightly

Assuming that Machi keeps the scheme of creating file names (in
response to ~append()~ and ~sequencer_new_range()~ calls) based on a
predictable client-supplied prefix and an opaque suffix, e.g.,

~append("foo",CoolData) -> {ok,"foo.s923.z47",ByteOffset}.~

... then we propose that all CoC and Machi parties be aware of this
naming scheme, i.e. that Machi assigns file names based on:

~ClientSuppliedPrefix ++ "." ++ SomeOpaqueFileNameSuffix~

The Machi system doesn't care about the file name -- a Machi server
will treat the entire file name as an opaque thing.  But this document
is called the "Name Game" for a reason!

What if the CoC client could peek inside of the opaque file name
suffix in order to remove (or add) the CoC location information that
we need?

** The details: legend

- ~T~   = the target CoC member/Cluster ID chosen at the time of ~append()~
- ~p~   = file prefix, chosen by the CoC client (This is exactly the Machi client-chosen file prefix).
- ~s.z~ = the Machi file server opaque file name suffix (Which we
  happen to know is a combination of sequencer ID plus file serial
  number.  This implementation may change, for example, to use a
  standard GUID string (rendered into ASCII hexadecimal digits) instead.)
- ~K~   = the CoC placement key

We use a variation of ~rs_hash()~, called ~rs_hash_with_float()~.  The
former uses a string as its 1st argument; the latter uses a floating
point number as its 1st argument.  Both return a cluster ID name
thingie.

#+BEGIN_SRC erlang
%% type specs, Erlang style
-spec rs_hash(string(), rs_hash:map()) -> rs_hash:cluster_id().
-spec rs_hash_with_float(float(), rs_hash:map()) -> rs_hash:cluster_id().
#+END_SRC

NOTE: Use of floating point terms is not required.  For example,
integer arithmetic could be used, if using a sufficiently large
interval to create an even & smooth distribution of hashes across the
expected maximum number of clusters.

For example, if the maximum CoC cluster size would be 4,000 individual
Machi clusters, then a minimum of 12 bits of integer space is required
to assign one integer per Machi cluster.  However, for load balancing
purposes, a finer grain of (for example) 100 integers per Machi
cluster would permit file migration to move increments of
approximately 1% of single Machi cluster's storage capacity.  A
minimum of 19 bits of hash space would be necessary to accomodate
these constraints.

** The details: CoC file write

1. CoC client chooses ~p~ and ~T~ (i.e., the file prefix & target cluster)
2. CoC client knows the CoC ~Map~
3. CoC client calculates a value ~K~ such that ~rs_hash_with_float(K,Map) = T~, using the method described below.
4. CoC client requests @ cluster ~T~: ~append_chunk(p,...) -> {ok,p.K.s.z,ByteOffset}~
5. CoC stores/uses the file name ~p.K.s.z~.

** The details: CoC file read

1. CoC client knows the file name ~p.K.s.z~ and parses it to find
   ~K~'s value.
2. CoC client knows the CoC ~Map~
3. Coc calculates ~rs_hash_with_float(K,Map) = T~
4. CoC client requests @ cluster ~T~: ~read_chunk(p.K.s.z,...) ->~ ... success!

** The details: calculating 'K', the CoC placement key

1. We know ~Map~, the current CoC mapping.
2. We look inside of ~Map~, and we find all of the unit interval ranges
   that map to our desired target cluster ~T~.  Let's call this list
   ~MapList = [Range1=(start,end],Range2=(start,end],...]~.
3. In our example, ~T=Cluster2~.  The example ~Map~ contains a single
   unit interval range for ~Cluster2~, ~[(0.33,0.58]]~.
4. Choose a uniformally random number ~r~ on the unit interval.
5. Calculate placement key ~K~ by mapping ~r~ onto the concatenation
   of the CoC hash space range intervals in ~MapList~.  For example,
   if ~r=0.5~, then ~K = 0.33 + 0.5*(0.58-0.33) = 0.455~, which is
   exactly in the middle of the ~(0.33,0.58]~ interval.
6. If necessary, encode ~K~ in a file name-friendly manner, e.g., convert it to hexadecimal ASCII digits to create file name ~p.K.s.z~.

** The details: calculating 'K', an alternative method

If the Law of Large Numbers and our random number generator do not create the kind of smooth & even distribution of files across the CoC as we wish, an alternative method of calculating ~K~ follows.

If each server in each Machi cluster keeps track of the CoC ~Map~ and also of all values of ~K~ for all files that it stores, then we can simply ask a cluster member to recommend a value of ~K~ that is least represented by existing files.

* 6. File migration (aka rebalancing/reparitioning/redistribution)

** What is "file migration"?

As discussed in section 5, the client can have good reason for wanting
to have some control of the initial location of the file within the
cluster.  However, the cluster manager has an ongoing interest in
balancing resources throughout the lifetime of the file.  Disks will
get full, hardware will change, read workload will fluctuate,
etc etc.

This document uses the word "migration" to describe moving data from
one CoC cluster to another.  In other systems, this process is
described with words such as rebalancing, repartitioning, and
resharding.  For Riak Core applications, the mechanisms are "handoff"
and "ring resizing". See the [[http://hadoop.apache.org/docs/current/hadoop-project-dist/hadoop-hdfs/HdfsUserGuide.html#Balancer][Hadoop file balancer]] for another example.

A simple variation of the Random Slicing hash algorithm can easily
accomodate Machi's need to migrate files without interfering with
availability.  Machi's migration task is much simpler due to the
immutable nature of Machi file data.

** Change to Random Slicing

The map used by the Random Slicing hash algorithm needs a few simple
changes to make file migration straightforward.

- Add a "generation number", a strictly increasing number (similar to
  a Machi cluster's "epoch number") that reflects the history of
  changes made to the Random Slicing map
- Use a list of Random Slicing maps instead of a single map, one map
  per possibility that files may not have been migrated yet out of
  that map.

As an example:

#+CAPTION: Illustration of 'Map', using four Machi clusters

[[./migration-3to4.png]]

And the new Random Slicing map might look like this:

| Generation number | 7          |
|-------------------+------------|
| SubMap            | 1          |
|-------------------+------------|
| Hash range        | Cluster ID |
|-------------------+------------|
| 0.00 - 0.33       | Cluster1   |
| 0.33 - 0.66       | Cluster2   |
| 0.66 - 1.00       | Cluster3   |
|-------------------+------------|
| SubMap            | 2          |
|-------------------+------------|
| Hash range        | Cluster ID |
|-------------------+------------|
| 0.00 - 0.25       | Cluster1   |
| 0.25 - 0.33       | Cluster4   |
| 0.33 - 0.58       | Cluster2   |
| 0.58 - 0.66       | Cluster4   |
| 0.66 - 0.91       | Cluster3   |
| 0.91 - 1.00       | Cluster4   |

When a new Random Slicing map contains a single submap, then its use
is identical to the original Random Slicing algorithm.  If the map
contains multiple submaps, then the access rules change a bit:

- Write operations always go to the latest/largest submap.
- Read operations attempt to read from all unique submaps.
  - Skip searching submaps that refer to the same cluster ID.
    - In this example, unit interval value 0.10 is mapped to Cluster1
      by both submaps.
  - Read from latest/largest submap to oldest/smallest submap.
  - If not found in any submap, search a second time (to handle races
    with file copying between submaps).
  - If the requested data is found, optionally copy it directly to the
    latest submap (as a variation of read repair which really simply
    accelerates the migration process and can reduce the number of
    operations required to query servers in multiple submaps).

The cluster-of-clusters manager is responsible for:

- Managing the various generations of the CoC Random Slicing maps,
  including distributing them to CoC clients.
- Managing the processes that are responsible for copying "cold" data,
  i.e., files data that is not regularly accessed, to its new submap
  location.
- When migration of a file to its new cluster is confirmed successful,
  delete it from the old cluster.

In example map #7, the CoC manager will copy files with unit interval
assignments in ~(0.25,0.33]~, ~(0.58,0.66]~, and ~(0.91,1.00]~ from their
old locations in cluster IDs Cluster1/2/3 to their new cluster,
Cluster4.  When the CoC manager is satisfied that all such files have
been copied to Cluster4, then the CoC manager can create and
distribute a new map, such as:

| Generation number | 8          |
|-------------------+------------|
| SubMap            | 1          |
|-------------------+------------|
| Hash range        | Cluster ID |
|-------------------+------------|
| 0.00 - 0.25       | Cluster1   |
| 0.25 - 0.33       | Cluster4   |
| 0.33 - 0.58       | Cluster2   |
| 0.58 - 0.66       | Cluster4   |
| 0.66 - 0.91       | Cluster3   |
| 0.91 - 1.00       | Cluster4   |

One limitation of HibariDB that I haven't fixed is not being able to
perform more than one migration at a time.  The trade-off is that such
migration is difficult enough across two submaps; three or more
submaps becomes even more complicated.

Fortunately for Machi, its file data is immutable and therefore can
easily manage many migrations in parallel, i.e., its submap list may
be several maps long, each one for an in-progress file migration.

* Acknowledgements

The source for the "migration-4.png" and "migration-3to4.png" images
come from the [[http://hibari.github.io/hibari-doc/images/migration-3to4.png][HibariDB documentation]].