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Combining Similar Time Series

This week was Monitorama 2019, in Portland. I was there. Many in the monitoring community were there. A great time was had by many. (note: I've never really considered myself part of the monitoring community, but perhaps should make more of an effort?)

Evan Chan gave a talk entitled: "Rich Histograms at Scale: A New Hope." (slides) In it, he made everyone aware of how much error exists if you do histograms the way that's easy in systems like Prometheus--"a couple of linear buckets"--and showed that to get even close to a 10% error rate for a span of values from 1000 - 6e10, you need 188 exponential buckets.

This presents a problem.

While it's not that big of a problem to query 10 time series to reconstruct latency estimates with histograms, it is a problem to make 188 queries to retrieve the buckets to reconstruct latency estimates with histograms.

Not to worry, though! Evan suggested that a richer histogram model, which stored all of the buckets in a single, rich time series, would provide better scalability here without sacrificing accuracy. And, using delta encoding, 188 buckets would be quite cheap to store (on the order of 1.8 bytes per bucket).

At the end of the talk I messaged one of my colleagues who was in the trenches with me when we rebuilt the system that hosts Heroku Metrics *(post is years out of date at this point). You see, co-locating similar time series data was exactly the design we used with InfluxDB (v0.0.76 or something) before 2015, and exactly the design we knew we'd keep in the new system. Because we knew our graphs would be composed of, say, 4 memory related metrics, we put them together in the same way you could put 188 histogram buckets together.

Non-Relational databases always talk about how you've got to design your schemas for how you want to query it. Relational databases say similar things about indexing strategies. There doesn't seem to be an equivalent mantra in the time-series world--perhaps because we're too busy worrying that if we can't write data fast enough, reads don't matter anyway?

Not sure! But, co-locating metrics that will be read together, or written together is very worth it, in much the same way that denormalizing relational data can be very worth it, or designing NoSQL table spaces with reads in mind is simply a requirement.

In Heroku's case, our metric co-location strategy uses the following general schema (stored compressed in Cassandra):

message Observation {
  string source = 1;              // e.g. collection-type://identifier/labels
  int64  timestamp = 2;           // unix timestamp in seconds
  Measurements measurements = 3;
  MetricType type = 4; // histogram, gauge, counter -- aggregation rules.

// HDRHistogram fields, aggregatable using the Merge function after reifying
// back into HDRHistogram objects
message HistogramSnapshot {
  int64 lowest_value = 1;
  int64 highest_value = 2;
  int32 significant_figures = 3;
  repeated int64 counts = 4;

message Measurements {
  repeated string names = 1;  // e.g. ["memory_cache", "memory_swap", ...]
  repeated double values = 2; // e.g. [0.15, 0.1, ...]
  HistogramSnapshot histogram_snapshot = 3;

This currently supports value cardinalities from 2 to 500, depending on the use case (the high cardinality stuff is typical for data store metrics), with an average of about 7.

A natural extension of this would be to turn Measurements.values into a matrix and do delta encoding. That would provide options for higher resolution data, or wider data across a single tag value (say, dyno in Heroku's case).

So, while Evan put forward that a richer model for histograms is needed for better accuracy, I'm here to suggest that, while maybe not trivial, we shouldn't be scared that his ideas can't or won't scale. They definitely can.

- 2019/06/07