Add details about supporting qps based sampler. (#158)

* Add details about supporting qps based sampler.

* Rename the qps to RateLimiting

trace/Sampling.md

@@ -12,7 +12,11 @@ The Sampling bit is always set only at the start of a Span, using a `Sampler`
 * `AlwaysSample` - sampler that makes a "yes" decision every time.
 * `NeverSample` - sampler that makes a "no" decision every time.
 * `Probability` - sampler that tries to uniformly sample traces with a given probability. When 
-applied to a child `Span` of a **sampled** parent `Span`, the child `Span` keeps the sampling decision.
+applied to a child `Span` of a **sampled** parent `Span`, the child `Span` keeps the sampling
+decision.
+* `RateLimiting` - sampler that tries to sample with a rate per time window (0.1 traces/second). 
+When applied to a child `Span` of a **sampled** parent `Span`, the child `Span` keeps the sampling 
+decision. For implementation details see [this](#ratelimiting-sampler-implementation-details)
 
 ### How can users control the Sampler that is used for sampling?
 There are 2 ways to control the `Sampler` used when the library samples:
@@ -33,3 +37,26 @@ The OpenCensus library samples based on the following rules:
 3. If the span is a child of a local `Span` the sampling decision will be:
    * If a "span-scoped" `Sampler` is provided, use it to determine the sampling decision.
    * Else keep the sampling decision from the parent.
+
+### RateLimiting sampler implementation details
+The problem we are trying to solve is:
+1. Getting QPS based sampling.
+2. Providing real sampling probabilities.
+3. Minimal overhead.
+
+Idea is to store the time that we last made a QPS based sampling decision in an atomic. Then we can
+use the elapsed time Z since the coin flip to weight our current coin flip. We choose our
+probability function P(Z) such that we get the desired sample QPS. We want P(Z) to be very
+cheap to compute.
+
+Let X be the desired QPS. Let Z be the elapsed time since the last sampling decision in seconds.
+```
+P(Z) = min(Z * X, 1)
+```
+
+To see that this is approximately correct, consider the case where we have perfectly distributed
+time intervals. Specifically, let X = 1 and Z = 1/N. Then we would have N coin flips per second,
+each with probability 1/N, for an expectation of 1 sample per second.
+
+This will under-sample: consider the case where X = 1 and Z alternates between 0.5 and 1.5. It is
+possible to get about 1 QPS by always sampling, but this algorithm only gets 0.75 QPS.