/**
* https://github.com/akka/akka/blob/master/akka-remote/src/main/scala/akka/remote/PhiAccrualFailureDetector.scala
* Calculation of phi, derived from the Cumulative distribution function for
* N(mean, stdDeviation) normal distribution, given by
* 1.0 / (1.0 + math.exp(-y * (1.5976 + 0.070566 * y * y)))
* where y = (x - mean) / standard_deviation
* This is an approximation defined in β Mathematics Handbook (Logistic approximation).
* Error is 0.00014 at +- 3.16
* The calculated value is equivalent to -log10(1 - CDF(y))
*/
public static double Normal(long nowTimestamp, long lastTimestamp, IWithStatistics statistics)
{
var duration = nowTimestamp - lastTimestamp;
var y = (duration - statistics.Avg) / statistics.StdDeviation;
var exp = Math.Exp(-y * (1.5976 + 0.070566 * y * y));
if (duration > statistics.Avg)
{
return(-Math.Log10(exp / (1 + exp)));
}
else
{
return(-Math.Log10(1 - 1 / (1 + exp)));
}
}
/**
* https://issues.apache.org/jira/browse/CASSANDRA-2597
* Regular message transmissions experiencing typical random jitter will follow a normal distribution,
* but since gossip messages from endpoint A to endpoint B are sent at random intervals,
* they likely make up a Poisson process, making the exponential distribution appropriate.
*
* P_later(t) = 1 - F(t)
* P_later(t) = 1 - (1 - e^(-Lt))
*
* The maximum likelihood estimation for the rate parameter L is given by 1/mean
*
* P_later(t) = 1 - (1 - e^(-t/mean))
* P_later(t) = e^(-t/mean)
* phi(t) = -log10(P_later(t))
* phi(t) = -log10(e^(-t/mean))
* phi(t) = -log(e^(-t/mean)) / log(10)
* phi(t) = (t/mean) / log(10)
* phi(t) = 0.4342945 * t/mean
*/
public static double Exponential(long nowTimestamp, long lastTimestamp, IWithStatistics statistics)
{
var duration = nowTimestamp - lastTimestamp;
return(duration / statistics.Avg);
}
