1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
//! Main interface module for Vivaldi network coordinates.
//!
//! For usage explanation and examples, please see the main [`crate`] documentation.
use core::time::Duration;
use serde::{Deserialize, Serialize};
use crate::height_vector::HeightVector;
//
// **** Features ****
//
#[cfg(feature = "f32")]
type FloatType = f32;
#[cfg(not(feature = "f32"))]
type FloatType = f64;
//
// **** Constants ****
//
// Vivaldi tuning parameters
const C_ERROR: FloatType = 0.25;
const C_DELTA: FloatType = 0.25;
// initial error value
const DEFAULT_ERROR: FloatType = 200.0;
// error should always be greater than zero
const MIN_ERROR: FloatType = FloatType::EPSILON;
//
// **** Structs ****
//
/// A `NetworkCoordinate<N>` is the main interface to a Vivaldi network coordinate.
///
/// # Generic Parameters
///
/// - `N`: Const generic for number of dimensions. For example, `NetworkCoordinate<3>` is a
/// 3-Dimentionsal Euclidean coordinate plus a height. Should be a positive number greater than
/// zero.
///
/// **Note:** Dimensions other than 2D or 3D are usually not useful. If you want to use one of
/// those dimensions, you can use type aliases ([`NetworkCoordinate2D`] or [`NetworkCoordinate3D`])
/// which are a little more ergonomic than using the generic here.
///
/// # Examples
///
/// For an explanation and examples of usage, please see the main [`crate`] documentation.
#[derive(Clone, Debug, Serialize, Deserialize)]
pub struct NetworkCoordinate<const N: usize> {
#[serde(flatten)]
heightvec: HeightVector<N>,
error: FloatType,
}
// type aliases for convenience
/// A 2D [`NetworkCoordinate`]. Includes a 2D Euclidean position and a height.
///
/// This type alias is just for convenience. It's functionally equivalent to
/// `NetworkCoordinate<2>`. For more information, see [`NetworkCoordinate`].
#[allow(clippy::module_name_repetitions)]
pub type NetworkCoordinate2D = NetworkCoordinate<2>;
/// A 3D [`NetworkCoordinate`]. Includes a 3D Euclidean position and a height.
///
/// This type alias is just for convenience. It's functionally equivalent to
/// `NetworkCoordinate<3>`. For more information, see [`NetworkCoordinate`].
#[allow(clippy::module_name_repetitions)]
pub type NetworkCoordinate3D = NetworkCoordinate<3>;
//
// **** Implementations ****
//
impl<const N: usize> NetworkCoordinate<N> {
/// Creates a new random [`NetworkCoordinate`]
///
/// # Example
///
/// ```
/// use vivaldi_nc::NetworkCoordinate;
///
/// // create a new 3-dimensional random NC
/// let a: NetworkCoordinate<3> = NetworkCoordinate::new();
///
/// // print the NC
/// println!("Our new NC is: {:#?}", a);
/// ```
#[must_use]
pub fn new() -> Self {
Self::default()
}
/// Given another Vivaldi [`NetworkCoordinate`], estimate the round trip time (ie ping) between them.
///
/// This is done by computing the height vector distance between between the two coordinates.
/// Vivaldi uses this distance as a representation of estimated round trip time.
///
/// # Parameters
///
/// - `rhs`: the other coordinate
///
/// # Returns
///
/// - the estimated round trip time as a `Duration`
///
/// # Example
///
/// ```
/// use vivaldi_nc::NetworkCoordinate;
///
/// // create some 2-dimensional NCs for the sake of this example. These will just be random
/// // NCs. In a real usecase these would have meaningful values.
/// let a: NetworkCoordinate<2> = NetworkCoordinate::new();
/// let b: NetworkCoordinate<2> = NetworkCoordinate::new();
///
/// // get the estimated RTT, convert to milliseconds, and print
/// println!("Estimated RTT: {}", a.estimated_rtt(&b).as_millis());
/// ```
///
#[must_use]
pub fn estimated_rtt(&self, rhs: &Self) -> Duration {
// estimated rss is euclidean distance between the two plus the sum of the heights
cfg_if::cfg_if! {
if #[cfg(feature = "f32")] {
Duration::from_secs_f32((self.heightvec - rhs.heightvec).len() / 1000.0)
} else {
Duration::from_secs_f64((self.heightvec - rhs.heightvec).len() / 1000.0)
}
}
}
/// Given another Vivaldi [`NetworkCoordinate`], adjust our coordinateto better represent the actual round
/// trip time (aka distance) between us.
///
/// # Parameters
///
/// - `rhs`: the other coordinate
/// - `rtt`: the measured round trip time between `self` and `rhs`
///
/// # Returns
///
/// - a reference to `self`
///
/// # Example
///
/// ```
/// use core::time::Duration;
/// use vivaldi_nc::NetworkCoordinate;
///
/// // We always have our own NC:
/// let mut local: NetworkCoordinate<2> = NetworkCoordinate::new();
///
/// // Assume we received a NC from a remote node:
/// let remote: NetworkCoordinate<2> = NetworkCoordinate::new();
///
/// // And we measured the RTT between us and the remote node:
/// let rtt = Duration::from_millis(100);
///
/// // Now we can update our NC to adjust our position relative to the remote node:
/// local.update(&remote, rtt);
/// ```
///
/// # Algorithm
///
/// This is an implementation of Vivaldi NCs per the original paper. It implements the following
/// alogirthm (quoting from paper):
///
/// ```text
/// // Incorporate new information: node j has been
/// // measured to be rtt ms away, has coordinates xj,
/// // and an error estimate of ej .
/// //
/// // Our own coordinates and error estimate are xi and ei.
/// //
/// // The constants ce and cc are tuning parameters.
///
/// vivaldi(rtt, xj, ej)
/// // Sample weight balances local and remote error. (1)
/// w = ei /(ei + ej)
/// // Compute relative error of this sample. (2)
/// es = ∣∣∣‖xi − xj‖ − rtt∣∣∣/rtt
/// // Update weighted moving average of local error. (3)
/// ei = es × ce × w + ei × (1 − ce × w)
/// // Update local coordinates. (4)
/// δ = cc × w
/// xi = xi + δ × (rtt − ‖xi − xj ‖) × u(xi − xj)
/// ```
///
pub fn update(&mut self, rhs: &Self, rtt: Duration) -> &Self {
// convert Durations into FloatType as fractional milliseconds for convenience
cfg_if::cfg_if! {
if #[cfg(feature = "f32")] {
let rtt_ms = rtt.as_secs_f32() * 1000.0;
let rtt_estimated_ms = self.estimated_rtt(rhs).as_secs_f32() * 1000.0;
} else {
let rtt_ms = rtt.as_secs_f64() * 1000.0;
let rtt_estimated_ms = self.estimated_rtt(rhs).as_secs_f64() * 1000.0;
}
}
// rtt needs to be positive
if rtt_ms < 0.0 {
// Note: `rtt` is guaranteed to be positive because `Duration` enforces it.
// If this panics, something changed where `Duration` now allows for negative
// values.
unreachable!();
}
// Sample weight balances local and remote error. (1)
// w = ei /(ei + ej )
let w = self.error / (self.error + rhs.error);
// Compute relative error of this sample. (2)
// es = ∣∣∣‖xi − xj‖ − rtt∣∣∣/rtt
let error = rtt_ms - rtt_estimated_ms;
let es = error.abs() / rtt_ms;
// Update weighted moving average of local error. (3)
// ei = es × ce × w + ei × (1 − ce × w)
// self.error = (es * C_ERROR * w + self.error * (1.0 - C_ERROR * w)).max(MIN_ERROR);
// NOTE: using `mul_add()` which is a little safer (avoid overflows)
self.error = (es * C_ERROR)
.mul_add(w, self.error * C_ERROR.mul_add(-w, 1.0))
.max(MIN_ERROR);
// Update local coordinates. (4)
// δ = cc × w
let delta = C_DELTA * w;
// xi = xi + δ × (rtt − ‖xi − xj ‖) × u(xi − xj)
self.heightvec =
self.heightvec + (self.heightvec - rhs.heightvec).normalized() * delta * error;
// if we ended up with an invalid coordinate, return a new random coordinate with default
// error
if self.heightvec.is_invalid() {
*self = Self::new();
// We should never get here because the call to `normalized()` above should catch any
// invalid `heightvec`
unreachable!();
}
// return reference to updated self
self
}
/// getter for error value - useful for consumers to understand the estimated accuracty of this
/// `NetworkCoordinate`
#[must_use]
pub const fn error(&self) -> FloatType {
self.error
}
}
//
// **** Trait Implementations ****
//
impl<const N: usize> Default for NetworkCoordinate<N> {
/// A default `NetworkCoordinate` has a random position and `DEFAULT_ERROR`
fn default() -> Self {
Self {
heightvec: HeightVector::<N>::random(),
error: DEFAULT_ERROR,
}
}
}
//
// **** Tests ****
//
#[cfg(test)]
mod tests {
use assert_approx_eq::assert_approx_eq;
use super::*;
#[test]
fn test_convergence() {
let mut a = NetworkCoordinate::<3>::new();
let mut b = NetworkCoordinate::<3>::new();
let t = Duration::from_millis(250);
(0..20).for_each(|_| {
a.update(&b, t);
b.update(&a, t);
});
let rtt = a.estimated_rtt(&b);
assert_approx_eq!(rtt.as_secs_f32() * 1000.0, 250.0, 1.0);
}
#[test]
fn test_mini_network() {
// define a little network with these nodes:
//
// slc has 80ms stem time to core entry Seattle
// nyc has 30ms stem time to core entry Virginia
// lax has 15ms stem time to core entry Los Angeles
// mad has 60ms stem time to core entry London
//
// we'll assume that traffic in the core moves at 50% the speed of light
//
// that gives us this grid of RTTs (in ms) for the core:
//
// | | Seattle | Virgina | Los Angeles | London |
// |-------------|---------|---------|-------------|--------|
// | Seattle | - | 52 | 20 | 102 |
// | Virginia | | - | 50 | 78 |
// | Los Angeles | | | - | 116 |
// | London | | | | - |
//
// Which gives us these routes (plus their reverse) and times (ms):
//
// SLC -> Seattle -> Virginia -> NYC = 80 + 52 + 30 = 162
// SLC -> Seattle -> Los Angeles -> LAX = 80 + 20 + 15 = 115
// SLC -> Seattle -> Londong -> MAD = 80 + 102 + 60 = 242
// NYC -> Virginia -> Los Angeles -> LAX = 30 + 50 + 15 = 95
// NYC -> Virginia -> London -> MAD = 30 + 78 + 60 = 168
// LAX -> Los Angeles -> London -> MAD = 15 + 116 + 60 = 192
// create the NCs for each endpoint
let mut slc = NetworkCoordinate::<2>::new();
let mut nyc = NetworkCoordinate::<2>::new();
let mut lax = NetworkCoordinate::<2>::new();
let mut mad = NetworkCoordinate::<2>::new();
// verify the initial error
let error = slc.error.hypot(nyc.error.hypot(lax.error.hypot(mad.error)));
assert_approx_eq!(error, 400.0);
// iterate plenty of times to converge and minimize error
(0..20).for_each(|_| {
slc.update(&nyc, Duration::from_millis(162));
nyc.update(&slc, Duration::from_millis(162));
slc.update(&lax, Duration::from_millis(115));
lax.update(&slc, Duration::from_millis(115));
slc.update(&mad, Duration::from_millis(242));
mad.update(&slc, Duration::from_millis(242));
nyc.update(&lax, Duration::from_millis(95));
lax.update(&nyc, Duration::from_millis(95));
nyc.update(&mad, Duration::from_millis(168));
mad.update(&nyc, Duration::from_millis(168));
lax.update(&mad, Duration::from_millis(192));
mad.update(&lax, Duration::from_millis(192));
});
// compute and test the root mean squared error
let error = slc.error + nyc.error + lax.error + mad.error;
assert!(error < 5.0);
}
#[test]
fn test_serde() {
// start with JSON, deserialize it
let s = "{\"position\":[1.5,0.5,2.0],\"height\":0.1,\"error\":1.0}";
let a: NetworkCoordinate<3> =
serde_json::from_str(s).expect("deserialization failed during test");
// make sure it's the right length and works like we expect a normal NC
assert_approx_eq!(a.heightvec.len(), 2.649_509, 0.001);
assert_approx_eq!(a.error, 1.0);
assert_eq!(a.estimated_rtt(&a).as_millis(), 0);
// serialize it into a new JSON string and make sure it matches the original
let t = serde_json::to_string(&a);
assert_eq!(t.as_ref().expect("serialization failed during test"), s);
}
#[test]
fn test_estimated_rtt() {
// start with JSON, deserialize it
let s = "{\"position\":[1.5,0.5,2.0],\"height\":25.0,\"error\":1.0}";
let a: NetworkCoordinate<3> =
serde_json::from_str(s).expect("deserialization failed during test");
let s = "{\"position\":[-1.5,-0.5,-2.0],\"height\":50.0,\"error\":1.0}";
let b: NetworkCoordinate<3> =
serde_json::from_str(s).expect("deserialization failed during test");
let estimate = a.estimated_rtt(&b);
assert_approx_eq!(estimate.as_secs_f32(), 0.080_099);
}
#[test]
fn test_error_getter() {
let s = "{\"position\":[1.5,0.5,2.0],\"height\":25.0,\"error\":1.0}";
let a: NetworkCoordinate<3> =
serde_json::from_str(s).expect("deserialization failed during test");
assert_approx_eq!(a.error(), 1.0);
}
}