fix(backend): correct EMA formula in EmaHealthTracker

crates/backend/src/health.rs

@@ -13,6 +13,10 @@ pub struct HealthConfig {
     pub unhealthy_error_rate: f64,
     /// Minimum requests before calculating error rate.
     pub min_requests: u64,
+    /// Smoothing factor for the EMA (0.0 < alpha <= 1.0).
+    /// Higher values weight recent observations more heavily.
+    /// Defaults to 0.1 for stable, noise-resistant latency tracking.
+    pub alpha: f64,
 }
 
 impl Default for HealthConfig {
@@ -21,6 +25,7 @@ impl Default for HealthConfig {
             degraded_latency: Duration::from_millis(500),
             unhealthy_error_rate: 0.5,
             min_requests: 10,
+            alpha: 0.1,
         }
     }
 }
@@ -57,8 +62,12 @@ impl HealthTracker for EmaHealthTracker {
         } else {
             self.error_count += 1;
         }
-        // EMA: new = (old + elapsed) / 2
-        self.latency_ema = (self.latency_ema + duration) / 2;
+        // EMA: new = alpha * sample + (1 - alpha) * old
+        let alpha = self.config.alpha;
+        let old_nanos = self.latency_ema.as_nanos() as f64;
+        let new_nanos = duration.as_nanos() as f64;
+        let ema_nanos = alpha * new_nanos + (1.0 - alpha) * old_nanos;
+        self.latency_ema = Duration::from_nanos(ema_nanos as u64);
     }
 
     fn latency_ema(&self) -> Duration {
@@ -101,34 +110,31 @@ mod tests {
         let mut tracker = EmaHealthTracker::new(HealthConfig::default());
         tracker.record(Duration::from_millis(100), true);
 
-        assert_eq!(tracker.latency_ema(), Duration::from_millis(50));
+        assert_eq!(tracker.latency_ema(), Duration::from_millis(10));
         assert_eq!(tracker.error_rate(), 0.0);
     }
 
     #[test]
     fn test_latency_ema_calculation() {
+        // Default alpha = 0.1: new = 0.1 * sample + 0.9 * old
         let mut tracker = EmaHealthTracker::new(HealthConfig::default());
 
-        // First request: 100ms -> EMA = (0 + 100) / 2 = 50ms
+        // First request: 100ms -> EMA = 0.1 * 100 + 0.9 * 0 = 10ms
         tracker.record(Duration::from_millis(100), true);
-        assert_eq!(tracker.latency_ema(), Duration::from_millis(50));
+        assert_eq!(tracker.latency_ema(), Duration::from_millis(10));
 
-        // Second request: 100ms -> EMA = (50 + 100) / 2 = 75ms
+        // Second request: 100ms -> EMA = 0.1 * 100 + 0.9 * 10 = 19ms
         tracker.record(Duration::from_millis(100), true);
-        assert_eq!(tracker.latency_ema(), Duration::from_millis(75));
+        assert_eq!(tracker.latency_ema(), Duration::from_millis(19));
 
-        // Third request: 100ms -> EMA = (75 + 100) / 2 = 87.5ms
-        // Duration division truncates, so we check the range
+        // Third request: 100ms -> EMA = 0.1 * 100 + 0.9 * 19 = 27.1ms
         tracker.record(Duration::from_millis(100), true);
         let ema = tracker.latency_ema();
         assert!(
-            ema >= Duration::from_millis(87) && ema <= Duration::from_millis(88),
-            "Expected ~87-88ms, got {:?}",
-            ema
+            ema >= Duration::from_millis(27) && ema <= Duration::from_millis(28),
+            "Expected ~27-28ms, got {:?}", ema
         );
     }
-
-    #[test]
     fn test_error_rate_below_min_requests() {
         let config = HealthConfig { min_requests: 10, ..Default::default() };
         let mut tracker = EmaHealthTracker::new(config);
@@ -165,6 +171,7 @@ mod tests {
             degraded_latency: Duration::from_millis(500),
             unhealthy_error_rate: 0.5,
             min_requests: 1,
+            alpha: 0.1,
         };
         let mut tracker = EmaHealthTracker::new(config);
 
@@ -179,11 +186,12 @@ mod tests {
             degraded_latency: Duration::from_millis(100),
             unhealthy_error_rate: 0.5,
             min_requests: 1,
+            alpha: 0.1,
         };
         let mut tracker = EmaHealthTracker::new(config);
 
         // Record high latency requests
-        for _ in 0..5 {
+        for _ in 0..30 {
             tracker.record(Duration::from_millis(200), true);
         }
 
@@ -201,6 +209,7 @@ mod tests {
             degraded_latency: Duration::from_millis(500),
             unhealthy_error_rate: 0.3,
             min_requests: 5,
+            alpha: 0.1,
         };
         let mut tracker = EmaHealthTracker::new(config);