[router] select first healthy worker on proxied get requests (#10827)

sgl-router/src/routers/http/router.rs

@@ -103,10 +103,11 @@ impl Router {
 
     fn select_first_worker(&self) -> Result<String, String> {
         let workers = self.worker_registry.get_all();
-        if workers.is_empty() {
+        let healthy_workers: Vec<_> = workers.iter().filter(|w| w.is_healthy()).collect();
+        if healthy_workers.is_empty() {
             Err("No workers are available".to_string())
         } else {
-            Ok(workers[0].url().to_string())
+            Ok(healthy_workers[0].url().to_string())
         }
     }
 
@@ -1119,6 +1120,13 @@ mod tests {
         }
     }
 
+    fn create_test_unhealthy_router() -> Router {
+        let router = create_test_regular_router();
+        let workers = router.worker_registry.get_all();
+        workers[0].set_healthy(false);
+        router
+    }
+
     #[test]
     fn test_router_get_worker_urls_regular() {
         let router = create_test_regular_router();
@@ -1140,4 +1148,16 @@ mod tests {
         // DashMap doesn't guarantee order, so just check we get one of the workers
         assert!(url == "http://worker1:8080" || url == "http://worker2:8080");
     }
+
+    #[test]
+    fn test_select_first_worker_with_unhealthy_worker() {
+        let router = create_test_unhealthy_router();
+        let result = router.select_first_worker();
+
+        assert!(result.is_ok());
+        let url = result.unwrap();
+
+        let worker = router.worker_registry.get_by_url(&url).unwrap();
+        assert!(worker.is_healthy());
+    }
 }