Tiny add e2e http request arrival metric (#14893)

sgl-model-gateway/src/middleware.rs

@@ -307,6 +307,8 @@ impl<B> OnRequest<B> for RequestLogger {
             span.record("request_id", request_id.0.as_str());
         }
 
+        RouterMetrics::record_http_request();
+
         // Log the request start
         info!(
             target: "sgl_model_gateway::request",

sgl-model-gateway/src/observability/metrics.rs

@@ -270,6 +270,10 @@ pub fn init_metrics() {
         "Time to load and initialize tokenizer"
     );
 
+    describe_counter!(
+        "sgl_router_http_requests_total",
+        "Total number of HTTP requests"
+    );
     describe_counter!(
         "sgl_router_http_responses_total",
         "Total number of HTTP responses by status code"
@@ -589,6 +593,16 @@ impl RouterMetrics {
         counter!("sgl_router_job_shutdown_rejected_total").increment(1);
     }
 
+    // This is different from the following:
+    // * sgl_router_requests_total: bump when a request is handled and response is to be returned, thus very different from this.
+    // * sgl_router_processed_requests_total: bump when routing decision is made.
+    // Here we want a metric to directly reflect user's experience ("I am sending a request")
+    // when viewing the router as a blackbox, and is bumped immediately when the request arrives.
+    // TODO: add route name
+    pub fn record_http_request() {
+        counter!("sgl_router_http_requests_total").increment(1);
+    }
+
     pub fn record_http_status_code(status_code: u16) {
         counter!("sgl_router_http_responses_total",
             "status_code" => status_code.to_string()