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I have appengine endpoint and trying to reduce latency on few first calls to newly created endpoint instance. Application is written in Java and endpoints are auto scaled.
To address this issue I configured idle instance, although even if instance is already created, first few calls routed to it consume some extra time. Following documentation I've implemented the custom servlet handling warm up requests and marked the EndpointsServlet as load on startup.
Inside the warm up servlet I've put code that initiates some commonly used services, load some data etc. Effect was almost impossible to notice.
After it I have implemented calls to methods exposed by the endpoint like that:
call("/_ah/api/teamly/v1/test/dummy")
It works for some cases (even most of them) and after calling few key methods instance is really ready to serve. The problem I'm facing now is that if I'm using auto scaling for some module I can't route the request to specific instance.
So the question is:
How should I properly warm up the endpoint instance to avoid load requests initiated from frontend.

You need to put a listener to /_ah/warmup and then make calls to any resources you want it to be warmed up. You can find detailed information at:
Configuring Warmup Requests to Improve Performance