Which methodology should be selected to patch application servers with requirements of no system downtime and quick recovery?

The ideal methodology for patching application servers with a requirement for no system downtime and quick recovery is blue-green deployment. This approach is designed specifically for minimizing downtime and ensuring a reliable and fast recovery process.

In a blue-green deployment, two identical environments (blue and green) are used. One environment runs the current production version (e.g., blue), while the other runs the new version with the applied patches (e.g., green). Once the new version has been thoroughly tested in the green environment and is deemed stable, traffic is redirected from the blue environment to the green. If any issues occur, it's straightforward to switch the traffic back to the blue environment, enabling quick recovery and minimizing downtime.

Rolling updates, while useful in certain scenarios, may still lead to temporary unavailability of components if not managed correctly. Patching directly can result in downtime since the application may need to be taken offline for the patches to be applied. The option of using three staging environments typically focuses on development and testing rather than the live deployment aspect, which can result in complexity rather than zero downtime. Thus, blue-green deployment stands as the most effective method for the specified requirements.