[bandito2]

On my Honda Reflex, it's called the "air injection control valve". It is part of the emissions equipment. That top outlet likely has a hose that comes from the airbox. That valve injects filtered air into the exhaust to help completely burn any left over unburned gasses coming from the engine. Also, if your muffler is like the Honda muffler, it has catalytic converter incorporated inside of it to help with emissions as well.

Have you traced where the small hose goes? On my Reflex the small hose goes up to a T-connector. At that T-connector one small hose goes to a small outlet from somewhere near the top side of the crankcase and picks up fumes that may have gotten past the piston. The other small hose from that goes to another small gizmo with 3 hose connections on it. (I'm pretty sure, though I don't have it in front of me now to check it for sure) On that gizmo , one of the other 2 comes from the carb and the other from the fuel evap canister somewhere near the gas tank.

Hope I didn't take you too far into the woods with all that. I'm not sure if your bike is set up in a similar way as mine. Most of these scooter motors are alike in a lot of ways so some parts may look slightly different and be placed in a slightly different place, but they are pretty basic and are hooked up similarly. But don't take it as gospel from me and it would actually be best to consult a service manual specific to you bike or compare to another bike like yours that has all the hoses hooked up properly.

HTH

very similar Not sure if or how it may be affecting performance for your bike with those hoses not hooked up, but it might be.