Using a shell "open" command to launch an AS

Using the shell “open” command to launch an AppleScript application like

open -a ~/my_applescript.app “parameter_name”

How to get the parameter “parameter_name” ?

Have you read “open”'s man page? (“man open”)
What are you trying with your code? To launch the app, use simply <<open /path/to/app>>. To pass parameters to the run handler, you may better use <<osascript -e ‘run script alias “path:to:script” with parameters {“a”,“b”,“c”}’>> (or similar).