There is not a URL that will restart the scheduler. There is a URL that will allow you to get an HTTP response in order to keep the scheduler alive. The scheduler engine is based on the IIS App Pool the site is running against. If the app pool shuts down or times out, the scheduler will not continue to run because the site is no longer running.
You can use this URL to perform what I mentioned above:
The page should give you the response of
SCHEDULER_PING_CONTENT_AVAILABILITY in the body of the html.