How to alert a user of a very important task on a mobile app?

We have a task application wherein a service provider must be able to see an incoming job right away as it is time sensitive.

We'd like an alert that's similar to a call (it has that urgency to it) without the alert being an actual "call". We feel that a push notification or even an SMS alert is too subtle.

I'm not sure what's the best way to do it.