Thank you for bringing up this topic.

Back then I always wondered why Instagram doesn’t display number of notifications in the red bubble like other apps instead of having silent push notification for every like and comment the user get. This can results in having 50, or 5000 Instagram push notifications on the lock screen. In other hand, Facebook has better notification strategy. It doesn’t send push notification when someone likes the user’s post. Its push notifications are more than informative updates.

A good example of personal push notification is Apple Map. It knows my regular destinations and the time I usually go to each one. Every time I get into my car, it lets me know the current estimated time based on real live data before I even unlock my phone.