I'm wondering if there is a limit to the number of apple push notifications we can send to users at one time ? in other words, can i send 100,000 push notifications at once using the APNS service?
If you are sending multiple notifications to the same device within a short period of time, the push service will send only the last one.
Look "Some Notifications Received, but Not All" in that documentation.
Apple's Tech Note was recently updated to address this question :
There are no caps or batch size limits for using APNs. The iOS 6.1 press release stated that APNs has sent over 4 trillion push notifications since it was established. It was announced at WWDC 2012 that APNs is sending 7 billion notifications daily.
If you're seeing throughput lower than 9,000 notifications per second, your server might benefit from improved error handling logic.
There's no limit on how much notification you can send to Apple APNS server but reminder to avoid using allot of connection because Apple may ban your IP if he think you are doing a DDOS attack.
Also if a user is offline (iPhone out of signal) only the latest push notification will be in saved in apple's APNS server
Yes, you can ! You can also use 20 connexions max for the sending of data.
来源：https://stackoverflow.com/questions/6421252/apple-push-notification-limitation