Get familiar with AlarmManager for scheduling events according time. And Service for background work. So the idea is to schedule event for 15 minutes after user press button. Once callback received you can start service that will send request to the server.
Use setRepeating
in AlarmManager
for schedule on each 15 minutes and cancel
for stop scheduled event.
Create new service that will perform web request and start it from BroadcastReceiver
that receive event from AlarmManager
.