There are two ways to monitor incoming calls in real time without using reports at all:

1. Use Passthru applet- You can put the Passthru applet at the end of every incoming flow for all your shifts. This applet will basically transfer all call details (who called,who picked up,date,time etc) to a URL hosted on your CRM. Please provide us the URL,we will make a GET call to that URL with the encoded call parameters and you can receive them from your end. 
This way,you will get all call details in real time on your CRM.
2. Use agent passthru- this will help you monitor which agent picked up which call at what time.
As soon as an agent picks up a call,we will make GET call to a URL provided by you and transfer the call details (caller's number,time,date and the agent's number who picked up). This will be received on your end.
This will be done in real time,as soon as the agent picks up a call,with no delay whatsoever. It will be like a pop up appearing on your CRM.
The URL will be entered in a box on the CONNECT applet under the heading "During the Call".