Is there a free ticketing system/incident management system which will help me in achieving the following?

1) If a service goes down then Nagios alerts the on-duty staff and pushes the status to some backend or DB as a ticket, say the initial status is "New".

2) The on-duty staff logs in through a frontend and acknowledges the new ticket by marking it as "In progress", so now the status of the ticket changes from "New" to "In progress".

3) If even after "n" number of minutes no person from on-duty staff has changed the ticket status to "In progress" then Nagios alerts the next level of contacts. Although if the on-duty staff has acknowledged the ticket then there is no need to alert the next level.

4) When the service comes up Nagios closes the ticket by marking it "Closed"

Now I already have Nagios monitoring set up and currently it alerts by sending text messages and mails, what I'm looking for is some framework which only escalates the issue(alerts the second level) if the first level(on-duty staff) fails to respond to the initial alert.

By "responding to the alert" I mean, the on-duty staff can login via some frontend and basically change the status to something like "Acknowledged" or "In progress".