How can I prevent several people from working on the same ticket?

You can create a separate department for every representative and lock the ticket on a specific department. If the ticket is locked, no other department can edit it.

Since Help Desk Ultimate v.2.10, you have a possibility to limit the access to every department:

1.Go to the Help Desk -> Manage departments backend page.

2.Choose the required department.

3.Specify the access to the department in the Admin Permissions tab.