When viewing the Drivers tab of the Live Monitoring, besides viewing the status of your drivers, you can also view whether your drivers are currently wanting to receive task.
When drivers wish to not receive any tasks for the time being, your driver avatar will have the pause sign in grey which signify they do not want to receive the task.
If your Auto-assign feature is active, the task will not be allocated to the driver who has paused receiving tasks however you can manually assign the task to the driver.
If you Auto-assign feature is inactive then it will not take any affects.