It was actually VERY fast for me. I received a phone call (cold call) on a Tuesday inquiring upon my interest in the position. After I agreed, they scheduled an interview for the following week. I had an interview early on a Monday morning, that evening they made a decision. It was quite incredible.
A word of caution, if going through a third party (subcontractor) to Unisys, prepare to run the gamut. I had my start date delayed twice due to persons dragging their feet on checks and rechecks. After that, it was rather straight forward and quick to get started.