Going by the opening day of SAW - The Ride, it will be absolutely packed. This is what SAW - The Ride was like when it first opened: http://themeparkvillage.com/images/stories/sawopeningday.jpg
The back of the queue was around eighty yards back from the actual entrance of the ride.
The first challenge you will face is arriving at the right time, the park opens at 10:00, but the tickets queue will probably be overflowing into the car park by 9:30. If you visit often, and have an annual pass or you have pre-booked your tickets, you can completely bypass the entrance queue and go straight to the turnstiles. Although, the office to purchase annual passes will probably have a queue stretching outside the building as well.
THE SWARM itself will probably have a queue of at least three hours. I'd strongly recommend buying Fastrack. Prices for Fastrack can be found here: http://thorpepark.com/prices/tickets.aspx?tabname=fastrack
As THE SWARM is located on the opposite side of the park from major rides such as Nemesis Inferno and Colossus, their queues will probably be reduced considerably, but should they be too long, Fastrack can be purchased for them as well.
Now, if you're planning on eating at one of the park's restaurants or food outlets, I'd recommend having lunch early. The period from 12:30 - 1:30 is usually very busy and crowded in the restaurants, even on quieter days. If you have it at around 12:00, you should be able to leave the restaurant before the rush starts, and what's more, while everybody has flocked to the restaurants, you can make the most of the reduced queue times around the park.
Hope you have a great day, and I'll be there too! Looking forward to THE SWARM now!
- LC12