Fuji-Q is a popular park and queues for most screamer attractions starts the instant the Park opens to the public in the morning. Japanese seem to have an insatiable patience for queuing for hours. To illustrate the point, on our visit on a Wednesday when the gates opened at 9am, hoards of Japanese youth sprinted to queue for eejanaika. By 9.30am the queue was so long that the posted wait time was 3 hr 40 min. 
The queue for Takabisha was 3 hours and 30 mins when we visited mid-morning. This was the tail end of the queue that wrapped around the corner. 
How to avoid queues
Luckily there is a way to avoid having to queue for the screamer coasters and I’d like to describe how you do that (like other smart Japanese park guests do). There is an onsite hotel called Highland Resort and Spa. This hotel can sell its guests a discounted entry ticket called a Free Pass. More importantly guests of the Hotel get access to the park 30 minutes before the general public. You must make use of this Hotel privilege in order to avoid potentially spoiling your day queuing for rides. That obviously means booking into the Hotel for atleast 1 night. Another advantage of staying overnight is you get complimentary access to the onsite ONSEN spa that is a god-send after a long day on your feet at the Park. Note at time of writing, a one day Free Pass purchased through the Hotel costed 4000 Yen and a two day pass through the Hotel costed 6800 Yen (usually 8300 Yen if bought at the gate).
In our case we gained entry to the Park (along with a large bunch of other Hotel guests) at 8.30am for a 9am park opening.
As soon as you get into the Park, DO NOT start queuing for a ride. Instead walk to the ticket office that is located near the roundabout. When I say walk, I really mean briskly follow the other hotel guests who are also heading that way. You’ll see why they do this soon. You’ll enter the Park via the basement of the Hotel, here’s the path to reach the ticket booth.
The reason you are visiting the ticket booth is to buy preferred tickets to the 5 screamer roller coasters. A preferred ticket (known on their guide book as ‘Zekkyo Preferred Ticket’) is similar to a FAST PASS at other US based theme parks. One preferred ticket to a screamer coaster of your choice will cost you an additional 1000 yen. The ticket booth typically opens just before 9am, so you will need to queue for 30 mins which is better than queuing for 3 hours for a ride. When you buy a preferred ticket you need to let the ticket operator know the time you want to redeem the ticket. There are a very limited number of preferred tickets so this is the reason you MUST get to the ticket booth before the park opens to the public. If you decide to buy tickets once the park has opened you will be joining a very long queue and you may miss out if they end up selling all the preferred tickets before you reach the head of the queue. Here’s the queue at 10am. 
There is likely to be a staff member at the ticket queue holding a sign board showing the status of preferred ticket sales. The entries with a cross indicates the particular time interval has been SOLD OUT. Note the order of columns is Takabisha, followed by eejanaika, followed by Dodonpa, followed by Fujiyama. Here’s the status of the board at 11.30am (eejanaika and Dodonpa are very popular, and current wait time for Takabisha is 2 hours). The Fujiyama column indicates the ride was temporarily closed due to high winds. 
I strongly suggest you buy at least 4 preferred tickets for eejanaika, Dodonpa, Fujiyama and Takabisha. Some people purchase more than one preferred ticket to each ride which is probably a reason why the tickets sell out so quickly in the morning. Please note the staff at the ticket booth have limited english. I advise you to take along the Park guide booklet so you can point to the rides and write down the time window you want to ride in 24 hour format. Time windows are in 1 hour intervals and you may enter the priority entrance of the ride at any time during the nominated 1 hour interval. To find a rides priority entrance is not always straight forward. Some rides are clearly marked with a sign in both Japanese and English. Other rides you need to enter via the exit.
Fuji-Q Highland Park 