C FIFO Queue

I was looking up info on implementing a FIFO queue in C and came across this code from a published book: http://www.cs.sunysb.edu/~skiena/392/programs/queue.c

Isn't this thing going to fail after you've queued QUEUESIZE times, regardless of dequeuing?

>>3
Queue is pronounced Q (cue || kyoo).

Also, how would you implement at FIFO queue? Got any standard algorithms you could recommend?