QPX (ITA's, and now Google's) system is responsible for calculating and searching airfares, i.e. the complete "solution" for "I want to get from A to B with those constraints". It's what responds when you ask google flight for a route, essentially. This is quite computationally complex due to many dimensions involved in airfare calculations. This system is essentially implemented on top of SBCL with some small bits of C++ (responsible, IIRC, for handling memory-mapped airfare data files).