From Traderpedia

Definition: A complex algorithm forming the core exchange process for matching orders between marketable buy or sell orders with corresponding resting bids or offers from different customers.

Whilst this sounds like it should be a simple process, correctly and quickly allocating orders is in fact an extremely difficult problem to solve effectively and efficiently. The problems of lag and delay that many traders experience when pulling or modifying orders on Eurex are a testament to the fact that the Eurexchange matching engine is already creaking at the seams under current orderlflow levels.

A number of different approaches have been taken by different exchanges to manage orderflow and matching - including prorata allocation, and fifo.