Is it possible to pick up some kind of mat. model to the program for profiling SQL queries?

Question

SQL

In general, this situation: At the time of taking the topic for the diploma, we were convinced that the mat. the model is not required, but almost by the time of the pre-defense, everything suddenly changed and now they do not allow if there is at least some mat in the diploma. models. I consulted with the mathematicians of my university, but as I understand it, they did not even understand what my program was about ... Please, tell me at least some kind of mat. the model is applicable to my task (absolutely any.
About the program:
The program listens on the port and intercepts all SQL queries (like MySQLProxyServer), then calculates the execution time, how much these packets weigh, how many lines came. Then it profiles and shows the query execution plan. Well and (in the future) there will be monitoring of the DBMS for load.A
few screenshots:

Answer 1

I also did not really understand the essence of your program,
try to pay attention to the queries themselves and relational algebra.