2. What does the rate of change of priority mean in written assignment 1, question 3?

If the priority is p at time t, and the rate of change of priority is x, then at time t+t', the priority is t'*x*p. Another definition you could use is that the new priority is t'*x + p, but here the value of x could also be negative!! But the value of priority is always positive.

1. What does a rigorous analysis mean?

The quantities of study here are the array size and therefore the number of threads and the time elapsed. A rigorous analysis would include testing for different values of array size (therefore number of threads) and giving a graphical interpretation. A comparison of results of the experiments in NT and UNIX and your general comments on the results.