Sorry, the textbook is not clear. Let's collect all these bugs to make our lives easier.
most popular mistake:
A(t) < = b + sigma+ rho*t (1)
D(t) < = sigma+ rho*t (2)
So: X(t) = A(t) - D(t) < = b (3)
(or other equivalent bugs)
You cannot get (3) from (1) and (2) since it is inequality in (1) or (2).
Some of you write down A(t) = b + sigma + rho * t or D(t) = sigma + rho*t. These are regarded as the same kind of error.
Lesson:
1. when you see "A(t) is regulated by (sigma, rho)", it only means A(t) <= sigma + rho*t,
the equality holds only in some special case (sigma packets are sent at time zero and the flow is constant-rate of rho packets per second).
2. When there is inequality, be careful.