We consider a flow defined by its function R(t), with R(t) = the number of bits observed since time t = 0.

1. The flow is fed into a buffer, served at a rate r. Call q(t) the buffer content at time t. We do the same assumptions as in the lecture, namely, the buffer is large enough, and is initially empty. What is the expression of q(t) assuming we know R(t) ? We assume now that, unlike what we saw in the lecture, the initial buffer content (at time t = 0) is not 0, but some value q0 ≥ 0. What is now the expression for q(t) ?

2. The flow is put into a leaky bucket policer, with rate r and bucket size b. This is a policer, not a shaper, so nonconformant bits are discarded. We assume that the bucket is large enough, and is initially empty. What is the condition on R which ensures that no bit is discarded by the policer (in other words, that the flow is conformant)?

We assume now that, unlike what we saw in the lecture, the initial bucket content (at time t = 0) is not 0, but some value b0 ≥ 0. What is now the condition on R which ensures that no bit is discarded by the policer (in other words, that the flow is conformant) ?