A tiny router has a queuing capacity to store 10 packets in its buffer. It has to drop any further packets arriving at it when its buffer is full. At every millisecond, the router either: i) sees an arrival with
probability 0:2, ii) completes forwarding of a packet with probability 0:6 (if its buffer is not empty; with
probability 0 otherwise), or iii) stays the same – no new arrival and no forwarding – with probability
0:2 (when the buffer is nonempty) or with probability 0:8 (when the buffer is empty).
Now determine the followings:
(a) The probability that the router has an empty buffer at any given millisecond.
(b) The probability that it has at least seven packets in its buffer at any given millisecond.