Packets arrive to a communication node with a single output link according to a Poisson

Process.

$($i$)$ Give the Kendall notation for the following cases:

A$.$ The packet lengths are exponentially distributed, the buffer capacity at the

node is infinite;

B$.$ The packet lengths are exponentially distributed, the buffer capacity at the

node has a finite capacity which is denoted N$.$

$($ii$)$ Consider an M$/$M$/1$ queue

A$.$ Packets arrive at a range of $10$ per hour. The average service completion time

is $150$ seconds. What is the expected number of packets in the system?

B$.$ How long on average does each packet spend in the queue and also waiting in

the buffer?

C$.$ Calculate the proportion of time that a M$/$M$/1/$N queueing system is empty.