A multiplexer is used to connect sensor nodes to a single external networking link as part of an industrial sensor network. The multiplexer has an arrival rate (l) of 1500 packets per second, and a service rate (?) of 3000 packets per second.

(a) What is the load (r) on the multiplexer? (b) If the maximum number of packets in the system (k) is 3, and the multiplexer can be modelled using an M/M/1/k queuing model, what is the probability of packet loss in the network?

(c) If the average number of packets in the multiplexer is given by:

E[N] = P 1- (k + 1)pk+1 1-pk+1