1. i Now consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of p n , the equilibrium...

1. i Now consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model.

ii. For the M/M/1 queue derive the form of
p_n
, the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distribution