Consider the M/G/1 queue with FIFO service. Assume that (1) the arrival rate is 1 customer per minute, and (2) the service times are exponentially distributed with average service time 45 seconds
a) Find the server utilization.
b) Find the average value of the waiting time in minutes
c) Find the probability that an arriving customer will wait in the queue for at least 1 minute
d) Find the probability that an arriving customer who finds the server busy will wait in the queue for at least 1 minute.