Messages arrive at a switching center in accordance with a Poisson Process having mean arrival rate of 180 messages/hour. They are then sent over a transmission line at the rate of 12 characters per second. The length of the messages is exponentially distributed with a mean of 144 characters.
A) What is the mean waiting time at the switching center?
B) What will be the mean number of messages waiting for transmission?
C) What is the probability that a message does not have to wait to be transmitted?