from its clients who request assistance in installing its software. Clients can email the center anytime. The firm currently employs one service consultant to respond to emails that form in a message queue at the software service center. The consultant responds to the messages with an exponentially distributed service time having an average of 3 minutes. Messages arrive at the service center in accordance with a Poison process having a rate of 15 every hour. The service center can serve an average of 20 clients per hour.

a) On the average how long does each message wait until the consultant starts to respond?

b) On the average how many messages are waiting in the message queue?

c.) What is the probability that exactly 2 messages will arrive at the service center in a 4 minute time interval?

d.) What percent of the time will an email be answered without needing to wait in the message queue? e.) What percent of the time is there exactly two emails in the message queue? f.) On the average how many emails are either in the message queue or being answered? g.) On the average, how long does an email spend time in both the message queue and being answered?