Q3. Q4. Suppose that incoming calls to an oice follow a Poisson process of rate A = 6 per hour. If the line is in use at the time of an incoming call, the secretary has a HOLD button that will enable a single additional caller to wait. Suppose that the lengths of conversations are exponentially distributed with a mean length of 5 minutes, that incoming calls while a caller is on hold are lost, and that outgoing calls can be ignored. Determine the fraction of calls that are lost. Consider a three server network where all new customers (arrivals forming a Poisson process of rate A = 2) go into Server 1, which has a service rate #1 = 6. From Server 1, 60% of the customers go into Server 2 and the remaining to Server 3. Server 2 has a service rate ,ug = 3, and Server 3 ,u3 = 2. Furthermore, customers depart from the system after their service is done in Servers 2 and 3. In the long run, what fraction of time is Server 2 idle while, simultaneously, Server 3 is busy? Assume that all service times are exponentially distributed