Consider a single server queueing system where customers arrive according to a Poisson

process with rate ?, service times are exponential with rate , and customers are served

in the order of their arrival. Suppose that a customer, denoted by A, arrives and fifinds one

customer is being served in the system and no customer is waiting. Let T be the amount

of time A spends in the system. Let N denote the number of customers waiting after A

at the moment customer A departs.

4. Consider a single server queueing system where customers arrive according to a Poisson process with rate A, service times are exponential with rate pa, and customers are served in the order of their arrival. Suppose that a customer, denoted by A, arrives and nds one customer is being served in the system and no customer is waiting. Let T be the amount of time A spends in the system. Let N denote the number of customers waiting after A at the moment customer A departs. (a) (4) Specify the distribution of T. (b) (4) Find E(N). (c) (4) Find P(N = 0)