Question $4$

$(30$ points$)$ In a system, an incoming customer is served by either clerk $1$ or $2,$ where service time

for clerk i is exponentially distributed with rate $$i per hour. Suppose that whichever clerk finishes

service first, starts serving a customer from the queue immediately. If both servers are busy and

there are ninety eight people waiting in the queue.

a$.(15$ points$)$ What is the expected time spent to serve these hundred customers? Suppose that

nobody else can enter the system.

b$.(15$ points$)$ Let assume that you enter the line before nobody leave the system. What is the

expected time you spend in the system $?$