A take$-$out restaurant$$s order processing system consists of a two$-$stage process: order placement and food preparation. Each customer must first place an order with a cashier $($server

$1)$ and then wait for the kitchen staff to prepare the food $($server $2).$ The service times at

server i are exponential with parameter $\backslash$lambda i

$,$ for i $=1,2.$ Any customer arriving at the order

placement station will wait in line if the server is busy. Upon completion of order placement,

the customer either waits for the food to be prepared, if the kitchen is free, or else waits at

the order placement station until the kitchen is free $($delaying the order placement of other

customers$).$ Customers leave the restaurant after receiving their food.

Suppose that when you arrive at the restaurant, there is only one customer in the system

who is currently at the order placement station. What is the expected total time you will

spend at the restaurant?