(a) Our local fast-food emporium, Burger Bliss, has yet to learn a lot about

queueing theory. So it does not require that all waiting customers form

a single line, and instead they make every arrival randomly choose one

of three lines formed before each server during the weekday lunch period.

But they are so traditional about managing their lines that barriers

have been placed between the lines to prevent jockeying. Suppose that

the overall stream of incoming customers has settled in at a constant

rate of 60th (Poisson-distributed) and that the time to complete a customer's

order is well described by an exponential distribution of mean

150 seconds, independent and identically from one customer to the

next. Assuming steady state, what is the average total system size?

(b) The BB has now agreed that it is preferable to have one line feeding the

three servers, so the barriers have been removed. What is the expected

steady-state system size now?