Problem
A retail chain is trying to finalize the design of their payment kiosk, for national rollout. Two options are on the drawing board: Design A: A pooled system with three human servers (each server provides exponentially distributed service at the rate of 10 customers/hour). Customers are expected to join the system in a Poisson process at the rate of 24/hour. Design B: A system with four human servers (each server provides exponentially distributed service at the rate of 10 customers/hour) with customers forming a separate line in front of each server. Customers are expected to join each queue at the rate of 8/hour. The average waiting time in the line is shorter in one of the two designs. What is that (shorter) average waiting time in the line (in hours)? Give your answer to four decimal place accuracy.