A coffee stand operates with five baristas, each of whom serve a separate line of customers. Customers arrive at each line in separate Poisson streams at the rate of 18/hour. The baristas are able to provide exponentially-distributed service at the rate of 23/hour. Two options for improvement of the coffee stand are being considered:

Design A: Merge the five arrival streams into a single Poisson stream with rate 90/hour, and pool the five existing baristas to serve it (they each continue to provide exponentially-distributed service at rate 23/hour).

Design B:Hire a 6th barista, and have the baristas (who each provide exponentially-distributed service at the rate of 23/hour) each serve a separate Poisson stream of customers who arrive at the rate of 15/hour.

Which design produces the lowest average time in system?

A coffee stand operates with five baristas, each of whom serve a separate line of customers. Customers arrive at each line in separate Poisson streams at the rate of 18/hour. The baristas are able to provide exponentially-distributed service at the rate of 23/hour. Two options for improvement of the coffee stand are being considered:

Design A: Merge the five arrival streams into a single Poisson stream with rate 90/hour, and pool the five existing baristas to serve it (they each continue to provide exponentially-distributed service at rate 23/hour).

Design B:Hire a 6th barista, and have the baristas (who each provide exponentially-distributed service at the rate of 23/hour) each serve a separate Poisson stream of customers who arrive at the rate of 15/hour.

Which design produces the lowest average time in system?

Design A and B produce equivalent performance

Design A

There is insufficient information to make a determination

Design B