Consider a queueing system with two types of customers. Type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour. Type 2 customers also arrive according to a Poisson process with a mean rate of 5 per hour. The system has two servers, and both serve both types of customers. For types 1 and 2, service times have an exponential distribution with a mean of 10 minutes. Service is provided on a first-come-first- served basis. Management now wants you to compare this system’s design of having both servers serve both types of customers with the alternative design of having one server serve just type 1 customers and the other server serve just type 2 customers. Assume that this alternative design would not change the probability distribution of service times.
(a) Without doing any calculations, indicate which design would give a smaller expected total number of customers in the system. What result are you using to draw this conclusion?
(b) Verify your conclusion in part (a) by finding the expected total number of customers in the system under the original design and then under the alternative design.