In each part, compare the two queuing systems described mathematically. Specifically, compare the utilization of, average waiting times of, and the average number of people in the systems. Also, give a brief description of the practical differences between the two systems (i.e. if you’re a business deciding on which system to use, what might be some additional considerations?). For question c, you can give a qualitative comparison only.
a) The first queuing system is two M/M/1 (one server) systems: two single queues (mean customer arrival rate of λ and mean service rate of each server μ). The second is an M/M/1 (single server) system with a single queue; customers arrive at mean rate 2λ, but the mean service rate of the server is 2μ.
b) The first system is the same one as the first system in part (a). The second is an M/M/2 (two servers) system with a single queue; customers arrive at mean rate 2λ, the mean service rate of each server is μ.
(c) Both systems are M/M/2 (two servers) queuing systems with mean customer arrival rate of 2λ and mean service rate of each server μ. The first has customers lining up in a single queue; the person at the front of the line gets served by the next available server. The second has two queues, with each queue going to one of the servers; when customers arrive at rate 2λ, they select the shorter of the two lines.