Consider a queueing system where customers arrive according

Consider a queueing system where customers arrive according to a Poissonprocess at a rate of 25 per hour and demand iid exponential service times. We havea choice of using either two servers, each of whom can process a customer in 4minutes on average, or a single server who can process a customer in 2 minutes onaverage. What is the optimal decision if the aim is to minimize the expected wait inthe system? In the queue?

Solution

mean waiting time for a customer using the first option of 2 servers = ( 25 * 4 /60) ^ 2 = 2.778...

mean waiting time for a customer using the 2nd option of 1 server = ( 25 * 2 / 60 ) = 0.834..

so, using the 2 nd option will be optimal....