Queueing theory is the mathematical study of customers waiting in lines for services. A queueing system can be as simple as a single server, like waiting to get cash from an ATM machine. Or it can be a complex network of servers, like components flowing through a factory assembly line.
The simplest queue is a single server with a waiting line and called an M/M/1 queue. Customers arrive in the queue at rate \(\lambda\) and the server handles them at rate \(\mu\).
A generalization is an M/M/c queue that has a single line feeding C servers. The next person in line is served by the next available server. It's like a load balancer.
We're interested in comparing the response times of the two queueing systems for different values of \(C\).