Little’s formula applies to an entire queueing system or to a subsystem of a larger system. For example, consider a single-server system composed of two sub-systems. The first subsystem is the waiting line, and the second is the service area, where service actually takes place. Let λ be the rate that customers enter the system and assume that λ = 60 per hour.

a. If the expected number of customers waiting in line is 2.5, what does Little’s formula applied to the first subsystem tell you?

b. Let µ be the service rate of the server (in customers per hour). Assuming that λ < µ (so that the server can serve customers faster than they arrive), argue why the rate into the second subsystem must be λ. Then, letting µ = 80 per hour, what does Little’s formula applied to the second subsystem tell you about the expected number of customers in service?