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 subsystems. The first subsystem is the waiting...

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