Consider a Single-Line, Single-Server Waiting Line System

Essay

Consider a single-line, single-server waiting line system. Suppose that there is only physical space for 2 units in the system (one in line and one being served). The arrival rate λ is 80 people per hour. The manager, Johnny Three Toes, has the choice among workers of different speeds to be the server. He wants to save money by hiring the slowest server that will result in an average number of units in the system (L) equal to 2.
a) Using Johnny Three Toes' strategy, what will the server's service rate per hour () need to be?
b) What is the probability of having 3 or more units in the system?
c) What is wrong with Johnny Three Toes' strategy?