Analytics Stories

CHAPTER 45The Waiting is the Hardest Part

I am sure everybody reading this thinks they spend too much time standing in line. Most people define the longest line at the supermarket as the line they are in. Things would be much worse, however, if Danish engineer A. K. Erlang (1878–1929) had not invented queueing theory, the mathematics of waiting lines, or queues. Erlang began working for the Copenhagen Telephone Company (CTC) in 1908. People would try to make phone calls, talk for an unknown time, and then hang up. Meanwhile, other people were trying to make calls. If CTC did not have enough phone lines or phone operators to connect the calls, callers would get very frustrated. Erlang figured out the mathematics for determining the number of operators and lines required to ensure that 99.99% of all callers could get through. Erlang's work marked the birth of queueing theory.

In this chapter, we will define the key terms in queueing theory and provide a spreadsheet that can be used to determine how a customer's time in the system and average number of customers present depends on the number of servers. We assume that all customers wait in a single line for the first available server. The idea of a single line began around 1970 (see www.cnn.com/style/article/design-of-waiting-lines/index.html), and many companies (including American Airlines, British Airways, and Wendy's) claim to have originated the single line (also known as the serpentine line). The serpentine line maximizes ...