The previous models all assumed, that customers would wait as long as it takes in order to get processed. In more realistic models, customers will leave the process before getting served because the waiting time gets too long. Some customers will not even enter the system, if the the demand is visibly too high (long waiting lines). In these cases, the outflow (completely served customers) will differ from the inflow (customer demand). But what fraction of demand will a business be able to serve?
There are four basic models of possible customer behaviour (which can additionally be mixed):
(1) All customers wait in line forever
(2) Some customers leave the line after a while
(3) Some customers do not enter if the line is too long
(4) Waiting time is absolutely impossible (inventory = 0)
Once one knows the probability, with which an incoming customer is not served, one can calculate how much business a company is missing because of waiting times. Instead of working with the rather complex formula for calculating this probability, the Erlang Loss Table can be used. This table denotes all probabilities for combinations of m (number of resources) and r (for the ratio between the processing time p and the arrival time a).
These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org.