How the customers will be served form a queuing discipline. Queuing discipline is closely related to the notion of fairness and efficiency. The order of the queuing discipline is usually first in first out (first come first serve) because it maintains fairness among customers.
However, waiting line queue can also be formed using other form of queuing discipline such as
At once : after class, after church service a bunch of people go out of a room at once. In a conference lunch, all the participants want to eat at the same hour. Vehicles in an intersection moves together after the red light turns into green. Passengers of an airplane departs at the same time. The actual order on which customers to be served is not that important in this case, we only know that all customers come at once and waiting to be served.
First in first out (FIFO) : first come first serve. This is the most popular queuing discipline it maintains fairness among customers.
Last in first out (LIFO) : the last customers will be served first. Goods inside a delivery truck usually arranged such that the first item enters the truck will be delivered last. Stack of pancakes are eaten from the last item on the top.
Loop : children in playground join the same queue after being served. Machines in a factories form a loop to be maintained.
Priority : certain type of preferred customers will be served first. Business class passengers will enter the airplane first before the economic class. Patient with severe cases will be served first in the hospital ahead of ordinary sickness.
There are many detail human behaviors such as changing to the shortest queue and leaving the queue when it is too long will also affect the queuing system.
In this tutorial, we are dealing mostly with a queuing system that forms a waiting line with queuing discipline of first in first out (FIFO) or the customers has arrived at once.
Preferable reference for this tutorial is
Teknomo, Kardi. (2014) Queuing Theory Tutorial