#
__Basic Terminology of Queueing Theory__

Terminology for study of queueing systems tends to be fairly standard.
Some variation sometimes occurs, and where there are popular alternative
forms of terminology, this will be made clear.
The three main concepts in queueing theory are *customers*, *queues*,
and *servers (service mechanisms)*. The meaning of these terms is
reasonably self-evident. In general, in a queueing system, customers for
the queueing system* *are generated by an *input source*. The
customers are generated according to a statistical distribution (at least,
that is the simplifying assumption made for modelling purposes) and the
distribution describes their *interarrival times*, in other words,
the times between arrivals of customers. The customers join a queue. At
various times, customers are selected for service by the *server (service
mechanism)*. The basis on which the customers are selected is called
the *queue discipline*. The head of the queue is the customer who
arrived in the queue first. Another piece of terminology which is sometimes
used is the *tail *of the queue. The meaning of this varies depends
upon the context and the source. It normally means either all of the queue
*except*
the head **or **the last item in the queue, in other words the customer
who arrived last and is at the back of the queue. Both uses are in common
usage, and the terminology *front* and *back* of the queue will
be used to describe the customers who arrived least recently and most recently
(respectively) to avoid ambiguity.

We will now look at each of these pieces of terminology in more detail.

##
__Input Source__

The input source is a population of individuals, and as such is called
the calling population. The calling population has a size, which is the
number of potential customers to the system. The size can either be finite
or infinite. As will become apparent, if the calling population is infinite,
various simplifying assumptions can be made which make the process of modelling
queues much easier. Most queueing models assume that the population is
infinite.
##
__Queue__

Queues can be either infinite or finite. If a queue is finite, it can only
hold a limited number of customers. Most queueing models assume an infinite
queue, even though this is almost certainly not strictly true in the majority
of applications of queueing theory. This assumption is made because it
makes the modelling process simpler. Also, if the maximum queue size is
significantly larger than the likely number of customers at any one time,
then to all intents and purposes it is infinite in size. The amount of
time which is a customer waits in the queue for is called the *queueing
time*. The number of customers who arrive from the calling population
and join the queue in a given period of time is modelled by a statistical
distribution.
##
__Queue Discipline__

The queue discipline is the method by which customers are selected from
the queue for processing by the service mechanisms (also called *servers*).
The queue discipline is normally first-come-first-served (FCFS), where
the customers are processed in the order in which they arrived in the queue,
such that the head of the queue is always processed next. Most queueing
models assume FCFS as the queue discipline, and only this discipline will
be considered in any detail in this project. More information on other
queueing disciplines is available in the section on queueing
theory variations.
##
__Service Mechanism__

The service mechanism is the way that customers receive service once they
are selected from the front of a queue. A service mechanism is also called
a server (in fact, this is the more common terminology). The amount of
time which a customer takes to be serviced by the server is called the
*service
time*. A statistical distribution is used to model the service time
of a server. Some queueing models assume a single server, some multiple
servers. For most general analysis, most queueing models assume that the
system has either a single server or allow the number of servers to become
a variable. This convention will be explored further in the section on
Kendall
notation.