The input source, also known as
the calling population, is the collection of potential customers
that might have need for the services offered by the system.
It is characterized by its size, N, which is often assumed
to be infinite for modeling purposes, and the probability distribution
governing the interarrival times.
The queue is the number of customers waiting for service,
and may be concentrated at a fixed location such as a bank
foyer or may be distributed in time and space such as airplanes
approaching a runway. The queue discipline defines the rules
by which customers are selected for service. A common discipline
is first-come-first-served (FCFS), otherwise known as first-in-first-out
(FIFO), but other possibilities are priority schemes or random
The service mechanism is the process by which customers are
served. The usual assumption is that service is provided by
one or more identical servers (channels) operating in parallel.
When dealing with a network of queues, however, various configurations
will be considered. The characteristics of service are the
number of channels, s, and the service time probability
The queuing system is the combination of the queue and the
The measures used to analyze the queuing system primarily
involve the number of customers in the system. This number
is represented by the state of the system. In the figure below
we show a state as a circle with the number in the circle indicating
the number of customers associated with the state. State 0
is the empty state when there are no customers and all servers
are idle. In states 1 through s, the customers are all
being served and there are none in the queue. For states greater
than s, all servers are busy and some customers must
wait in the queue.