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
selection.
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 distribution.
The queueing system is the combination of the queue and
the service channels.
The measures used to analyze the queueing 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.
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