The population of potential customers
is refered to as the calling population. Use examples from Table
7.1
The calling population can be finite or infinite.
In the systems with large population, we usually assume
the population is infinite.
The key difference between ``finite'' and ``infinite''
population model is how the arrival rate is defined.
In an infinite population model, the arrival rate
is not affected by the number of customers in the system. Usually the
system is viewed as an open system, customers come from outside
the system and leave the system after finishing the work.
In a finite population model, the arrival rate at
a server is affected by the population in the system. Usually the
system is viewed as a closed system, customers (with a fixed
population) don't leave the system, they merely move around system
from one server to another, from one queue to another.
System capacity:
the maximum number of customers allowed in
the system is called the system capacity. Examples:
Telephone booth: capacity is one. When the server is
busy (the booth occupied), the incoming customer is turned away.
A typical TCP/IP packet buffer has a limit of 4096
bytes.
The number of simultaneous connections allowed at a
web server usually is a fixed constant.
The arrival process:
for infinite population
inter-arrival time characterized by a
random distribution, e.g. Poisson distribution
scheduled arrivals, such as patients to a
physician's office; airline flight arrives at an airport. The
interarrival time may be a constant, or a constant with a small random
fluctuation.
at least one customer is assumed to always be
present in the queue, so the server is never idle because of the lack
of the customers, e.g. parts in an assembly line.
for finite population:
Define a customer is pending when it is
outside queueing system, and it is a member of the potential calling
population.
E.g. when simulating a local area network, if a particular computer is
powered off, we say it is pending. As soon as it is powered on,
the customer (computer) will demand service from the network.
Define runtime of a given customer as the
length of the time from departure from the queueing system until the
customer's next arrival to the queue. Runtime essentially is the time
when the customer is being serviced.
The arrival rate in a finite population model is a function of the
number of pending customers.
