Example: A traffic engineer
is interested in the traffic intensity at a particular street
corner during the 1 – 2 a.m. time period. Using a mechanical
counting device, the number of vehicles passing the corner is
recorded during the one hour interval for several days of the
week. Although the numbers observed are highly variable, the
average is 50 vehicles. The engineer wants a probability model
to answer a variety of questions regarding the traffic.
To use the distribution for the example, we must assume that
vehicles arrive independently and that the average arrival rate
is constant. This does not mean that the vehicles pass in a
steady stream with a fixed interval between cars. Rather, with
the assumption of randomness, vehicle arrivals are extremely
variable; the rate of 50 per hour is an average.