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Modelling arrival of vehicle at section of road is an important step in traffic
flow modelling.
It has important application in traffic flow simulation where vehicles are to
be generated how vehicles arrive at a section.
The vehicle arrival is obviously a random process.
This is evident if one observe how vehicles are arriving at a cross section.
Some times several vehicles come together, while at other times, they come
sparsely.
Hence, vehicle arrival at a section need to be characterized statistically.
Vehicle arrivals can be modelled in two inter-related ways; namely modelling
what is the time interval between the successive arrival of vehicles or
modelling how many vehicle arrive in a given interval of time.
In the former approach, the random variables the time denoting interval between
successive arrival of vehicle can be any positive real values and hence some
suitable continuous distribution can be used to model the vehicle arrival.
In the later approach, the random variables represent the number of vehicles
arrived in a given interval of time and hence takes some integer values.
Here in this approach, a discrete distribution can be used to model the
process.
This chapter presents how some continuous distributions can be used to model the
vehicle arrival process.
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