|
Models are necessary to simulate the real world scenario to some extent, or in
some cases, they can even provide the exact scenario.
Characteristics of traffic changes with time, place, human behavior etc. The
models in traffic engineering are necessary to predict the behavior of traffic
in proper planning and design of the road network.
The models can be microscopic and macroscopic.
In the present chapter, a macroscopic model has been discussed known as cell
transmission model which tries to simulate the traffic behavior.
In the classical methods to explain macroscopic behaviour of traffic, like
hydrodynamic theory, differential equations need to be solved to predict
traffic evolution.
However in situations of sudden high density variations, like bottle-necking,
the hydrodynamic model calls for a shock wave (an ad-hoc).
Hence these equations are essentially piecewise continuous which are difficult
to solve.
Cell transmission models are developed as a discrete analogue of these
differential equations in the form of difference equations which are easy to
solve and also take care of high density changes.
In this lecture note the hydrodynamic model and cell transmission model and
their equivalence is discussed.
The cell transmission model is explained in two parts, first with only a source
and a sink, and then it is extended to a network.
In the first part, the concepts of basic flow advancement equations of CTM and
a generalized form of CTM are presented.
In addition, the phenomenon of instability is also discussed.
In the second segment, the network representation and topologies are
established, after which the model is discussed in terms of a linear program
formulation for merging and diverging.
|
