The solution of the traffic assignment problem is based on known flow/speed relations defined for the given network links. In real applications, there are many different road types, each with its own flow/speed function. One of the standard computer programs for the solution of this problem, Emme/2, has an upper bound on the total number of operators that can be used in the database of flow/speed functions. A method is proposed to reduce the actual number of functions needed to be stored in the database. The forms of the functions are typically similar, and thus a subset of the functions can be stored, and use these to compute the rest of the functions. This requires the solution of a statistical problem related to linear and non-linear regression. Correlation coefficients between each pair of functions must be computed to see how well they can be expressed in terms of each other. Given the background explained above, a graph problem is posed based on the relation between the functions, with each node of the graph representing a function, and the graph edges representing the correlation between the functions. The problem of reducing the number of functions needed to be stored is reformulated as a graph partitioning problem. The nodes of the graph are partitioned into a smaller number of subsets, where the functions corresponding to nodes within a subset are highly correlated. A base function is chosen from each subset, and only these base functions are stored in the database. Thus the objective of the graph partitioning problem is to minimise the number of resulting subsets of nodes, where the nodes in each subset are related to each other according to some user defined criteria. Consequently, the graph partitioning problem can be presented and solved independently of the underlying statistical problem and traffic application, and standard graph theoretical algorithms and techniques can be used as a part of the solution methods. Several methods are proposed both for partitioning the graph, and for choosing a base function from each subset. Numerical test results, showing how well the methods perform and comparing them, are given on the underlying application. (A)
Samenvatting