Improved bush-based methods for network contraction

Abstract

Calculating equilibrium sensitivity on a bush can be done very efficiently, and serve as the basis for a network contraction procedure. The contracted network (a simplified network with a few nodes and links) approximates the behavior of the full network but with less complexity. The network contraction method can be advantageous in network design applications where many equilibrium problems must be solved for different design scenarios. The network contraction procedure can also be used to increase the accuracy of subnetwork analysis. This method requires calculating travel time derivatives between two nodes, with respect to the demand between them, assuming that the flow distributes in a way that equilibrium is maintained. Previous research describes two methods for calculating these derivatives. This paper presents a third method, which is simpler, faster, and just as accurate. The method presented in this paper reformulates the linear system of equations defining these sensitivities as the solution to a convex programming problem, which can be solved by making minor modifications to static user equilibrium algorithms. In addition, the model is extended to capture the interactions between the path travel times and network flows, and a heuristic is proposed to compute these interactions. The accuracy and complexity of the proposed methodology are evaluated using the network of Barcelona, Spain. Further, numerical experiments on the Austin, Texas regional network validate its performance for subnetwork analysis applications.

Generating a Spatiotemporal Dynamic Map for Traffic Analysis Using Macroscopic Fundamental Diagram

“…The errors of the predicted traffic pattern, which are described by the average travel time and the average travel distance, are both less than 5%. In Jafari's contraction simulation experiment [15], the vehicle travel time error between the complete network and contracted network is reported to be less than 6.7%. Taking Jafari's work as a benchmark, we conclude that the proposed method can ensure analysis accuracy.…”

“…However, this method caused a serious inconsistency problem due to the different spatial structures of the sketch planning zones and the complete network. Taking the vehicle routing transition brought about by map abstraction into consideration, a bush-based sensitivity analysis method [14] and improved bush based methods used for network contraction [15] were put forward successively. A contracted network only includes limited subnetworks, origins, and destinations, with artificial links connecting each OD pair.…”

Mean‐standard deviation model for minimum cost flow problem

“…In this section, we identify the derivatives 𝝃 using sensitivity analysis, using similar techniques as in Boyles [9] and Jafari and Boyles [26]. The derivative of the optimal solution vector with respect to the weight parameter 𝜆 can be interpreted as the sensitivity of the solution to changes in 𝜆.…”

Heuristic Coarsening for Generating Multiscale Transport Networks

“…Within transportation, a limited number of studies report explicit algorithmic work on graph coarsening. In [8] and [10] a bush-based approach is proposed for replacing a regional network with a smaller one, containing all of the sub-network, and zones. Artificial arcs are created to represent "all paths" between each origin and sub-network boundary node, under the assumption that the set of equilibrium routes does not change.…”