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Improving the efficiency of repeated dynamic network loading through marginal simulation

发布时间：2014-3-2111:1:55来源：作者：Ruben Corthout, Willem Himpe, Francesco Viti, Rodric Frederix, Chris M.J. Tampère

Ruben Corthout,

Willem Himpe,

Francesco Viti,

Rodric Frederix,

Chris M.J. Tampère

Keywords

Marginal simulation; Dynamic network loading; Marginal Computation (MaC) algorithm; Computational efficiency

Abstract

Currently, the applicability of macroscopic Dynamic Network Loading (DNL) models for large-scale problems such as network-wide traffic management, reliability and vulnerability studies, network design, traffic flow optimization and dynamic origin–destination (OD) estimation is computationally problematic. The main reason is that these applications require a large number of DNL runs to be performed. Marginal DNL simulation, introduced in this paper, exploits the fact that the successive simulations often exhibit a large overlap. Through marginal simulation, repeated DNL simulations can be performed much faster by approximating each simulation as a variation to a base scenario. Thus, repetition of identical calculations is largely avoided. The marginal DNL algorithm that is presented, the Marginal Computation (MaC) algorithm, is based on first order kinematic wave theory. Hence, it realistically captures congestion dynamics. MaC can simulate both demand and supply variations, making it useful for a wide range of DNL applications. Case studies on different types of networks are presented to illustrate its performance.

Article Outline

1. Introduction

1.1. Applications with repeated DNL simulations

1.2. State-of-the-art approaches to save computation time

1.3. Contributions

1.4. Outline of the paper

2. Marginal DNL simulation

2.1. Concept

2.2. General methodology

3. MaC: a marginal algorithm for the link transmission model

3.1. Base model

3.1.1. The link transmission model

3.1.2. Model discrepancy between MaC and LTM

3.2. The MaC algorithm

3.2.1. Read input

3.2.2. Impose variation onto input variables

3.2.3. Activate part of network

3.2.4. Simulate

3.2.4.1. Calculate flows

3.2.4.2. Check flow changes

3.2.4.3. Affect link boundaries, propagate activation (if necessary) and update cumulatives

3.2.4.4. Deactivate (if possible)

3.2.5. Post-process

3.3. Sources of error

3.3.1. Activation thresholds

3.3.2. Model discrepancy: single-commodity approximation

4. Numerical analyses

4.1. Detailed performance analysis

4.2. Sensitivity analysis on different types of networks

4.2.1. Impact of network type and size

4.2.2. Sensitivity to parameter settings

4.2.2.1. Upstream activation threshold (εup)

4.2.2.2. Downstream activation threshold (εdown)

4.2.2.3. Turning fraction interval (T)

4.2.3. Sensitivity to size of variations

4.2.4. Recommendations

5. Conclusions and future research

References

Figures

Fig. 1.

General framework for marginal DNL simulation.

Fig. 2.

Node and link notations.

Fig. 3.

Demand variation – imposing changes and initial activation.

Fig. 4.

Example of flow change check for an active node.

Fig. 5.

Checks and actions taken for each incoming link a during step 3 of a node update.

Fig. 6.

Checks and actions taken for each outgoing link b during step 3 of a node update.

Fig. 7.

Expanding affected and active area.

Fig. 8.

CDF of the explicitly simulated changes in link flows compared to the base simulation.

Fig. 9.

CDF of the absolute error of flow changes (MaC vs. explicit simulation with LTM).

Fig. 10.

CDF of the relative error of flow changes (MaC vs. explicit simulation with LTM) dependent on the size of the flow changes (only RAF).

Fig. 11.

Sensitivity of the relative error of flow changes (MaC vs. explicit simulation with LTM) for different sizes of the demand variations.

Tables

Table 1. Deactivation rules.

Table 2. Characteristics of the evaluated networks.

Table 3. Performance of MaC on different networks.

Table 4. Sensitivity of accuracy and computational efficiency to εup.

Table 5. Sensitivity of accuracy and computational efficiency to εdown.

Table 6. Sensitivity of accuracy and computational efficiency to T.