Coordinated ramp metering for freeway networks – A model-predictive hierarchical control approach

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Abstract

A nonlinear model-predictive hierarchical control approach is presented for coordinated ramp metering of freeway networks. The utilized hierarchical structure consists of three layers: the estimation/prediction layer, the optimization layer and the direct control layer. The previously designed optimal control tool AMOC (Advanced Motorway Optimal Control) is incorporated in the second layer while the local feedback control strategy ALINEA is used in the third layer. Simulation results are presented for the Amsterdam ring-road. The proposed approach outperforms uncoordinated local ramp metering and its efficiency approaches the one obtained by an optimal open-loop solution. It is demonstrated that metering of all on-ramps, including freeway-to-freeway intersections, with sufficient ramp storage space leads to the optimal utilization of the available infrastructure.

Introduction

Ramp metering aims at improving the freeway traffic conditions by appropriately regulating the inflow from the on-ramps to the freeway mainstream. Ramp metering strategies can be classified as fixed-time or traffic-responsive (see Papageorgiou and Kotsialos, 2002, for an overview). Fixed-time strategies are derived off-line for particular times of the day, based on historical demands (see, e.g., Wattleworth, 1965). Due to the absence of real-time measurements, they may lead either to overload of the mainstream flow (congestion) or to underutilization of the freeway.

Traffic-responsive ramp metering strategies are based on real-time measurements from sensors installed in the freeway network and the on-ramps and can be further classified as local or coordinated. Local ramp metering strategies make use of measurements from the vicinity of a single ramp and include feed-forward control approaches, such as the demand-capacity strategy and its variations (Masher et al., 1975), feedback control approaches, such as the ALINEA strategy and its variations (Papageorgiou et al., 1991, Papageorgiou et al., 1998, Smaragdis and Papageorgiou, 2003, Smaragdis et al., 2004), as well as neural network (e.g., Zhang and Ritchie, 1997) or fuzzy-logic based (e.g., Vukanovic and Ernhofer, 2006) approaches. On the other hand, coordinated ramp metering strategies make use of measurements from an entire region of the network to control all metered ramps included therein. Coordinated ramp metering approaches include multivariable control strategies (e.g., Papageorgiou et al., 1990b, Diakaki and Papageorgiou, 1994), optimal control strategies (e.g., Papageorgiou and Mayr, 1982, Zhang et al., 1996, Chen et al., 1997, Zhang and Recker, 1999, Bellemans et al., 2002, Hegyi et al., 2003, Zhang and Levinson, 2004, Gomes and Horowitz, 2006), and further heuristic algorithms (Jackobson et al., 1988, Hourdakis and Michalopoulos, 2002; see Hadi, 2005, for an overview).

Local ramp metering applied independently to multiple ramps of a freeway network would be highly efficient in case of unconstrained ramp queues for vehicle storage. However, ramp queues must be restricted to avoid interference with adjacent street traffic, in which case mainstream congestion may be reduced but cannot be avoided by merely local control. Thus, limited ramp storage space and the requirement of equity (for drivers using different on-ramps) are the main reasons for coordinated ramp metering.

Another major issue to be adequately addressed when designing traffic-responsive ramp metering strategies, is the manifest uncertainty of the mainstream flow capacity. Recent works (Elefteriadou et al., 1995, Lorenz and Elefteriadou, 2001, Cassidy and Rudjanakanoknad, 2005) have demonstrated that traffic breakdown in merge areas may occur at different flow values on different days, even under similar environmental conditions. Naturally, highway capacity differences become even more pronounced in case of adverse environmental conditions (Keen et al., 1986). In contrast, the critical occupancy (at which capacity flow occurs) was found to be fairly stable (Cassidy and Rudjanakanoknad, 2005) even under adverse environmental conditions (Keen et al., 1986, Papageorgiou et al., 2006). In view of the uncertainty of real highway capacity, any ramp metering strategy attempting to achieve a pre-specified capacity flow value, will either lead to overload and congestion (on days where the real capacity happens to be lower than its pre-specified value) or to underutilization of the infrastructure (on days where the real capacity happens to be higher than its pre-specified value). Note that most known coordinated ramp metering strategies belong to this class; in particular, model-based optimal control strategies (even those employing a model-predictive application mode) belong to this class with a pre-specified capacity value included in their model parameters (unless their capacity-related model parameters are estimated sufficiently accurately and rapidly in real time). The only known ramp metering strategies that target the (more stable) critical occupancy (rather than capacity) is ALINEA, a local strategy, and its aforementioned multivariable-regulator extensions. The issue of highway capacity uncertainty is explicitly considered when designing a hierarchical ramp metering strategy in this paper.

Kotsialos et al. (2002b) presented AMOC, an open-loop optimal control tool for large-scale freeway networks including a powerful numerical optimization algorithm. AMOC is able to consider coordinated ramp metering, route guidance and, recently, variable speed limits as well as integrated control combining any of the mentioned control measures. Kotsialos and Papageorgiou, 2001, Kotsialos and Papageorgiou, 2004 presented in detail the results from AMOC’s application to the problem of coordinated ramp metering at the Amsterdam ring-road.

Due to various inherent uncertainties (including the capacity uncertainty), the open-loop optimal solution delivered by optimal control approaches becomes suboptimal when directly applied to the freeway traffic process. Therefore, in this paper, the AMOC optimal results are cast in a model-predictive frame; in addition, to improve control robustness even further and address the particular capacity uncertainty, sub-ordinate local regulators (ALINEA) are introduced with set-points derived appropriately from AMOC’s optimal results. This leads to a hierarchical control scheme similar to that proposed by Papageorgiou (1984), albeit with a more sophisticated optimal control methodology. Preliminary results of this approach have been presented by Kotsialos et al. (2005).

The rest of this paper is organized as follows. In Section 2 the freeway network traffic flow model used for both simulation and control design purposes is presented. Section 3 introduces the formulation of the AMOC optimal control problem for ramp metering. The hierarchical control structure is described in Section 4 while the results of applying ALINEA, as a stand-alone strategy, as well as the proposed hierarchical control scheme are presented and compared in Section 5. The main conclusions are summarized in Section 6.

Section snippets

Traffic flow modeling

A validated second-order traffic flow model is used for the description of traffic flow on freeway networks and provides the modeling part of the optimal control problem formulation. In fact, the same model is used in this study for the traffic flow simulator (METANET) and for the control strategy (AMOC) albeit with different external disturbances (i.e., demands and turning rates) and model parameter values affecting capacity. Since traffic assignment aspects of the traffic process are not

Formulation of the optimal control problem

The coordinated ramp metering control problem is formulated as a discrete-time dynamic optimal control problem with constrained control variables over a given optimization horizon KP, which can be solved very efficiently even for large-scale networks by a suitable feasible-direction algorithm (Papageorgiou and Marinaki, 1995). Thus, the freeway traffic flow is considered as the process under control via the various ramp meters installed at the network entrances. The state of the process is

Hierarchical control

The solution provided by AMOC is of an open-loop nature, i.e., it does not make use of measurements during the horizon KP, other than the initial state x(0). As a consequence, its direct application over the whole horizon KP may lead to real traffic states that are increasingly diverging from the calculated optimal ones due to errors associated with the initial state estimate, the prediction of the disturbances, the model parameters used and the existence of unpredictable incidents in the

The Amsterdam network

For the purposes of this study, the counter-clockwise direction of the Amsterdam ring-road A10, which is about 32 km long, is considered. There are 21 on-ramps on this freeway, including the ftf junctions with the merging freeways A8, A4, A2 and A1; and 20 off-ramps, including the connections with A8, A4, A2 and A1. The topological network model may be seen in Fig. 3. The model parameters for this network were determined from validation of the network traffic flow model against real data (

Conclusions

Extensive simulation results of applying local feedback control, ideal open-loop control and rolling-horizon hierarchical coordinated control to the Amsterdam ring-road have been presented. Uncoordinated local control with ALINEA is quite successful in reducing the TTS and lifting congestion up to a certain degree depending on the imposed queue-length restrictions. However, congestion creation and spillback (e.g., on A4) are unavoidable in the realistically restricted cases. On the other hand,

Acknowledgements

This work was partly funded by the European Commission in the framework of the project EURAMP (IST-2002-23110). The content of this paper is under the sole responsibility of the authors and in no way represents views of the European Commission. The authors would like to thank Mr. F. Middelham from the AVV-Rijkwaterstaat, The Netherlands, for providing the necessary data for the Amsterdam ring-road.

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