The Model Predictive Control (MPC) framework has shown great potential for the control of Variable Speed Limits (VSLs) and Ramp Metering (RM) installations. However, the implementation to large freeway networks remains challenging. One major reason is that, by considering the VSLs to be discrete decision variables, an extremely difficult Mixed Integer Nonlinear Programming (MINLP) optimization problem has to be solved within every controller sampling interval. Consequently, many related papers relax the MINLP problems by considering the VSLs to be continuous variables. This paper proposes two novel MPC algorithms for coordinated control of discrete VSLs and continuous RM rates that do not make this relaxation. The proposed algorithms use a distributed control architecture and an alternating optimization scheme to relax the MINLP optimization problems but still consider the VSLs as discrete variables and, hence, offer a trade-off between computational complexity and system performance. The performance of the proposed algorithms is evaluated in a case study. The case study shows that relaxing the VSLs to be continuous variables with a distributed architecture results in a significant performance loss. Furthermore, both proposed algorithms have a lower computational complexity than the more conventional centralized approach and, as a result, they do manage to solve all optimization problems within the sampling intervals. Moreover, one of the proposed algorithms has a system performance that is remarkably similar to the optimal performance of the centralized approach.@en

This paper proposes a Logic-Based Traffic Flow Control algorithm (LB-TFC) for integrated control of Ramp Metering (RM) installations and Variable Speed Limits (VSLs) in order to reduce traffic jams created at bottlenecks. LB-TFC estimates, for each control time step, the number of vehicles that should be held back or released by the control measures (i.e. the VSLs and the RM rates) in order to avoid the capacity drop (maximizing the outflow of the bottleneck). Afterwards, based on the resulting estimated number of vehicles, the VSLs and/or the RM rates are increased or decreased in a pre-specified order. In order to avoid or reduce traffic breakdowns, the proposed controller (LB-TFC) anticipates the future evolution of the bottleneck density by using a feed-forward structure. As a result, the performance of the controller is very efficient and similar to the one obtained with an optimal controller while the implementation of the controller (with an almost instantaneous computation time) and the tuning of the parameters are easy. In the second part of this work, published in a separate paper ('Part 2: Simulation and Comparison'), LB-TFC is simulated, analyzed and compared for two freeways (one synthetic network and one stretch of the ring-road freeway SE-30 in Seville, Spain).

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This paper simulates, analyzes, and compares, for two case studies (one synthetic freeway and one real-life freeway), the behavior of Logic-Based Traffic Flow Control (LB-TFC), an integrated control strategy for Ramp Metering (RM) installations and Variable Speed Limits (VSLs) that was proposed and derivated in the first part of the work ('Part 1: Controller'). For the first case study, which was presented in the first part of the work, the control performance of LB-TFC is compared with the ones obtained with the optimal solution and with the Mainstream Traffic Flow Control (MTFC) + PI-ALINEA algorithm. Moreover, the robustness of the considered controllers is analyzed for this case study concluding that LB-TFC is quite robust, specially when comparing with MTFC + PI-ALINEA. For the second study (a stretch of the ring-road freeway SE-30 in Seville, Spain), data from 10 different days have been used in order to simulate the performance of the considered controllers using real data for the afternoon peak period. In order to properly deal with a bottleneck with a dynamically changing number of lanes, the equations used for MTFC + PI-ALINEA have been slightly modified for the second case study. For both case studies, LB-TFC provides a robust performance that, in most cases, is close to the optimal one and that improves the reduction in the Total Time Spent (TTS) obtained with MTFC + PI-ALINEA. Moreover, this paper studies the tuning of the control parameters and the advantages and disadvantages of LB-TFC.

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