ture traffic states, which results in model-based traffic control strategies. Model-based coordinated control strategies [2, 3, 20, 52, 71, 96, 183] do not introduce the feedback control only to adjust the control actions to the current detected traffic states, but also to use the feedback data along with a prediction model to make effective decisions in a long term run.
In the following subsections, we present some of the well-known urban traffic con- trol approaches.
RULE-BASED CONTROL STRATEGIES
Similar to ACCEZZ for freeway networks, fuzzy-logic controllers with genetic algorithms or neural network algorithms are also applied in urban traffic systems. In [114], an urban traffic control scheme is proposed. It applies a fuzzy-logic controller as local intersec- tion controller, and heuristic technique to coordinate the control results obtained from fuzzy-logic controllers and to derive the green time for each phase in a traffic signal cy- cle. In each fuzzy-logic controller, an evolutionary algorithm is applied to learn and update in real-time the fuzzy sets.
A more complex urban network control with a hierarchical architecture is given in [34] based on a fuzzy neural decision support concept. The architecture has three lay- ers. The lowest layer includes intersection agents that control individual intersections in the traffic network. The middle layer consists of zone agents that control several pre- assigned intersection agents. The highest level includes one regional control agent man- aging all zone agents. In each layer, every agent can obtain traffic data and makes deci- sions independently. Both lower and upper layer agents can cooperate with each other. For zone agents, the fuzzy rules are adjusted using an evolutionary algorithm. Several techniques including reinforcement learning, weight adjustment, and tuning the fuzzy relations have been used to adapt the dynamics of the agents.
OPTIMAL CONTROL APPROACHES
In recent years, a number of model-based optimization control strategies based on sim- ple traffic models have been proposed, e.g. PRODYN [57], CRONOS [19, 20], OPAC [66], RHODES [210], and MOTION [17]. They can predict the traffic behavior of the net- work. However, the models used in these control schemes are relatively simple traffic flow models. This in fact limits the performance.
UTOPIA/SPOT [164] is a hierarchical system with simple local intersection con- trollers and a central controller for an area of an urban network. The central controller optimizes the control actions for the whole area based on a simple model of the net- work. The local controller makes decisions based on only the local information, but with a penalty term to guarantee that the local decisions are not too far from the de- cisions made by the central controller. Therefore, UTOPIA/SPOT partially avoids the online computational effort but on the other hand, may result in suboptimal solutions.
A linear quadratic optimal control approach, Traffic-responsive Urban Control (TUC) [1, 137], is developed based on a store-and-forward model [2]. Instead of op- timizing the control inputs (i.e. green times), TUC optimizes a linear multi-variable feedback regulator off-line, where the feedback gain matrices are solutions of the cor- responding algebraic Riccati equation. Therefore, the TUC strategy reduces the online computational complexity significantly by moving the time-consuming optimization to
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the off-line part. However, when the real traffic conditions change, the feedback control law needs to be re-designed according to the new current traffic conditions, which is also computationally complex if it occurs frequently.
Dynamic Intersection Signal Control Optimization (DISCO) [157] is a dynamic ur- ban traffic optimization-based control approach developed using the cell transmission model. It considers the fundamental diagram and can capture traffic phenomena such as shock waves and queue dynamics. The timing plans of urban traffic networks are determined by solving an optimization problem using a genetic algorithm. Despite all advantages, this optimal control approach is open-loop. It solves the optimization prob- lem based on the approximation of the future disturbances, which can be inaccurate (specially if unpredictable incidents occur). Moreover, mismatches between the model and the real world and inaccuracies in estimating initial traffic states can always happen. Under these circumstances, the control results obtained from optimal control methods are not the best control actions anymore.
SCOOT (Split Cycle Offset Optimization Technique) [203], which is an adaptive sys- tem that responds automatically to fluctuations in traffic flow, is the most common traf- fic control system used in the United Kingdom. However, widely used strategies like SCOOT and SCATS [159], although applicable to large-scale networks, are less efficient under saturated traffic conditions [135]. On the other hand, more advanced traffic- responsive strategies like OPAC [66], PRODYN [57], and RHODES [210] use optimiza- tion algorithms with exponential increase of complexity, which do not permit a cen- tral network-wide application. Thus, most available strategies face limitations when it comes to saturated traffic conditions that are frequently occurred in traffic networks. [30] proposed a dynamic method to control an oversaturated traffic network by using a bang-bang control method for the oversaturated intersections. In [2], the problem of network-wide signal control is formulated as a quadratic-programming problem that aims at balancing the link queues in order to minimize the risk of queue spillback. Fur- thermore, multiple control approaches have been proposed that use computationally inefficient optimization algorithms, such as genetic algorithms [157], and ant colony op- timization [36]. However, because of their high computational demands, the real-time and network-wide implementation of these methods might not be feasible.
MODEL PREDICTIVE CONTROL
Model predictive control known also as receding horizon control has been in the traffic control context recently [52, 65, 71, 96, 223]. The MPC method proposed in [52] is com- putationally intensive and it can describe different traffic scenarios. It needs historical data to estimate the traffic flow rate of each intersection.
An MPC scheme is proposed in [223] based on an extended model of [131], which is capable of simulating the traffic dynamics in all traffic scenarios (unsaturated, saturated, and over-saturated traffic conditions). The MPC controller gives effective performance but it is not applicable to large-scale urban networks.
On the other hand, a distributed control structure can be developed to avoid the ex- ponential growth of the computation time of centralized MPC, when the network scale increases. The problem of finding optimal signal timing plans for a large number of traffic lights is a challenging problem because of the exponential growth of joint tim- ing plans that need to be taken care of as the network size grows. However, if we de- compose the problem into smaller subproblems, we may be able to find a sufficiently