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In car-following models, the driver reacts according to his physical and psychological abilities which may change over time. However, most car-following models are deterministic and do not capture the stochastic nature of human perception. It is expected that purely deterministic traffic models may produce unrealistic results due to the stochastic driving behaviors of drivers. This paper is devoted to the development of a distinct car-following model where a stochastic process is adopted to describe the time-varying random acceleration which essentially reflects the random individual perception of driver behavior with respect to the leading vehicle over time. In particular, we apply coupled Langevin equations to model complex human driver behavior. In the proposed model, an extended Cox-Ingersoll-Ross (CIR) stochastic process will be used to describe the stochastic speed of the follower in response to the stimulus of the leader. An important property of the extended CIR process is to enhance the non-negative properties of the stochastic traffic variables (e.g. nonnegative speed) for any arbitrary model parameters. Based on stochastic process theories, we derive stochastic linear stability conditions which, for the first time, theoretically capture the effect of the random parameter on traffic instabilities. Our stability results conform to the empirical results that the traffic instability is related to the stochastic nature of traffic flow at the low speed conditions, even when traffic is deemed to be stable from deterministic models.

Available online xxxx Keywords: Over-saturated urban networks Network or macroscopic fundamental diagram (NFD or MFD) Time-delayed feedback gating traffic control a b s t r a c tRecent studies demonstrated the efficiency of feedback-based gating control in mitigating congestion in urban networks by exploiting the notion of macroscopic or network fundamental diagram (MFD or NFD). The employed feedback regulator of proportional-integral (PI)-type targets an operating NFD point of maximum throughput to enhance the mobility in the urban road network during the peak period, under saturated traffic conditions. In previous studies, gating was applied directly at the border of the protected network (PN), i.e. the network part to be protected from over-saturation. In this work, the recently developed feedback-based gating concept is applied at junctions located further upstream of the PN. This induces a time-delay, which corresponds to the travel time needed for gated vehicles to approach the PN. The resulting extended feedback control problem can be also tackled by use of a PI-type regulator, albeit with different gain values compared to the case without time-delay. Detailed procedures regarding the appropriate design of related feedback regulators are provided. In addition, the developed feedback concept is shown to work properly with very long time-steps as well. A large part of the Chania, Greece, urban network, modelled in a microscopic simulation environment under realistic traffic conditions, is used as test-bed in this study. The reported results demonstrate a stable and efficient behaviour and improved mobility of the overall network in terms of mean speed and travel time.

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Empirical and research evidence suggests that traffic-responsive signal control strategies are generally not as efficient in over-saturated traffic conditions characterized by queue spillbacks. Recent studies on (MFD/NFD) have identified a destabilizing gridlock process that arises in congested networks which precludes efficient operation. The MFD has also been used to develop urban traffic control solutions (e.g. perimeter or gating control) to avoid congestion. The purpose of this paper is to explore the benefits of combining gating with locally adaptive traffic signals through micro-simulation of the Chania, Greece traffic network. Two adaptive traffic signal strategies are considered with the perimeter control strategy. The results of the combined gating/adaptive signal control scheme are compared to gating under fixed traffic signals and the implementation of adaptive signals only. The convincing outcome of this simulation study motivates the real-field implementation of gating/perimeter control in the cities, without even changing the existing adaptive control strategies.