A note on the optimal control of an oversaturated intersection

Guardabassi, G.; Locatelli, A.; Papageorgiou, M.

doi:10.1016/0191-2615(84)90024-9

Cited by 18 publications

(4 citation statements)

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“…As a consequence, the necessary and sufficient condition in [6] for decreasing both queue lengths to zero is different from the necessary condition in [5].…”

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confidence: 86%

Optimal Steady-State Control for Isolated Traffic Intersections

Haddad

Schutter

Mahalel

et al. 2010

IEEE Trans. Automat. Contr.

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Abstract-A simplified isolated controlled vehicular traffic intersection with two movements is considered. A discreteevent max-plus model is proposed to formulate an optimization problem for the green-red switching sequence. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the problem becomes a linear programming (LP) problem. Also, in this case, the steady-state control problem can be solved analytically. A sufficient and necessary condition for steady-state control is derived, and the structure of optimal steady-state traffic control is revealed. Our condition is the same as the necessary condition in [5] for both queue lengths to be non-increasing at an isolated intersection.

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“…As a consequence, the necessary and sufficient condition in [6] for decreasing both queue lengths to zero is different from the necessary condition in [5].…”

mentioning

confidence: 86%

Optimal Steady-State Control for Isolated Traffic Intersections

Haddad

Schutter

Mahalel

et al. 2010

IEEE Trans. Automat. Contr.

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“…In other words, the trajectory in the queue state plane should reach the origin without reaching any axis before. Guardabassi et al (1984) showed that the two-stage optimal solution exists if and only if the origin belongs to the reachable region. 3.…”

Section: Solution Existence Conditionmentioning

confidence: 99%

Quasi-optimal feedback control for an isolated intersection under oversaturation

Sun

Wang

et al. 2016

Transportation Research Part C: Emerging Technologies

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How to manage signalized intersections under oversaturated conditions is a long-standing problem in traffic science and engineering. However, although research works in this area date back to 1960s, an on-line control strategy with theoretically bounded performance is missing, even for the control of an isolated intersection under oversaturation. This paper makes one step further in this area by proposing a QUEUE-based quasi-optimal feedback control (abbreviated as QUEUE) strategy for an isolated oversaturated intersection. The QUEUE strategy is intuitive, simple, and proved to match the off-line optimum in the case of constant demand. More importantly, the bounds of sub-optimality of the QUEUE strategy can be specified quantitatively in general piece-wise constant demand cases. To better deal with the maximum queue constraints, the oversaturation period is divided into the queuing period and the dissipation period with two different objectives. In the queuing period, the primary objective is to keep the queue length within the maximum value; but for the dissipation period, the primary objective is to eliminate all queues at the earliest time. Interestingly, we found that both control objectives can be realized with the same QUEUE strategy. Numerical examples show that the QUEUE strategy approximates the off-line optimum very well. The average sub-optimality in comparison with the off-line optimum in the challenging conditions with Poisson distributed random demand is below 5%.

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“…He derived an expression for the average delay per vehicle for a given movement, based on theoretical analysis and empirical results. Other papers (e.g., Mazloumi, 2008;Rouphail and Akcelik, 1992) aimed to improve the delay estimation formula for oversaturated conditions, while others proposed different models, methods, and strategies for controlling oversaturated isolated intersections (Chang and Lin, 2000;Gazis, 1964;Guardabassi et al, 1984;Improta and Cantarella, 1984;Kashani and Saridis, 1983;Michalopoulos and Stephanopoulos, 1978;Talmor and Mahalel, 2007) where the control objective was to minimize delays or to maximize the intersection capacity. With proper sensors it is easier to measure queue lengths than to estimate delays.…”

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confidence: 99%

Modeling nonlinear road traffic networks for junction control

Péter

2012

International Journal of Applied Mathematics and Computer Science

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The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used. The structure describes the inner-inner, inner-outer and outer-outer relations, and laws of a network area. The research examines the nonlinear equation system. The analysed model can be applied to the testing and planning of large-scale road traffic networks and the regulation of traffic systems. The elaborated model is in state space form, where the states are vehicle densities on a particular lane and the dynamics are described by a nonlinear state constrained positive system. This model can be used directly for simulation and analysis and as a starting point for investigating various control strategies. The stability of the traffic over the network can be analyzed by constructing a linear Lyapunov function and the associated theory. The model points out that in intersection control one must take the traffic density values of both the input and the output sections into account. Generally, the control of any domain has to take the density of input and output sections into consideration.

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A note on the optimal control of an oversaturated intersection

Cited by 18 publications

References 1 publication

Optimal Steady-State Control for Isolated Traffic Intersections

Optimal Steady-State Control for Isolated Traffic Intersections

Quasi-optimal feedback control for an isolated intersection under oversaturation

Modeling nonlinear road traffic networks for junction control

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