Quasi-optimal Feedback Control for Signalized Intersections Under Oversaturation
Henry X. Liu, University of Michigan, Ann Arbor
How to manage signalized intersections under oversaturated conditions is a long-standing problem in traffic science and engineering. This paper proposes a QUEUE-based quasi-optimal feedback control strategy for oversaturated intersections.
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 oversaturated intersections. 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%.
The primary contribution of this paper is that we find an innovative way of approximating the off-line optimal control strategy for an oversaturated intersection with an on-line feedback control method. The feedback strategy is based on the availability of detected queue size data, while perfect knowledge or reliable prediction of future demand is not needed. It is proved to match the off-line optimum in case of constant arrival flow rate, and the upper bounds of the sub-optimality from the off-line optimum are quantified in general cases.
Different from the feedback control models proposed in the past, in our proposed method, maximum queue constraints are considered explicitly. In this paper, we divide the whole oversaturation period into two parts, the queuing period with a primary objective of keeping the queue length within the maximum value, and the dissipation period with a primary objective of eliminating all queues at the earliest time. Thus, the maximum queue constraints are carefully considered in the queuing period, but can be considered in a simplified way or even omitted in the dissipation period. Interestingly, we found that the two different objectives can be achieved with similar methods.
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