Quasi-optimal feedback control for an isolated intersection under oversaturation

Abstract

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%.

Intersection Traffic Control Based on Multi-Objective Optimization

“…Lin et al [11] constructed a signal priority procedure model to minimize the vehicle delay and the weighted average number of vehicles stops. Sun et al [12] studied the oversaturation state of intersections, and constructed an optimization model that minimizes the waiting time of the first vehicle in the waiting queue. Liu and Xu [13] set up a simple calculation model of the main line phase difference of intersections, which requires the following inputs: the green signal ratio, the driving time per vehicle, the distance between intersections, and the length of the public cycle.…”

Integration of Model‐Based Signal Control and Queue Spillover Control for Urban Oversaturated Signalized Intersection

“…Mathematical Problems in Engineering 7 where represents the optimal target which reflects the total travel time in this paper. The fitness function can be calculated based on the above formula (17). If ≥ 0, the result is equal to the inverse of 1+ 2 .…”

“…However, these strategies obtain optimal timing according to historical data rather than real-time data, which is difficult to adapt to the real-time traffic conditions [16]. Therefore, extensive research on online control strategies has been proposed [17].…”

“…Xiang et al [16] proposed a static state feedback control strategy to relieve the waiting vehicles in lanes. Sun et al [22] presented a queue-based quasi-optimal feedback control strategy to limit queue length and extended it afterwards [17]. More recently, Ren et al [23] proposed a method to identify potential spillover conditions and to prevent it periodically.…”

Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

“…Discussions on the road networks that consist of many oversaturated intersections can be found in researches done by Chang and Sun [4], Di Febbraro and Sacco [5], Dotoli and Fanti [6], Ma [7,8], and Sun et al [9,10]. In the research done by Varaiya [11] and Le et al [12], the study of pressure-based signal control developed stability properties of a decentralized signal timing policy for networks with stochastic arrivals.…”