Traffic congestion is one of the challenges that face urban cities’ planners. It affects the environment as it increases the emissions of CO2 and affects the logistics systems as it may increase the travel time of different vehicles. Scheduling traffic signals is one of the ways to solve this problem. In the urban traffic signal scheduling problem, it is desired to get the optimum schedule for each considered traffic signal to maximize or minimize a specific objective function(s); these schedules determine the active and inactive traffic phases during each cycle time. In this paper, a mathematical programming model for solving the urban traffic signal scheduling problem is presented, the proposed mathematical model captures the physical constraints of the problem. Furthermore, a firefly-based rolling horizon approach is proposed to solve the problem. Both methods are used to solve a traffic-responsive system, which is considered the future of traffic control systems. The performance of both methods has been simulated using the SUMO traffic simulator to verify the solutions. The performance of the solutions was measured using the average queue length of the roads, the average waiting time, and the average travel time. The proposed methods have been applied to a real case study, and the results were remarkable.

中文翻译：

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具有物理约束的实时交通信号调度的数学编程模型和基于萤火虫的启发式算法

交通拥堵是城市规划者面临的挑战之一。它会影响环境，因为它会增加二氧化碳的排放量，并会影响物流系统，因为它可能会增加不同车辆的行驶时间。调度交通信号是解决这个问题的方法之一。在城市交通信号调度问题中，希望得到每个考虑的交通信号的最优调度以最大化或最小化特定目标函数；这些时间表确定了每个循环时间期间的活动和非活动交通阶段。在本文中，提出了一种用于解决城市交通信号调度问题的数学规划模型，所提出的数学模型捕获了问题的物理约束。此外，提出了一种基于萤火虫的滚动地平线方法来解决这个问题。这两种方法都用于解决交通响应系统，这被认为是交通控制系统的未来。使用 SUMO 交通模拟器对两种方法的性能进行了模拟，以验证解决方案。使用道路的平均排队长度、平均等待时间和平均旅行时间来衡量解决方案的性能。所提出的方法已应用于实际案例研究，效果显着。使用道路的平均排队长度、平均等待时间和平均旅行时间来衡量解决方案的性能。所提出的方法已应用于实际案例研究，效果显着。使用道路的平均排队长度、平均等待时间和平均旅行时间来衡量解决方案的性能。所提出的方法已应用于实际案例研究，效果显着。