A new macroscopic traffic flow model is proposed, which considers driver presumption based on driver reaction and traffic stimuli. The Payne–Whitham (PW) model characterizes the traffic flow based on a velocity constant C 0 which results in unrealistic density and velocity behavior. Conversely, the proposed model characterizes traffic behavior with velocities based on the distance headway. The performance of the proposed and PW models is evaluated over a 300 m circular road for an inactive bottleneck. The results obtained show that the traffic behavior with the proposed model is more realistic.

SUMMARYComputing a realistic velocity profile for a mobile robot is a challenging task due to the large number of kinematic and dynamic constraints involved. In order for a mobile robot to complete its task it must be able to plan and follow a trajectory. It may also be necessary to follow a given velocity profile, depending on the environment. Temporal planning, or following a given velocity profile, can be used to minimize time of motion and to avoid moving obstacles. For example, assuming the mobile robot is a smart wheelchair, it must follow a prescribed path while following a strict speed limit. This paper presents a temporal planning algorithm that is implemented on a wheeled mobile robot to be used in an indoor setting, such as a hospital ward. The path planning stage is accomplished by using cubic spline functions. A trajectory is created by assigning an arbitrary time of 1 s to each segment of the path. This trajectory is made feasible by applying a number of constraints and using a linear scaling technique. When a velocity profile is given, a non-linear time scaling technique is used to fit the mobile robot's linear velocity to the given velocity profile. A method for avoiding moving obstacles is also implemented. Simulation and experimental results showed good agreement with each other. The main contribution of this paper is in developing a temporal planning algorithm, which is capable of moving on an uneven surface (graded non-flat), and its implementation on the mobile robot at the robotics lab in the University of Saskatchewan. This algorithm is computationally very efficient as it requires low computation cost and does not involve major iterations.

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The design and management of infrastructure is a significant challenge for traffic engineers and planners. Accurate traffic characterization is necessary for effective infrastructure utilization. Thus, models are required that can characterize a variety of conditions and can be employed for homogeneous, heterogeneous, equilibrium and non-equilibrium traffic. The Lighthill-Whitham-Richards (LWR) model is widely used because of its simplicity. This model characterizes traffic behavior with small changes over a long idealized road and so is inadequate for typical traffic conditions. The extended LWR model considers driver types based on velocity to characterize traffic behavior in non lane discipline traffic but it ignores the stimuli for changes in velocity. In this paper, an improved model is presented which is based on driver reaction to forward traffic stimuli. This reaction occurs over the forward distance headway during which traffic aligns to the current conditions. The performance of the proposed, LWR and extended LWR models is evaluated using the first order upwind scheme (FOUS). The numerical stability of this scheme is guaranteed by employing the Courant, Friedrich and Lewy (CFL) condition. Results are presented which show that the proposed model can characterize both small and large changes in traffic more realistically. Doi: 10.28991/cej-2021-03091632 Full Text: PDF

The anisotropic Zheng and Jiang models characterize traffic with a constant rearward velocity. They also consider a constant driver sensitivity which can result in unrealistic behavior. In this paper, a new anisotropic model based on a variable rearward velocity is proposed. The transition width, driver reaction, and sensitivity at transitions are used to characterize this velocity. This width impacts traffic alignment with forward conditions and driver reaction can be aggressive, slow or typical. The performance of the proposed, Zheng and Jiang models is evaluated over a 2000 m circular (ring) road with an inactive traffic bottleneck. Results are presented which show that traffic evolution with the proposed model is more realistic than with the Zheng and Jiang models. INDEX TERMS Anisotropic model, driver reaction, rearward velocity, transition dynamics, Zheng model, Jiang model.