Vehicular Traffic Flow at a Non-Signalised Intersection
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1 Introduction Besides various theoretical efforts aiming to understand the basic principles governing the spatial-temporal structure of traffic flow, considerable attempts have been made towards realistic problems involving optimization of vehicular traffic flow. While the existing results in the context of highway traffic seem to need further manipulations in order to find direct applications, researches on city traffic have more feasibility in practical applications [1–4]. We believe that optimisation of traffic flow at a single intersection is a substantial ingredient for the task of global optimisation of city networks. Isolated intersections are fundamental operating units of complex city networks and their thorough analysis would be inevitably advantageous not only for optimisation of city networks but also for local optimization purposes. Recently, physicists have paid notable attention to controlling traffic flow at intersections and other traffic designations such as roundabouts [5–9]. In this respect, our objective in this paper is to study another aspect of conflicting traffic flow at intersections. In principle, the vehicular flow at the intersection of two roads can be controlled via two distinctive schemes. In the first scheme the traffic is controlled without traffic lights. In the second scheme, signalized traffic lights control the flow. In the former scheme, approaching car to the intersection yield to traffic at the perpendicular direction by adjusting its velocity to a safe value to avoid collision. According to driving rules, the priority is given to the nearest car to the intersection. It is evident that this scheme is efficient if the density of cars is low. When the density of cars increases, this method fails to optimally control the traffic and long queues may form which gives rise to long delays. At this stage the implementation of the second scheme is unavoidable. Therefore it is a natural and important question to find out under what circumstances the intersection should be controlled by traffic lights? More concisely, what is the critical density beyond which the non-signalised schemes begins to fail.
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M. Ebrahim Fouladvand and Somayyeh Belbasi
2 Description of the Problem We now present our CA model. Consider two perpendicular one dimensional closed chains each having L sites. The chains represent urban roads accommodating unidirectional vehicular traffic flow. They cross each other at the sites i1 = i2 = L2 on the first and the second chain respectively. With no loss of generality we take the direction of traffic flow in the first chain from south to north and in the second chain from east to west (see Fig. 1 for illustration). The discretisation of space is such that each car occupies an integer number of cells denoted by Lcar . The car position is denoted by the location of its head cell. Time elapses in discrete steps of Δt sec and velocities take discrete values 0, 1, 2, . . . , vmax in which vmax is the maximum velocity of cars.
Fig. 1. Intersection of two uni-directional streets.
To be more specific, at each step of tim
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