道路交通信號控制機(jī)無電纜協(xié)調(diào)控制的實(shí)現(xiàn)（開題報(bào)告+論文+外文翻譯+文獻(xiàn)綜述+答辯PPT）,道路,交通信號,控制,節(jié)制,電纜,協(xié)調(diào),調(diào)和,實(shí)現(xiàn),開題,報(bào)告,講演,呈文,論文,外文,翻譯,文獻(xiàn),綜述,答辯,ppt The traffic flow controlled by the traffic lights in the speed gradient continuum model Rui Jiang*, Qing-Song Wu Abstract In this paper, we have studied the traffic flow controlled by the traffic lights on a circuit road using the SG model. The single light situation, the synchronized light strategy, the green wave light strategy and the random switching light strategy are investigated. The spatio-temporal patterns are presented. Our simulations show that the plot of flow against density depends mainly on the distance between the lights and the cycle time. The capacity decreases with the increase of cycle time. For small distance between the lights, the lights do not behave as a bottleneck and the plot of flow against density looks just like a fundamental diagram. For the non-equidistant traffic lights situation, the results depend on the distribution of the distance between the lights. ? 2005 Elsevier B.V. All rights reserved. Keywords: Traffic flow; Traffic light; Speed gradient model 1. Introduction Mobility is nowadays one of the most important significant ingredients of a modern society, so the investigation of traffic flow has been given considerable attention for several decades [1-18]. A variety of approaches have been applied to describe the collective properties of traffic flow. Traditionally, two types, microscopic and macroscopic models are distinguished. The former simulate the motion of every vehicle while the latter concentrate on the collective behavior of vehicles. For this reason, macroscopic models are more suitable for real-time simulations, short-term traffic predictions, developing and controlling on-line speed-control systems and evaluating average travel time, fuel consumption, and vehicle emissions, etc. The development of macroscopic traffic flow models began with the seminal LWR model presented by Lighthill and Whitham [7] and Richards [8]. The LWR model is known as the kinematic wave model, and it employs the conservation equation in the following form: Pt + ruTx = 0, (1) where r is the traffic density, u is the space mean speed, t and x represent time and space, respectively. For the speed u, the existence of an equilibrium speed-density relationship is assumed u = ueerT (2) Using the LWR model, a variety of simple traffic flow problems can be reproduced analytically by the method of characteristics [7] and numerically by finite differences [19]. However, the LWR model has its deficiencies, the most fatal one is that the speed is solely determined by the equilibrium speed-density relationship (2), no fluctuation of the speed around the equilibrium values is allowed, thus, the model is not able to predict interesting non-equilibrium traffic flow phenomena such as "clusters" and ‘‘stop-and-go waves’’ etc. In order to overcome the shortcomings in the LWR model, the high-order models are introduced by replacing equilibrium speed-density relationship (2) with a dynamic speed evolution equation. These high-order models are categorized into two classes. In the first class of models, the dynamic speed evolution equation has the form: where Tr is relaxation time, c0 is propagation speed of small disturbance. The left-hand side of Eq. (3) is the acceleration of vehicles. The first term on the right-hand side of Eq. (3) is relaxation term, representing the process that driver adjusts the speed of the vehicle to equilibrium; the second term is anticipation term, representing the process that driver reacts to the traffic ahead. c0 has different expression in different models. For example, c0 is taken as a constant in Payne model [9] while c0 — \pu'e(p)\ in Zhang's non-equilibrium model [10]. However, there is a common problem in this class of models. For the hyperbolic equation system constituted by Eqs. (1) and (3), there are two characteristic speeds X\—u t c0 and l2 — u2c0, where the characteristic speed l1 — u t c0 is always greater than the macroscopic traffic speed u, which destroys the basic discipline of traffic flow—vehicles are anisotropic particles, they only respond to the stimuli ahead and are not affected by the vehicles behind. The problem leads to negative speed and wrong-way travel as pointed out by Daganzo [20].1 Recently Jiang et al. [11,21] as well as Aw and Rascle [22] and Zhang [23] and Xue and Dai [24] proposed a second class of high-order models. In this second class of models, the dynamic speed evolution equation has form: where c0 is taken as a constant in Jiang et al's model2 while c0 — pu'e(p)\ in Aw and Rascle's model and Zhang's model. 3These models are different from the first class of models in that the anticipation term is a speed gradient term instead of a density gradient term. Thus, hereafter these models are referred to as speed gradient (SG) models. The SG model equation system consisting of Eqs. (1) and (4) has two characteristic speeds: l1 — u — c0 and l2 — u. This enables the model not to produce the characteristic speed greater than the macroscopic traffic speed. Thus, it can embody the property that vehicles are anisotropic and does not exhibit the wrong-way problem. In this sense, the SG model is more realistic for describing the traffic flow. In urban traffic, the flow is controlled by traffic lights. The traffic signal is an essential element for managing the transportation network. When the traffic is light, the traffic signals usually require no special attention. In contrast, when the traffic demand is heavy, the operation of traffic signals requires careful regulation. Given its importance, the research on traffic light control is by no means complete. Brockfeld et al. [27] have studied optimizing traffic lights for city traffic. They have shown that the flow throughout is improved by traffic light control strategies. They have also shown that the derivation of the optimal cycle time in the network can be reduced to a simpler problem of a single street. A number of traffic signal control models have developed in the past. Basically, they can be classified by two approaches. The first approach is developed mainly for undersaturated traffic. Vehicles move more or less at the design speed and there is no congestion. The other one is developed mainly for oversaturated traffic. The queues persist and cannot be cleared totally. With the transition from undersaturated to oversaturated traffic remaining unclear, it is hard to judge how to switch the operation from one mode to the other, which has a crucial impact on the rush hour traffic in a big city. Recently, Huang and Huang [28] and Sasaki and Nagatani [29] have studied the problem. Huang and Huang use a cellular automaton model while Sasaki and Nagatani use an optimal velocity car-following model. Both are microscopic models. They both found that the traffic saturated in certain density range and the value of the saturated current does not depend on the cycle time and the control strategies. In this paper, we study the problem from the macroscopic point of view. For the purpose, we use the SG model for simulation. Our study shows that quite different results are obtained from those of microscopic models, in particular, the saturated current depends on the cycle time. The paper is organized as follows. In Section 2, the numerical scheme is briefly reviewed and the traffic light conditions are presented. In Section 3, the simulations are carried out and the results are analyzed and compared with those from microscopic simulations. The conclusions are given in Section 4. 3.1. Single light In this subsection, we investigate the situation that there is only one traffic light on the road. The road is assumed to be a ring, i.e., the periodic boundary condition is adopted. We denote the length of the road as L. In Fig. 1, we show the plot of the flow against the density, where L — 5000 m, T — 100 s, a = 0:5. Here T is the cycle time of the light and a is the ratio of red light. For a realistic point of view, T is restricted in the range 20^00 s. When the density is low erorc1T, the flow increases with increasing density. When the density is higher than the critical density rc1, the flow saturates at the constant capacity Q. When the density increases furthermore and is higher than the second critical density rc2, the flow decreases with increasing density. This is as expected, i.e., the traffic light behaves as a bottleneck. We study the spatio-temporal pattern of the traffic flow induced by the traffic light. In Fig. 2(a), we show the typical pattern in the low-density range erorc1T, where the density r — 0:02: The cars move almost freely except near the light and the traffic jam located at the traffic light. Due to the existence of the traffic light, the density fluctuations are observed. In Fig. 2(b), we show the typical pattern in the high-density range er4rc2T, where the density r — 0:11: The densities are almost. than that in Fig. 2(a). Downstream of the light, a stable low-density region occurs. With the increase of the density, the traffic jam becomes wider and wider and the low-density region shrinks (cf. Fig. 2(d) where r — 0:07). Next we investigate the effect of T. In Fig. 3, we show the plots of the flow against the density under different T with L fixed at 5000 m. One can clearly see that with the increase (decrease) of T, the capacity Q decreases (increases). Moreover, with the increase of T, the dependence of Q on T becomes weaker. When T is larger than 300 s, Q is almost independent of T. The dependence of Q on T may be explained as follows. When the cycle time is short, the drivers of the queued cars remain sensitive to the car ahead. Once its preceding car starts, he will start his car almost with no delay. Moreover, the length of the queue is small when the cycle time is short. For the above two reasons, the total delay of the cars are relatively small. This leads to large capacity. When the cycle time is long, the drivers are not so sensitive and the length of the queue is large. Therefore, the total delay of the cars is relatively large. This results in small capacity. In this sense, the SG model has implicitly taken the sensitivity of drivers into account.4 We point out that the field data are needed to examine these results. This is due to that our results are somewhat different from those of microscopic simulations and  presently we do not know the exact origin of the difference.5 For example, in the work of Tomer et al. [32], where a stochastic car-following model is used, it is shown that the largest capacity is reached at an intermediate cycle time. In the work of Sasaki and Nagatani [29], where the optimal velocity model is used and Huang and Huang [28], where the Nagel-Schreckenberg cellular automaton model is used, it is shown that the capacity is independent of the cycle time. In Fig. 4, we show the plots of the flow against the density under different L, and with T fixed at 100 s. One can see that for not so small L, the results are qualitatively unchanged. The variation of L only affects rc1 and rc2: rc1(rc2) increases (decreases) with the decrease of L. But when L is larger than 10,000 m, the plot is almost independent of L. However, we notice that for L — 1000 m, different results are observed. For the case, there is no saturation of traffic flow. The flow first increases with the increase of density. After it reaches a maximum, it decreases with the increase of density. This is because the system is so small that the stable low density as in Figs. 2(c) and (d) cannot be maintained. For example, in Fig. 5, we show the spatio-temporal pattern 3.2. Synchronized traffic lights In the synchronized traffic light situation, there is more than one light on the road and all lights change simultaneously from red (green) to green (red). Firstly, we study the case where all lights are equidistant. We denote the distance between two neighbor lights as D and the number of lights as N. In Fig. 1, we also show the relationship between the flow and the density for N — 2, D — 5000 m, T — 100 s, a — 0:5. One can see that the results are the same as in single light case. In Fig. 6, we show the spatio-temporal pattern of the traffic flow induced by the traffic light in this case. The periodic structures are observed, and the patterns in each period are almost the same as the corresponding patterns in Fig. 2. We have carried out the simulations under different values of N, D, and T. It is found that whatever N is, the plot of the flow against the density is the same as that in single light case provided D — L and D is not so small and the cycle time is the same. The periodic structures exist and the number of period equals to N. When D is small, the flow is slightly higher in the intermediate density range in the synchronized traffic light situation. For example see Fig. 7. Next we study the case where the lights are not equidistant. A naive expectation is that the results are solely determined by the minimum distance between the successive lights. However, it is not the case. This can be seen from Fig. 8 where N — 4 and T—lOOs, curve 2 is the result of equidistant traffic lights with D — 1000 m, curve 3 is the result of equidistant traffic lights with D — 2000 m, curve 1 is the result of non-equidistant traffic lights in which lights 1 and 2 and lights 1 and 4 are 2000 m from each other while lights 2 and 3 and lights 3 and 4 are 1000 m from each other (see Fig. 9). Curve 1 is between curves 2 and 3. This means the results are determined by the distribution of the distance between the lights. 4. Conclusion In this paper, we have studied the traffic flow controlled by the traffic lights on a circuit road using the SG model. The single light situation, the synchronized light strategy, the green wave light strategy and the random switching light strategy are investigated. The spatio-temporal patterns are presented. From the simulations, one can see that the single light situation, the synchronized light strategy and the green wave light strategy may be viewed as special cases of the random switching light strategy. Our simulations show that the plot of flow against density depends mainly on the distance between the lights and the cycle time. The capacity decreases with the increase of cycle time. For small distance between the lights, the lights do not behave as a bottleneck and the plot of flow against density looks just like a fundamental diagram. For the non-equidistant traffic lights situation, the results depend on the distribution of the distance between the lights. From our simulation, we may draw the conclusion that if the distance between the lights is small, the benefits of green wave strategy are obvious. We hope the result may be helpful for traffic engineering. In our future work, we will investigate the situation of the mixed traffic flow controlled by the traffic lights and compare the results with the present ones.