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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Three-detector problem and Newell's method ： ウィキペディア英語版 Three-detector problem and Newell's method The Three-detector problem〔Daganzo, Carlos. 1997. Fundamentals of transportation and traffic operations. Oxford: Pergamon.〕 is a problem in traffic flow theory. Given is a homogeneous freeway and the vehicle counts at two detector stations. We seek the vehicle counts at some intermediate location. The method can be applied to incident detection and diagnosis by comparing the observed and predicted data, so a realistic solution to this problem is important. Newell G.F.〔Newell, G. F. 1993. "A simplified theory of kinematic waves in highway traffic. Part I, General theory". Transportation Research. Part B, Methodological. 27B (4).〕〔Newell, G. F. 1993. "A simplified theory of kinematic waves in highway traffic. Part II. Queuing at freeway bottlenecks". Transportation Research. Part B, Methodological. 27B (4).〕〔Newell, G. F. 1993. "A simplified theory of kinematic waves in highway traffic. Part III. Multi-destination flows". Transportation Research. Part B, Methodological. 27B (4).〕 proposed a simple method to solve this problem. In Newell's method, one gets the cumulative count curve (N-curve) of any intermediate location just by shifting the N-curves of the upstream and downstream detectors. Newell's method was developed before the variational theory of traffic flow was proposed to deal systematically with vehicle counts.〔Daganzo, Carlos F. 2005. "A variational formulation of kinematic waves: solution methods". Transportation Research. Part B, Methodological. 39B (10).〕〔Daganzo, Carlos F. 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions". Transportation Research. Part B, Methodological. 39B (2).〕〔Daganzo, Carlos F. 2006. "On the variational theory of traffic flow: well-posedness, duality and applications". Networks and Heterogeneous Media. 1 (4).〕 This article shows how Newell's method fits in the context of variational theory. == A special case to demonstrate Newell's method == Assumption. In this special case, we use the Triangular Fundamental Diagram (TFD) with three parameters: free flow speed $v\_f$, wave velocity -w and maximum density $k\_j$ (see Figure 1). Additionally, we will consider a long study period where traffic past upstream detector (U) is unrestricted and traffic past downstream detector (D) is restricted so that waves from both boundaries point into the (t,x) solution space (see Figure 2). The goal of three-detector problem is calculating the vehicle at a generic point (P) on the "world line" of detector M (See Figure 2). Upstream. ''Since'' the upstream state is uncongested, there must be a characteristic with slope $v\_f$ that reaches P from the upstream detector. Such a wave must be emitted $\backslash tau\_1=L\_U/v\_f$ times unit earlier, at point P' on the figure. ''Since'' the vehicle number does not change along this characteristic, we see that the vehicle number at the M-detector calculated from conditions upstream is the same as that observed at the upstream detector $\backslash tau\_1$ time units earlier. ''Since'' $\backslash tau\_1$ is independent of the traffic state (it is a constant), ''this result is equivalent to'' shifting the smoothed N-curve of the upstream detector (curve U of Figure 3) to the right by an amount $\backslash tau\_1$. Downstream. Likewise, ''since'' the state over the downstream detector is queued, there will be a wave reaching P from a location $P\_2$ with wave velocity . The ''change'' in vehicular label along this characteristic can be obtained from the moving observer construction of Figure 4, for an observer moving with the wave. In our particular case, the slanted line corresponding to the observer is parallel to the congested part of TFD. This means that the observer flow is independent of the traffic state and takes on the value: $k\_j(-w)$. Therefore, in the ''time'' that it takes for the wave to reach the middle location, $\backslash tau\_2=L\_D/(-w)$, the change in ''count'' is $\backslash delta=k\_j(-w)\backslash tau\_2=k\_jL\_D$; i.e., the change in count equals the number of vehicles that fit between M and D at jam density. ''This result is equivalent to'' shifting the D-curve to the right $\backslash tau\_2$ units and up $\backslash delta$ units. Actual count at M. In view of the Newell-Luke Minimum Principle, we see that the actual count at M should be the lower envelope of the U'- and D'-curves. This is the dark curves, M(t). The ''intersections'' of the U'- and D'- curves denote the shock's passages over the detector; i.e., the times when transitions between queued and unqueued states take place as the queue advances and recedes over the middle detector. The ''area'' between the U'- and M-curves is the delay experienced upstream of location M, ''trip times'' are the horizontal separation between curves U(t), M(t) and D(t), ''accumulation'' is given by vertical separations, etc. Mathematical expression. In terms of the function N(t,x) and the detector location ($x\_u$, $x\_m$, $x\_d$) as follows: : $$ N(t,x_m)= \min\ \qquad (1) where $L\_U=x\_m-x\_u$ and $L\_D=x\_d-x\_m$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Three-detector problem and Newell's method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.