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Cell Transmission Model (CTM) is a popular numerical method proposed by Carlos Daganzo〔Daganzo C.F., The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research Part B: Methodological, Volume 28, Issue 4, August 1994, Pages 269-287〕 to solve the kinematic wave equation.〔Lighthill and Witham, On kinematic waves: II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London (Series A). 229(1178). pp. 317-345, 1955〕〔Richards, Shock waves on the Highway. Operations Research. 4(1). pp. 42-51, 1956〕 Lebacque 〔Lebacque, The godunov scheme and what it means for first order traffic flow models. In J. B. Lesort, editor, 13th ISTTT Symposium, pages 647–678, Elsevier, New York, 1996〕 later showed that CTM is indeed the first order discrete Godunov approximation.〔Godunov, A Difference Scheme for Numerical Solution of Discontinuous Solution of Hydrodynamic Equations, Math. Sbornik, 47, 271-306, 1959〕 ==Background== CTM predicts macroscopic traffic behavior on a given corridor by evaluating the flow and density at finite number of intermediate points at different time steps. This is done by dividing the corridor into homogeneous sections (hereafter called cells) and numbering them i=1, 2… n starting downstream. The length of the cell is chosen such that it is equal to the distance traveled by free-flow traffic in one evaluation time step. The traffic behavior is evaluated every time step starting at t=1,2…m. Initial and boundary conditions are required to iteratively evaluate each cell. The flow across the cells is determined based on μ(k) and λ(k), two monotonic functions that uniquely define the fundamental diagram as shown in Figure 1. The density of the cells is updated based on the conservation of inflows and outflows. Thus, the flow and density are derived as: Where: and represent density and flow in cell i at time t. Similarly , , ,and represents jam density, capacity, wave speed, and free-flow speed respectively of the fundamental diagram. File:Demand_and_supply_functions.gif|Figure 1. Demand and supply functions (Figure obtained from Laval 〔Laval J. A. Hybrid Models of Traffic Flow: Impacts of Bounded Vehicle Accelerations. Ph.D. dissertation, UC Berkeley, 2004〕 CTM produces results consistent with the continuous Kinematic wave equation when the density specified in the initial condition changes gradually. However, CTM replicates discontinuities and shock that take a span of few cells of space but moves at correct speed predicted by the Kinematic wave equation. It was observed that as time passes, the CTM approximations result in spreading the shock to a growing number of cells. To eliminate spreading of certain shocks, Daganzo (1994) proposed a modification to the CTM that ensures shocks separating a lower upstream density and greater downstream density do not spread. CTM is robust and the simulation results do not depend on the order in which the cells are evaluated because the flow entering a cell is dependent only on the current conditions within the cell and is unrelated to the flow exiting the cell. Thus, CTM can be applied for the analysis of complex networks and non-concave fundamental diagrams. 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「Cell Transmission Model」の詳細全文を読む スポンサード リンク
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