Go back to Carlos Daganzo's Publications PageCell-transmission models of highway traffic are discrete versions of the simple continuum (kinematic wave) model of traffic flow that are convenient for computer implementation. They are in the Godunov family of finite difference approximation methods for partial differential equations. In a cell-transmission scheme one partitions a highway into small sections (cells) and keeps track of the cell contents (number of vehicles) as time passes. The record is updated at closely spaced instants (clock ticks) by calculating the number of vehicles that cross the boundary separating each pair of adjoining cells during the corresponding clock interval. This average flow is the result of a comparison between the maximum number of vehicles that can be sent by the cell directly upstream of the boundary and those that can be received by the downstream cell.
The sending (receiving) flow is a simple function of the current traffic density in the upstream (downstream) cell. The particular form of the sending and receiving functions depends on the shape of the highway’s flow-density relation, the proximity of junctions and on whether the highway has special (e.g., turning) lanes for certain (e.g., exiting) vehicles. Although the discrete and continuum models are equivalent in the limit of vanishingly small cells and clock ticks, the need for practically sized cells and clock intervals generates numerical errors in actual applications.
This paper shows that the accuracy of the cell-transmission approach is enhanced if the downstream density that is
used to calculate the receiving flow(s) is read R clock intervals earlier than the current time, where R is a non-negative
integer that should be carefully chosen. The rationale for the introduction of this lag is explained in the paper. The
lagged cell-transmission model is related (but not equivalent) to both Godunov’s first order method for general flow-density
relations and Newell’s exact method for concave flow density relations. It is easier to apply and more general than the
latter, and more accurate than the former. In fact, if the flow-density relation is triangular and the lag is chosen
optimally, then the lagged cell-tansmission model is a conservative, second order, finite difference scheme. As a result, very
accurate results can be obtained with relatively large cells. Accuracy formulae and sample illustrations are presented for
both the triangular and the general case.
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