provided a linear approximation of the relationship between O-D flows and link flows, based on a marginal computation method that performs a perturbation analysis using the kinematic wave theory.
, where the approximation of the DTA with the QDTA model to solve the O-D estimation problem was able to generate interesting results in terms of traffic measures reproduction.
This condition can be alternatively seen from the supply side by producing a minor change to the network features, for instance, by changing the speed limit on a link and detecting only local changes of traffic conditions or, from the demand side, by slightly changing the demand, for instance, adding one vehicle to an O-D pair, and detecting only negligible changes of traffic flow patterns.
[x.sub.i] = estimated O-D matrix for departing time interval i, i = 1 ...
(4) We also provide an approach, accompanying the initial application to categorical O-D pairs on the Shanghai metro network, for determining the theoretical maximum accuracy of our proposed assignment model.
Section 4 is an initial application of the proposed approach to the Shanghai metro network, demonstrating how to assign passenger flows for categorical O-D pairs and determine the theoretical maximum accuracy of the proposed assignment model.
These data have been used for O-D matrices estimation [11, 12], demand analysis [13, 14], travel behavior analysis , operational management, public transit planning [16-18], and so on.
Chan  developed two applications based on Oyster card data in the London Underground: one of these estimated an O-D flow matrix, while the other constructed rail service reliability metrics.
The reserve capacity was proposed as the largest multiplier [mu] applied to a given existing O-D demand matrix that can be allocated to a transportation network without violating any individual link capacity .
In the above model, the upper-level model maximizes the O-D matrix multiplier without violating the capacity constraints (2) for every individual link.
The result of the reserve capacity model which is considered may underestimate the capacity of the passenger network, because only the existing O-D demand pattern that is more congruous with the network topology would achieve a higher value of network capacity .
(i) It is hard to decide an exact existing (or predetermined) O-D matrix, because the real travel demand pattern is changing at different hours every day and different days every week.