The most likely trip matrix estimated from traffic counts

Markov models for Bayesian analysis about transit route origin–destination matrices

“…This approach is much cheaper than the method of large-scale sampling. For economic reasons, however, the number of selected links is relatively small in practice, resulting in a highly underspecified problem with a huge number of unknown parameters (entries) but many fewer observations (see e.g., Van Zuylen and Willumsen 1980). Furthermore, in some applications, even were counts to be observed on every link, the O-D matrix would still be underspecified (Hazelton, 2001;Li 2005).…”

“…The solution obtained by Van Zuylen and Willumsen (1980) (12) is given by: satisfy the following recursive equations…”

“…A much better approach in terms of utilizing prior information was developed by Maher (1983) and Hazelton (2001), who carried out Bayesian analysis to combine prior information with current observations on traffic flow. Recently, Li (2005) has developed a general approach to draw inference about O-D matrices; this approach can be nicely linked to many existing methods, such as the Bayesian approaches of Maher (1983) and Hazelton (2001), and the maximum entropy method of Van Zuylen and Willumsen (1980).…”

“…In practice, large-scale direct sampling for statistical inference for O-D matrices is usually too expensive (Van Zuylen and Willumsen 1980;Li, 2005;Li and Cassidy, 2007). A common approach for the estimation of an O-D matrix is to calculate its entries using traffic counts obtained on pre-selected links of a transport network, without imposing any specific model on the entries.…”

“…In order to deal with this underspecified problem, Van Zuylen and Willumsen (1980) proposed a maximum entropy method that determines an O-D matrix such that the chosen trip matrix adds as little information as possible to the knowledge contained in the data collected on pre-selected links of a transport network.…”