Dynamic identification of origin–destination matrices in the presence of incomplete observations

It is quite often in practice that observation information of traffic flows is incomplete due to failures of facilities or insufficient installment of sensors. In this paper, we investigate problems of dynamic identification of origin–destination matrices when traffic counts are unavailable in some entrances and/or exits of a traffic system. To deal with non-linearity and inestimability problems in conventional research frameworks, identification problems with incomplete information are reformulated as optimization problems with linear equality constraints and non-negative inequality constraints. An algorithm is then suggested for identification of origin–destination matrices with incomplete observation information. Finally, numerical examples are provided to illustrate the proposed algorithm for some incomplete information patterns.