Abstract
A stochastic continuous-time aggregate variable model which emphasises the stochastic elements of traffic flow on motorways is presented. The model consists of a nonlinear dynamic system with a martingale forcing term. The problem of estimating local traffic conditions from noisy disaggregate data (detector measurements) is discussed. Using results of abstract martingale theory with respect to nonlinear optimal filtering for counting process observations a recursive estimation algorithm is obtained. The algorithm, which is very appropriate for use in automatic motorway control and surveillance systems, performs very well. Finally, the optimal control of traffic flow is discussed with an emphasis on speed control.