Developing a Stochastic Model of Queue Length at a Signalized Intersection

Abstract

This paper proposes a stochastic hybrid dynamic model of the queue-length at a signalized intersection. The flow rate along with traffic light variables are used to define the evolution of the queue-lengths and it evolves as a piecewise linear function, being the integral of the difference between arrival and departure rate; these arrival and departure rates are described by stochastic AR model with mode-dependent parameters. The mode changes are modeled by a first order 2 or 3-state Markov process. The traffic flow rate is described using a mode-dependent first autoregressive (AR) stochastic process. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia and synthetic data from VISSIM traffic simulator. The model thus obtained via EM parameter estimation is validated by using the online particle filter. This technique can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator as crucial part for the synthesis of traffic light control.