2012/11/19 by Ke Han, Han, Ke, Terry L. Friesz +3
Mathematics · #90B20 #90B50 #90C11 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:90B20 #msc:90B50 #msc:90C11
paper · pdf · doi:10.48550/arxiv.1211.4625
15 pages, 7 figures, current version is accepted for presentation at the 92nd Annual Meeting of Transportation Research Board
arxiv created 2012/11/19 · arxiv updated 2012/11/21
This paper is concerned with adaptive signal control problems on a road network, using a link-based kinematic wave model (Han et al., 2012). Such a model employs the Lighthill-Whitham-Richards model with a triangular fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is applied so that the system dynamics can be determined without knowledge of the traffic state in the interior of each link. A Riemann problem for the signalized junction is explicitly solved; and an optimization problem is formulated in continuous-time with the aid of binary variables. A time-discretization turns the optimization problem into a mixed integer linear program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang, 2004; Lo, 1999b), the proposed framework does not require modeling or computation within a link, thus reducing the number of (binary) variables and computational effort. The proposed model is free of vehicle-holding problems, and captures important features of signalized networks such as physical queue, spill back, vehicle turning, time-varying flow patterns and dynamic signal timing plans. The MILP can be efficiently solved with standard optimization software.