  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.
