Biblio

We consider global stability of a flow network model for vehicular traffic. Standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions. In this paper, we show that the network model nonetheless exhibits a mixed monotonicity property. Mixed monotonicity allows us to prove global asymptotic stability by embedding the system in a larger system that is monotone.

Abstract We present an efficient computational procedure for finite abstraction of discrete-time mixed monotone systems by considering a rectangular partition of the state space. Mixed monotone systems are decomposable into increasing and decreasing components, and significantly generalize the well known class of monotone systems. We tightly overapproximate the one-step reachable set from a box of initial conditions by computing a decomposition function at only two points, regardless of the dimension of the state space. We first consider systems with a finite set of operating modes and then extend the formulation to systems with continuous control inputs. We apply our results to verify the dynamical behavior of a model for insect population dynamics and to synthesize a signaling strategy for a traffic network.

Abstract We study the problem of selecting offsets of the traffic signals in a network of signalized intersections to reduce queues of vehicles at all intersections. The signals in the network have a common cycle time and a fixed timing plan. It is assumed that the exogenous demands are constant or periodic with the same period as the cycle time and the intersections are under-saturated. The resulting queuing processes are periodic. These periodic processes are approximated by sinusoids. The sinusoidal approximation leads to an analytical expression of the queue lengths at every intersection as a function of the demands and the vector of offsets. The optimum offset vector is the solution of a quadratically constrained quadratic program (QCQP), which is solved via its convex semidefinite relaxation. Unlike existing techniques, our approach accommodates networks with arbitrary topology and scales well with network size. We illustrate the result in two case studies. The first is an academic example previously proposed in the literature, and the second case study consists of an arterial corridor network in Arcadia, California.