Network Capacity Maximization Using Route Choice and Signal Control with Multiple OD Pairs

In this paper, we investigate a hybrid dynamical system which incorporates flow swap process, green-time proportion swap process, and flow divergence for a general network with multiple Origin-Destination (OD) pairs and multiple routes, where flow swap process is specified in which traffic swaps from more costly to less costly input links, green-time proportion swap process is specified in which green time at each intersection swaps from less pressurized stages to more pressurized stages, flow may diverge at each intersection from one OD pair to other OD pairs. Unlike the dynamical system model, where bottleneck delays need to be intentionally constructed to yield the equilibrium flow vector and green-time proportion vector, we propose a novel control policy to fill the gap by only adjusting the green-time proportion vector. We derive a sufficient condition for the existence of equilibrium of the dynamical system under the mild constraints that 1) the travel cost function and stage pressure function should be continuous functions and 2) the flow and green-time proportion swap processes project all flow and green-time proportion vectors on the boundary of the feasible region onto itself. We derive the condition of unique equilibrium for fixed green-time proportion vector and show that with varying green-time proportion vector, the set of equilibria is a compact, non-convex set, and with the same partial derivative of travel cost function with respect to the flow and green-time proportion vectors. Finally, we prove the stability of the proposed dynamical system by using Lyapunov stability analysis.