  A control scheme for the multi-gated perimeter traffic flow control problem
of cities is presented. The proposed scheme determines feasible and optimally
distributed input flows for the various gates located at the periphery of a
protected network. A parsimonious model is employed to describe the traffic
dynamics of the protected network. To describe traffic dynamics outside of the
protected area, the state-space model is augmented with additional state
variables to account for vehicle queues at store-and-forward origin links at
the periphery. The perimeter flow control problem is formulated as a convex
optimisation problem with finite horizon, and constrained control and state
variables. It aims to equalise the relative queues at origin links and to
maintain the vehicle accumulation in the protected network around a desired set
point, while the system's throughput is maximised. For real-time control, the
optimal control problem is embedded in a rolling-horizon scheme using the
current state of the system as the initial state as well as predicted demand
flows at entrance links. Furthermore, practical flow allocation policies for
single-region perimeter control without explicitly considering entrance link
dynamics are presented. These policies allocate a global perimeter-ordered flow
to candidate gates at the periphery of a protected network by taking into
account the different geometric characteristics of origin links. The proposed
flow allocation policies are then benchmarked against the multi-gated perimeter
flow control. A study is carried out for a 2.5 square mile protected network
area of San Francisco, CA, including fifteen gates of different geometric
characteristics. The results have showed that the proposed scheme is able to
manage excessive queues outside of the protected network and to optimally
distribute the input flows, which confirms its efficiency and equity
properties.
