Vehicle Distribution and Routing in a Large Automated Transportation Network
Alan J. Pue
Doctoral Dissertation, Year: 1981, Advisor: John S. Baras
The problem of efficiently routing vehicles from many origins to many destinations in a large Automated Guideway Transit (AGT) network is formulated into an optimization problem. First, a system using a vehicle-follower strategy is modeled at various levels of complexity by aggregating states over sections of guideway link. At the simplest level, the state variables are the link densities while a more complex model includes the specific vehicle-follower control dynamics by defining a link velocity as an additional state variable. Discrete vehicle simulations of a merge junction, diverge-merge junction, and a station are used to show the models adequately represent actual link density and delay. All models are nonlinear and nonconvex.
An optimal control problem is formulated by devising a performance index based on total system delay (time averaged travel time) subject to the dynamic flow constraints of the network. Duality theory is applied to decompose the overall network dynamics into vehicle type (origin-destination pair) subnetwork constraints that are decoupled into vehicle type (origin-destination pair) subnetwork constraints that are decoupled in vehicle type state and control but coupled through the interconnection variables of total density and total control. The resulting structure of the subnetwork dynamics is then exploited to allow a distributed control computation where each node in the network only needs to communicated with neighboring nodes to optimize the dual function objective. An upper level coordinating control, localized to each link, seeks to satisfy the interconnection constraint that the sum of individual vehicle type densities is equal to the total vehicle density on the link. As a result, all control computations can be performed in a completely decentralized manner where information exchange only occurs between physically adjacent wayside control computers. Convergence of the algorithm is proven.
Computational studies of a 4 station, 58 link network is used to demonstrate the efficacy of the proposed algorithm. It is shown and proven that no duality gap exists for the problem (convex cost and non-convex constraints). Moreover, several suboptimal control schemes with reduced computational requirements are presented and evaluated.