Transportation state estimation and optimization techniques aim to use accurate state representation and optimized decisions to guide planning and operational management decisions. This talk is intended to present a state-space-time (SST) based modeling framework using two representative examples, namely (i) how to estimate macroscopic and microscopic freeway traffic states from heterogeneous measurements, and (ii) how to optimize transportation systems and ride-sharing services involving vehicular routing decisions with pickup and delivery time windows (VRPPDTW).
A wide range of time-discretized network flow models have been proposed to represent transportation systems through space-time or time-expanded networks. By adding additional state dimensions (e.g., cumulative vehicle counts as macroscopic state variables, and vehicle speed as microscopic state variables), we are able to construct a systematic representation to map heterogeneous traffic measurements to essential system states through simplified kinematic wave and car following models proposed by Gordon Newell. This allows us to fully incorporate multiple data sources, including loop detector counts, vehicle travel time readings, and GPS location samples, in a consistent traffic state estimation framework to capture traffic congestion dynamics and driving behavior variations.
The state-space-time modeling framework also enables us to prebuild many complex state transition constraints into a well-structured hyper network, so that the resulting optimization model can be nicely reformulated as multi-commodity network flow models with a very limited number of side constraints. The resulting relaxed problem can be solved by computationally efficient forward dynamic programming algorithms within a Lagrangian decomposition framework. In this talk, we will walk through examples of recasting several classic transportation systems optimization problems using the SST framework, namely solving large-scale VRPPDTW problems by intelligently enumerating passenger carrying states, and considering complex signal phasing transitions in a joint signal control and routing problem.