Estimating the Critical Density of Road Transportation Networks using Infinitesimal Perturbation Analysis of Hybrid Systems

Abstract

Traffic congestion can be eliminated by restraining the number of vehicles within an urban region to be below its critical density. To achieve that, [1], [2] proposed a route-reservation architecture that makes appropriate routing schedules according to a region's critical density, and controls vehicle departure times, so that vehicles arrive at their destination in the earliest possible time while avoiding roadsegments that are expected to be at their critical density. However, the critical density is not always known and may vary depending on the road conditions. In this paper, we adobe the Stochastic Fluid Modeling framework to model the critical density of a homogeneous region of the road network and employ the route-reservation scheme to control traffic within this region for congestion-free operation. To derive the critical density, we employ Infinitesimal Perturbation Analysis (IPA) that provides a stochastic approximation which can be employed in an on-line fashion to capture the dynamic changes in the critical density value as a consequence of different incidents.

Optimal Reservation Volume of Urban Roads Based on Travel Reservation Strategy

“…If no reservation section exists on path r, then ε ue,w r � 1; otherwise, ε ue,w r � 0. Equation (15) ensures that the sum of all path fows through link a is equal to q ue a . δ ue,w a,r are path-link relations.…”

“…Terefore, in recent years, scholars have preferred to mine trafc fow data to determine reservation volumes [14]. Menelaou et al [15] replaced the capacity constraint with the density constraint and used infnitesimal perturbation analysis to capture the dynamic change in the critical density value. By comparing the estimated capacity and critical density distribution function, Geistefeldt and Shojaat [16] showed that the relative variability of the capacity is lower than that of the critical density.…”