Abstract
This paper proposes an approximation method of expected delay for signalized arterial roads under stochastic arrivals. This method is based on variational theory of traffic flow (VT). In VT under stochastic arrivals, traffic flow dynamics is described as the solution of the stochastic shortest path problem in the network on a space-time domain, which cannot be solved exactly. We, thus, propose the approximation method that consists of the following two procedures: (i) solution space reduction based on the characteristics of the shortest path; (ii) analytical evaluation of multiple integral by Clark approximation. Throughout the experimental comparison with a Monte Carlo simulation, we demonstrate that the error of the proposed method is extremely small. Finally, we show a case study of a coordinated traffic signal optimization as an application of the proposed method.
