Interactions between driver information,route choice,and optimal signal timing on a simple network

The interaction between driver information, route choice, and optimal traffic signal settings was investigated using a simple two-route system with a single “T” intersection and a fixed O-D demand. The logit model and the method of successive averages (MSA) were used to calculate the route choice probabilities and the stochastic equilibrium assignment. Given an assignment, signal settings which minimized average intersection delay were calculated; flow reassignment and new optimal signal settings were then obtained and this iterative process continued until convergence. The calculations were performed either directly in a combined assignment/signal optimization model or in stages using the output flows of an assignment model as inputs to TRANSYT-7F and iterating between the two models. Results show that a unique joint signal timing/assignment equilibrium is reached in all cases provided that a certain precision in drivers' perceptions is not reached. If driver information increases to this precision (bifurcation point) and beyond, results show clearly that the unique joint signal timing/assignment equilibrium no longer exists. In fact, three joint equilibria points exist after the bifurcation point. Two of these points are stable and one is not. It was found that the system yields the lowest total intersection delay when the joint equilibrium is such that all traffic and hence the major part of green time is assigned to only one of the two routes. Although this may not be feasible to implement in practice, the results indicate clearly for this simple example that there is a trade-off between a system with minimum total delay but no unique joint signal-settings/assignment equilibrium (achieved when drivers have nearly perfect information about the system) and a system with a unique joint equilibrium but with higher total delay (achieved when drivers have reasonably good but somewhat limited information). In most cases the second system seems appropriate for a number of practical reasons.