Global Optimization of Signal Settings Subject to Either System Optimal or User Equilibrium Traffic Assignment

1 BACKGROUND In the last three decades various researchers had been facing the problem of maximizing global network performances by optimizing traffic signals. The main difficulty of the problem arises from the existing interaction between network performance and users' route choice. In fact, drivers make their travel choices in order to minimize their own travel time. Simultaneous choices performed by different drivers lead to the so-called descriptive User Equilibrium (UE). As traffic controller sets signals on the basis of the observed traffic patterns, its action changes the network performance and so stimulates drivers to adjust their route choice in order to find their new minimal paths. A wide review of the scientific literature on this matter can be found in Cipriani and Gori (2000) or in Tale and Van Zuylen (2000). In the following, we deal with only some fundamentals steps, which are necessary to introduce the object of the paper. Allsop (1974) and Gartner (1974) proposed independently each other an iterative approach that integrates signal settings and traffic assignment, in order to simulate the actual process where signal control and route choice are adjusted reciprocally. Smith (1979) pointed out that it is not guaranteed that such an iterative method converges even to a local optimum. Indeed, it may also lead to increase the total travel time. Moreover, it has been observed that also the actual process of adjusting signal settings depending on current traffic conditions, as performed by flow-responsive signals, may worsen the total travel time on the network even by 30% (Smith, 1980). Thus, Smith and Van Vuren (1993) proposed a new signal policy (called Po) that ensures consistency with user equilibrium. Cantarella and Sforza (1995) showed that flow responsive policies that set signals independently each other are sub-optimal with respect to global policies where all signals are set to minimize one objective function describing the global network performance, according to user equilibrium 737