## 5 Conclusions  
The stability of traffic equilibria in a road network with adaptive signal control is a particularly challenging issue since the responsiveness of the signal settings to route choices introduces an additional dimension into the day-to-day dynamics of the traffic system. In this study, the joint evolution of traffic flows and adaptive signal control has been investigated by means of a nonlinear dynamical systems approach, with a specific focus on the fixed-point stability property. We have shown how a Logit form signal setting policy can be used, upon the proper calibration of the embedded control parameter, to counter the emergence of instabilities possibly arising as a consequence of various behavioral factors and network conditions. For the sake of analytical tractability, the theoretical part of this study has addressed the very simple case of a two-route network with an intersection controlled by a two-phase traffic signal. The subsequent analysis conducted on a small but somewhat more realistic network appears to support numerically the findings emerging from the analytical investigation. Nonetheless, we are aware that more complicated scenarios in terms of network size and control strategies should be considered in future research in order to strengthen the conclusions of this study. The findings of this research may have significant policy implications for the design and evaluation of integrated traffic management and information systems. The state of a traffic system and the long-term outcome of its dynamic evolution are the result of the interplay between a number of factors related to the physical and functional configuration of the network and to the behavioral features of the users. In general terms, stability is ensured as long as the parameters representing these factors remain within certain ranges. Since tradeoffs between the effects of the influencing factors are possible, the idea underlying the present study is that properly calibrated signal control can be leveraged to compensate for the destabilizing effect of one or more of the other system parameters. The examples presented in this paper demonstrate, in particular, that the proposed control policy can be used, up to a certain limit, to offset the instability likely to arise in ATIS environments as a result of the dissemination of accurate traffic information and navigational advice. Our analysis also shows that the range of signal-setting options available to the traffic manager to preserve equilibrium stability may be significantly restricted by increasing levels of network congestion. Moreover, a comparison between the Logit control policy and the Equisaturation signal setting method was carried out in this study. Although the stability regions in terms of \(\theta\) appear to be the same for both policies, our results indicate that the former may be instrumental in achieving a lower average intersection delay at equilibrium. An additional advantage of the proposed policy over Equisaturation is that the embedded control parameter may be calibrated to optimize objectives other than delay minimization while preserving fixed-point stability. Further developments of the research described in this paper should pursue the implementation of the proposed modeling approach on networks of realistic size and structure. In addition, the approach adopted in this study could be refined by introducing a rigorous delay minimization process aimed at the determination of optimal values of the control parameter \(\gamma\). The analyses presented in this paper were purposely designed to assess the parametric effect of \(\theta\) on the fixed-point stability region of the combined route choice-signal control problem. However, it is envisaged that in practical applications of the proposed approach, a single value of the parameter could be of interest. Such a fixed value should be the result of a calibration process reflecting the average level of drivers' information about travel times in the specific situation being considered.