###### Abstract  
Adaptive traffic signal control has the potential to promote the efficient use of road intersections, thus contributing to the effectiveness of urban traffic management schemes. However, the reaction of drivers to repeatedly updated signal settings and the ensuing route choice dynamics may trigger the emergence of various kinds of network instability. In this study, the joint evolution of traffic flows and adaptive signal settings in a road network is investigated at the level of day-to-day dynamics with an explicit focus on the stability issue. We show how a Logit form signal control policy can be used, in interaction with route choice, to counter the emergence of instabilities possibly arising as a consequence of various behavioral factors and network conditions. After providing a general formulation of the model as a discrete time, deterministic nonlinear dynamical system, an explicit analysis of fixed-point stability is carried out for a simple network. Numerical results obtained from the implementation of the model on two example networks are presented in order to support the analytical findings of this study. We conclude that, in an integrated traffic management and information system, a properly calibrated adaptive signal control policy has the potential to offset the destabilizing effect of highly accurate driver information supplied by navigational aids. Our findings also suggest that the Logit-like control policy performs better than the Equisaturation signal setting method, in terms of average intersection delay at equilibrium, for all levels of driver information and travel demand tested in the experiment. t +
Footnote †: journal: Applied Sciences  
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from an equilibrium perspective [4; 5; 6; 7], the emphasis of more recent research efforts has shifted toward the joint modeling of adaptive signal control and day-to-day route choice dynamics [8; 9; 10]. The day-to-day dynamic approach to route choice modeling, pioneered by the works of [PERSON] [11] and [PERSON] [12], realistically recognizes that the temporal evolution of network states does not necessarily converge to equilibrium conditions but may rather lead to other types of long-term outcomes, such as periodic or aperiodic attractors. The theoretical and practical relevance of day-to-day assignment models is further substantiated by their close connection with the issue of stability and the analysis of attraction domains of traffic equilibria [13; 14; 15; 16]. More recently, the day-to-day dynamic approach has been adopted for the simulation of route choice in the context of cutting-edge traffic scenarios, such as the operation of a road network used by mixed flows of autonomous and human-driven vehicles [17]. The effects of specific behavioral traits of travelers on the evolution of network states have also been modeled within a day-to-day dynamic framework [18]. Parallel to the stream of studies addressing the theoretical aspects of day-to-day traffic dynamics, an active area of research dealing with the empirical analysis of repeated route choice behavior in real or simulated settings has developed [19; 20; 21; 22; 23]. The study of the joint dynamics of day-to-day route choice and adaptive signal control under real-time information was addressed by [PERSON] and [PERSON] [24] through a simulation and assignment procedure. Numerical experiments were carried out by the authors in order to compare the effectiveness of different combinations of signal control strategies and levels of information availability. [PERSON] [8] presented a formal definition of the combined day-to-day signal control and traffic assignment problem based on a discrete time, deterministic process model with exponentially smoothed cost and flow updating rules. He provided fixed-point stability conditions considering different approaches to the determination of signal settings. Related works by [PERSON] et al.