We aim to reduce the social cost of congestion in many smart city applications. In our model of congestion, agents interact over limited resources after receiving signals from a central agent that observes the state of congestion in real time. Under natural models of agent populations, we develop new signalling schemes and show that by introducing a non-trivial amount of uncertainty in the signals, we reduce the social cost of congestion, i.e., improve social welfare. The signalling schemes are efficient in terms of both communication and computation, and are consistent with past observations of the congestion. Moreover, the resulting population dynamics converge under reasonable assumptions.
Most research and applications of network equilibrium models are based on the assumption that traffic volumes on roadways are virtually certain to be at or near their equilibrium values if the equilibrium volumes exist and are unique. However, it has long been known that this assumption can be violated in deterministic models. This paper presents an investigation of the stability of stochastic equilibrium in a two-link network. The stability of deterministic equilibrium also is discussed briefly. Equilibrium is defined to be stable if it is unique and the link volumes converge over time to their equilibrium values regardless of the initial conditions. Three models of route choice decision-making over time are formulated, and the stability of equilibrium is investigated for each. It is shown that even when equilibrium is unique, link volumes may converge to their equilibrium values, oscillate about equilibrium perpetually, or converge to values that may be considerably different from the equilibrium ones, depending on the details of the route choice decision-making process. Moreover, even when convergence of link volumes to equilibrium is assured, the convergence may be too slow to justify the standard assumption that these volumes are usually at or near their equilibrium values. When link volumes converge to non-equilibrium values, the levels at which the volumes stabilize typically depend on the initial link volumes or perceptions of travel costs. Conditions sufficient to assure convergence to equilibrium in two of the three models of route choice decision-making are presented, and these conditions are interpreted in terms of the route choice decision-making process. This paper introduces and illustrates some novel stochastic policies that assign parking spaces to cars looking for an available parking space. We analyze in detail both the main features of a single park, i.e., how a car could conveniently decide whether to try its luck at that parking lot or try elsewhere, and the case when more parking lots are available, and how to choose the best one. We discuss the practical requirements of the proposed strategies in terms of infrastructure technology and vehicles' equipment and the mathematical properties of the proposed algorithms in terms of robustness against delays, stability, and reliability. Preliminary results obtained from simulations are also provided to illustrate the feasibility and the potential of our stochastic assignment policies. The paper formulates link-flow definitions of equilibrium and stability, and gives conditions which guarantee the existence, uniqueness and stability of traffic equilibria. Junction delays in towns usually depend on the traffic flow along intersecting links; the theory presented here is designed to be applicable when there are such junction interactions.