Hemant Gehlot

Hemant Gehlot, Harsha Honnappa, Satish V. Ukkusuri

Congestion pricing has become an effective instrument for traffic demand management on road networks. This paper proposes an optimal control approach for congestion pricing for day-to-day timescale that incorporates demand uncertainty and elasticity. Travelers make the decision to travel or not based on the experienced system travel time in the previous day and traffic managers take tolling decisions in order to minimize the average system travel time over a long time horizon. We formulate the problem as a Markov decision process (MDP) and analyze the problem to see if it satisfies conditions for conducting a satisfactory solution analysis. Such an analysis of MDPs is often dependent on the type of state space as well as on the boundedness of travel time functions. We do not constrain the travel time functions to be bounded and present an analysis centered around weighted sup-norm contractions that also holds for unbounded travel time functions. We find that the formulated MDP satisfies a set of assumptions to ensure Bellman's optimality condition. Through this result, the existence of the optimal average cost of the MDP is shown. A method based on approximate dynamic programming is proposed to resolve the implementation and computational issues of solving the control problem. Numerical results suggest that the proposed method efficiently solves the problem and produces accurate solutions.

Hemant Gehlot, Satish V. Ukkusuri

Non-recurrent congestion is a major problem in traffic networks that causes unexpected delays during travels. In such a scenario, it is preferable to use adaptive paths or policies where next link decisions on reaching junctions are continuously adapted based on the information gained with time. In this paper, we study a traffic assignment problem in stochastic time-dependent networks. The problem is modeled as a fixed-point problem and existence of the equilibrium solution is discussed. We iteratively solve the problem using the method of successive averages (MSA). A novel network loading model inspired from Link transmission model is developed that accepts policies as inputs for solving the problem. This network loading model is different from the existing network loading models that take predefined paths for input flows. We demonstrate through numerical tests that solving traffic assignment problem with the proposed loading modeling scheme is more efficient as compared to solving the problem using path-based network loading models.

Hemant Gehlot, Shreyas Sundaram, Satish V. Ukkusuri

We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we consider the problem of finding an optimal control (or switching) sequence to maximize the sum of the weights of the components whose states are brought back to the maximum value. We first provide several characteristics of the optimal policy for the general (fully heterogeneous) version of this problem. We then show that under certain conditions on the rates of repair and deterioration, we can explicitly characterize the optimal control policy as a function of the states. When the deterioration rate (when not being repaired) is larger than or equal to the repair rate, and the deterioration and repair rates as well as the weights are homogeneous across all the components, the optimal control policy is to target the component that has the largest state value at each time step. On the other hand, if the repair rates are sufficiently larger than the deterioration rates, the optimal control policy is to target the component whose state minus the deterioration rate is least in a particular subset of components at each time step.