Optimal path selection in a continuous-time route reservation architecture

In this work, we adopt the route reservation architecture proposed in [1] and adapt the reservation algorithm so that route reservations are made based on continuous-time intervals (instead of fixed discrete-time intervals). Using the continuous-time reservation architecture, we formulate a mixed integer linear programming (MILP) problem to obtain the optimal path of any vehicle, avoiding roads that are at-capacity. Since the MILP problem is hard to solve efficiently, we also propose a heuristic iterative algorithm that is based on Dijkstra's algorithm, is of low-complexity and provides close-to-optimal results, as compared to the MILP obtained solution (at least for small problems where MILP provided a solution in reasonable time). The simulation results further indicate that the Dijkstra-based heuristic can be solved more efficiently in continuous-time rather than discrete-time for high-demand scenarios.