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The “asymmetry” between spatiotemporally varying passenger demand and fixed-capacity transportation supply has been a long-standing problem in urban mass transportation (UMT) systems around the world. The emerging modular autonomous vehicle (MAV) technology offers us an opportunity to close the substantial gap between passenger demand and vehicle capacity through station-wise docking and undocking operations. However, there still lacks an appropriate approach that can solve the operational design problem for UMT corridor systems with MAVs efficiently. To bridge this methodological gap, this paper proposes a continuum approximation (CA) model that can offer near-optimal solutions to the operational design for MAV-based transit corridors very efficiently. We investigate the theoretical properties of the optimal solutions to the investigated problem in a certain (yet not uncommon) case. These theoretical properties allow us to estimate the seat demand of each time neighborhood with the arrival demand curves, which recover the “local impact” property of the investigated problem. With the property, a CA model is properly formulated to decompose the original problem into a finite number of subproblems that can be analytically solved. A discretization heuristic is then proposed to convert the analytical solution from the CA model to feasible solutions to the original problem. With two sets of numerical experiments, we show that the proposed CA model can achieve near-optimal solutions (with gaps less than 4% for most cases) to the investigated problem in almost no time (less than 10 ms) for large-scale instances with a wide range of parameter settings (a commercial solver may even not obtain a feasible solution in several hours). The theoretical properties are verified, and managerial insights regarding how input parameters affect system performance are provided through these numerical results. Additionally, results also reveal that, although the CA model does not incorporate vehicle repositioning decisions, the timetabling decisions obtained by solving the CA model can be easily applied to obtain near-optimal repositioning decisions (with gaps less than 5% in most instances) very efficiently (within 10 ms). Thus, the proposed CA model provides a foundation for developing solution approaches for other problems (e.g., MAV repositioning) with more complex system operation constraints whose exact optimal solution can hardly be found with discrete modeling methods. 

We have performed combined elastic neutron diffuse, electrical transport, specific heat, and thermal conductivity measurements on the quasi–one-dimensional Ba 3 Co 2 O 6 (CO 3 ) 0.7 single crystal to characterize its transport properties. A modulated superstructure of polyatomic CO 3 2− is formed, which not only interferes the electronic properties of this compound, but also reduces the thermal conductivity along the c-axis. Furthermore, a large magnetic entropy is observed to be contributed to the heat conduction. Our investigations reveal the influence of both structural and magnetic effects on its transport properties and suggest a theoretical improvement on the thermoelectric materials by building up superlattice with conducting ionic group. 

Since passenger demand in urban transit systems is asymmetrically distributed across different periods in a day and different geographic locations across the cities, the tradeoff between vehicle operating costs and service quality has been a persistent problem in transit operational design. The emerging modular vehicle technology offers us a new perspective to solve this problem. Based on this concept, we propose a variable-capacity operation approach with modular transits for shared-use corridors, in which both dispatch headway and vehicle capacity are decision variables. This problem is rigorously formulated as a mixed integer linear programming model that aims to minimize the overall system cost, including passenger waiting time costs and vehicle operating costs. Because the proposed model is linear, the state-of-the-art commercial solvers (e.g., Gurobi) can be used to obtain the optimal solution of the investigated problem. With numerical experiments, we demonstrate the feasibility of the mathematical model, verify the effectiveness of the proposed model in reducing overall system costs in transit systems, as well as the robustness of the proposed model with different parameter settings.