• Propose a novel QBM for electrified traffic flow. • Overcome the bottleneck of tracking vehicle battery levels in queueing models. • The computational complexity of QBM is independent of fleet size and road capacity. • Discuss the properties of both the steady-state and discrete versions of the QBM. • Numerical experiments reveal several important insights. Electrification is an inevitable trend for future transportation systems. A low-complexity system model that accurately captures the impact of endogenous congestion induced by electric vehicles on energy consumption is fundamental for decision-making in large-scale electric transportation systems. However, this remains an open challenge. To address this gap, this paper proposes a novel Queue-Battery Model (QBM), extending the link queue model through continuous battery state dynamics. The model embeds a system of partial differential equations (PDEs) that describe the states of electric vehicles in both time and battery dimensions into a multi-class fluid queuing network, thus overcoming the bottleneck of tracking vehicle battery levels in queueing models. QBM effectively captures the impact of endogenous congestion on energy consumption. Moreover, its computational complexity is independent of fleet size and road capacity, providing a scalable foundation for rapid decision-making in large-scale electric transportation systems. We discuss the properties of the steady-state QBM. By recognizing the governing PDEs as a linear advection equation system, we implement an upwind difference scheme to ensure numerical stability, providing a computationally efficient tool for large-scale network analysis. The analysis and experimental evidence show that the complexity of the algorithm is a linear function of the product of the network size, the number of time steps, and the number of battery discretization levels. The model’s validity is extensively verified through agent-based simulations under various demand scenarios. Numerical experiments reveal several important findings: (1) As demand increases, the single commodity space-time battery network flow model increasingly underestimates energy consumption (by a substantial 57.2%) compared with QBM. (2) The QBM exposes a systematic ’optimism bias’ in mean-based models, revealing that a seemingly safe 80% average state of charge masks critical tail risks where vulnerable vehicles drop to nearly 40% due to queue-induced depletion. (3) In accident scenarios, the number of vehicles with lower battery levels continues to rise for a longer period after the incident ends, taking more time to return to normal conditions. (4) The average battery level of vehicles exiting the network shows a multi-peak pattern in response to increasing demand. (5) There exists a moderate level of demand that maximizes the aggregate battery level of vehicles exiting the network. This metric balances the network’s throughput and the average energy consumption of vehicles, serving as a critical indicator for traffic demand management.
Hu et al. (Thu,) studied this question.