The bottleneck model has been widely used in the past fifty years to analyze the morning commute. To reduce the complexity of analysis, most previous studies adopted discontinuous scheduling preference (DSP). However, this handling destroys the continuity in departure rate and differentiability in travel time and cumulative departures. This paper considers an exponential scheduling preference (ESP), which supposes the unit schedule delay cost for commuters exponentially changes with time. With this scheduling preference, we analytically derive solutions and economic properties of user equilibrium and social optimum in the bottleneck model. The first-best, time-varying toll and the optimal single-step toll scheme with ESP are also studied. Results indicate that ESP eliminates the discontinuity in departure rate and non-differentiability in travel time and cumulative departures, which makes the process of morning commute smooth. The ignorance of ESP will lead to underestimation in the queueing time and bias in travel behavior analysis and policymaking.

Unmanned aerial vehicles (UAVs) are increasingly crucial across various fields. There is a growing interest in using federated learning (FL) methods to enhance the efficiency of UAV operations. Nevertheless, incumbent methods remain encumbered by significant drawbacks, including high energy consumption from extensive parameter exchanges, the imperative for homogeneous networks, and sensitivity to single-point failures. These difficulties are compounded by the unreliable nature of communication channels and the current inability to effectively manage the diversity of UAV models, highlighting the imperative for more resilient and adaptable FL solutions. To address these issues, we propose an efficient and robust decentralized FL framework for heterogeneous UAV networks. Our framework first leverages the knowledge distillation where UAVs transmit embeddings instead of model parameters to reduce the number of transmission parameter. UAVs update their local models using embeddings generated by other UAVs, which also enables UAVs with diverse architectures to participate in training. Moreover, our framework incorporates a filtering mechanism to remove malicious embeddings, ensuring resilience against adversities in UAV networks. Extensive experiments on various datasets validate the effectiveness and practical deployment potential of our framework.