Multiple factors can influence the public transport level of service. All take root in the network structure and the operating regime, i.e. how the bus lines are arranged atop the street network and how the service frequency is adjusted to meet urban mobility patterns. This is known as the bus network design problem and has been the subject of several studies. The problem is so challenging that most studies until now resort to strong assumptions such as a static description of the peak hour demand, homogeneous user behavior, and equal trip lengths. Potential effects of different types of user behavior and trip lengths patterns on the user and/or operator cost have not been investigated whatsoever. Moreover, none of the existing studies have considered the effects of bus network structure on private car users, the level of interactions between the modes, and the passenger mode choice that depends on traffic conditions.

This paper aims to close this gap and provide a general framework considering multiple trip length patterns, two types of user behavior, and the effects that the bus network structure might have on the traffic performance and passenger mode choice. For modeling different trip length patterns, we use the trip length distribution as an intermediate level of abstraction. To capture complex modal interactions and quantify the operating speeds, we apply the recently proposed three-dimensional macroscopic fundamental diagram. We use the operating speed for each mode to determine the mode choice at the trip length level. This way, we are able to solve the optimal bus network design problem under the free-flow/saturated traffic conditions in an analytical way, while considering more realistic settings including a dynamic description of the peak hour demand, mixed traffic, and different mode choice decisions depending on trip lengths and walking preferences.

Numerical analysis reveals that all the tested factors, including demand intensity, user behavior, and trip length patterns, have significant effects on the operator and user cost function. Results show that the probability of choosing any given mode follows certain distribution that varies across the trip length patterns, indicating the importance of modeling the mode choice at the trip length level. Furthermore, the results indicate that users can benefit if they are willing to adjust the number of transfers to minimize the walking distance at the origin and the destination. Moreover, we show that the optimal bus network design determined for the uniform trip pattern underestimates the number of required buses, which leads to passenger congestion at stops during the peak period. This, however, does not happen when we take into account the actual trip length distribution for the bus network design. A comparison with a simplified approach that considers the bus system only, reveals the value of accounting for the complex bi-modal interactions, especially for higher demand levels. Finally, we show that by allowing the design parameters to vary across cardinal directions we provide more flexibility for the bus system to serve the passenger demand while reducing the operator cost compared to the existing approaches.

多种因素会影响公共交通服务水平。一切都植根于网络结构和运营体制，即公交线路如何在街道网络上布置，以及如何调整服务频率以适应城市交通模式。这被称为总线网络设计问题，并已成为多项研究的主题。这个问题是如此具有挑战性，以至于迄今为止的大多数研究都采用了强有力的假设，例如对高峰时段需求的静态描述、同质的用户行为和相等的行程长度。尚未调查不同类型的用户行为和行程长度模式对用户和/或运营商成本的潜在影响。此外，现有研究均未考虑公交网络结构对私家车用户的影响，

本文旨在缩小这一差距，并提供一个考虑多种出行长度模式、两种类型的用户行为以及公交网络结构可能对交通性能和乘客模式选择产生的影响的通用框架。为了对不同的行程长度模式进行建模，我们使用行程长度分布作为抽象的中间级别。为了捕捉复杂的模态相互作用并量化运行速度，我们应用了最近提出的三维宏观基本图。我们使用每种模式的运行速度来确定行程长度级别的模式选择。通过这种方式，我们能够以分析的方式解决自由流/饱和交通条件下的最优公交网络设计问题，

数值分析表明，所有测试因素，包括需求强度、用户行为和行程长度模式，对运营商和用户成本函数都有显着影响。结果表明，选择任何给定模式的概率遵循在出行长度模式中变化的特定分布，表明在出行长度级别对模式选择进行建模的重要性。此外，结果表明，如果用户愿意调整换乘次数以最小化起点和目的地的步行距离，则用户可以受益。此外，我们表明，为统一出行模式确定的最佳公交网络设计低估了所需的公交车数量，从而导致高峰期停靠站的乘客拥堵。然而，这 当我们考虑公交网络设计的实际行程长度分布时，不会发生这种情况。与仅考虑总线系统的简化方法进行比较，揭示了考虑复杂双模式交互的价值，尤其是对于更高的需求水平。最后，我们表明，与现有方法相比，通过允许设计参数在主要方向上变化，我们为公交系统提供了更大的灵活性，以满足乘客需求，同时降低运营成本。