Public transport systems are considered to be a crucial aspect of a sustainable urban development, as they allow more passengers to efficiently travel across an urban area at low environmental and economic costs. Multiple factors can influence the public transport level of service. All take roots in the network structure and the operating regime, i.e. how 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 function have not been investigated whatsoever. Moreover, the existing studies have not considered the effects of the bus network structure on private car users, the level of interactions between the two modes, and the passenger mode choice that depends on the 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, the proposed approach combines all origin-destination pairs with the same trip length and uses the trip length distribution as an intermediate level of abstraction. As such, it allows to solve the optimal bus network design problem in an analytical way, while considering a more realistic setting including network congestion, mixed traffic, and different mode choice decisions depending on trip lengths and walking preferences. Numerical analysis reveals that both, the user behavior and the trip length patterns, have significant effects on the operator and user cost function. Results show that the probability of choosing any given mode is not constant across the user trip lengths, but follows certain distribution. This distribution is not unique, but varies across the trip length patterns, indicating the importance of modeling the mode choice at the trip length level. Finally, the analysis demonstrates the significance of addressing simplifications made in previous studies.

This study proposes a novel flexible bus dispatching system where a fleet of fully automated modular bus units, together with conventional buses, serves the passenger demand. These modular bus units can either operate individually or combined (forming larger modular buses with a higher passenger capacity). This provides enormous flexibility to manage the service frequencies and vehicle allocation, reducing thereby the operating cost and improving passenger mobility. We develop an optimization model used to determine the optimal composition of bus units and the optimal service frequency at which the buses (both conventional and modular) are dispatched across each bus line. We explicitly account for the dynamics of traffic congestion and complex interactions between the modes at the network level based on the recently proposed three-dimensional macroscopic fundamental diagram (3D-MFD). To the best of our knowledge, this is the first application of the 3D-MFD and modular bus units for the frequency setting problem in the domain of bus operations. Numerical results show the improvements in the total system cost made by adapting the number of combined modular bus units and their dispatched frequencies to the evolution of both, the car and the passenger demand. A comparison with the commonly used approach that considers only the bus system (neglecting the complex multimodal interactions and congestion propagation) reveals the value of the proposed modeling framework.