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In urban road networks, the interactions between different modes can clearly impact the overall travel production. Although those interactions can be quantified with the multi-modal macroscopic fundamental diagram; so far, no functional form exists for this diagram to explicitly capture operational and network properties. In this paper, we propose a methodology to generate such functional form, and we show its applicability to the specific case of a bi-modal network with buses and cars. The proposed functional form has two components. First, a three dimensional lower envelope limits travel production to the theoretical best-case situation for any given number of vehicles for the different modes. The lower envelopes parameters are derived from topology and operational features of the road network. Second, a smoothing parameter quantifies how interactions between all vehicle types reduce travel production from the theoretical best-case. The smoothing parameter is estimated with network topology and traffic data. In the case no traffic data is available, our functional form is still applicable. The lower envelope can be approximated assuming fundamental parameters of traffic operations. For the smoothing parameter, we show that it always hold similar values even for different networks, making its approximation also possible. This feature of the proposed functional form is an advantage compared to curve fitting, as it provides a reasonable shape for the multi-modal macroscopic fundamental diagram irrespective of traffic data availability. The methodology is illustrated and validated using simulation and empirical data sets from London and Zurich.

The Macroscopic Fundamental Diagram (MFD) has been recognized as a powerful framework to develop network-wide control strategies. Recently, the concept has been extended to the threedimensional MFD, used to investigate traffic dynamics of multi-modal urban cities, where different transport modes compete for, and share the limited road infrastructure. In most cases, the macroscopic traffic variables are estimated using either loop detector data (LDD) or floating car data (FCD). Taking into account that none of these data sources might be available, in this study we propose novel estimation methods for the space-mean speed of cars based on: (i) the automatic vehicle location (AVL) data of public transport where no FCD is available; and (ii) the fused FCD and AVL data sources where both are available, but FCD is not complete. Both methods account for the network configuration layout and the configuration of the public transport system. The first method allows one to derive either uni-modal or bi-modal macroscopic fundamental relationships, even in the extreme cases where no LDD nor FCD exist. The second method does not require a priori knowledge about FCD penetration rates and can significantly improve the estimation accuracy of the macroscopic fundamental relationships. Using empirical data from the city of Zurich, we demonstrate the applicability and validate the accuracy of the proposed methods in real-life traffic scenarios, providing a cross-comparison with the existing estimation methods. Such empirical comparison is, to the best of our knowledge, the first of its kind. The findings show that the proposed AVL-based estimation method can provide a good approximation of the average speed of cars at the network level. On the other hand, by fusing the FCD and AVL data, especially in case of sparse FCD, it is possible to obtain a more representative outcome regarding the performance of multi-modal traffic.

Pick-up and delivery services are essential for businesses in urban areas. However, due to the limited space in city centers, it might be unfeasible to provide sufficient loading/unloading spots. As a result, this type of operations often interferes with traffic by occupying road space (e.g., illegal parking). In this study, a potential solution is investigated: Dynamic Delivery Parking Spots (DDPS). With this concept, based on the time-varying traffic demand, the area allowed for delivery parking changes over time in order to maximize delivery opportunities while reducing traffic disruptions. Using the hydrodynamic theory of traffic flow, we analyze the traffic discharging rate on an urban link with DDPS. In comparison to the situation without delivery parking, the results show that although DDPS occupy some space on a driving lane, it is possible to keep the delay at a local level, that is, without spreading to the network. In this paper, we provide a methodology for the DDPS design, so that the delivery requests can be satisfied while their negative impacts on traffic are reduced. A simulation study is used to validate the model and to estimate delay compared to real situations with illegal parking, showing that DDPS can reduce system's delay.

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