A multi commodity flow model incorporating flow reduction functions

In this article an improved multi-commodity network flow (MCNF) model is introduced to holistically assess a multi modal transportation system and to identify the optimal flows achievable. The principal innovation of this model, that distinguishes it from recent approaches, is the inclusion of flow reduction functions (FRF) to automatically scale the flows on specific parts of the network. Reduced flows occur for many reasons but typically as a result of congestion, accidents, road works, and human behaviour. The inclusion of flow reductions permits a more accurate and reliable assessment and reduces overestimated flows. In practice, the speed of vehicles also affects the flow and the level of congestion. Consequently, model extensions have been introduced to facilitate the identification of the most appropriate speed on each link in the network. As the FRF are non-linear, it is necessary to approximate them using piecewise linear mathematical functions and to solve the MCNF using Separable Programming techniques. Several real-life case studies demonstrate the potential of the proposed approach and its general applicability. The numerical investigations highlight the capacity losses incurred, for different FRF, and the ease in which different functions can be chosen and evaluated.