Inflow-dependent quickest multi-commodity flow problem with partial lane reversals
Durga Prasad Khanal, Shiva Prakash Gupta, Urmila Pyakurel, Tanka Nath Dhamala · Journal of Industrial and Management Optimization · 2025
Flow models with flow-dependent transit time act in accordance with the traversal time depending on the entire amount of flow currently traveling along that arc. These models offer a more realistic representation of urban traffic dynamics compared to those assuming fixed transit times. Factors such as rush hour patterns, traffic density, vehicle speeds, and road conditions significantly influence transit times, reflecting the inherent complexity of urban transportation networks. The quickest multi-commodity flow problem seeks to optimize the transport of multiple commodities from sources to destinations in possible minimum time by adhering the capacity constraints on the arcs. In this research, we extend the quickest multi-commodity flow over time problem in two-way network topology, where anti-parallel arcs exist between the pair of adjacent nodes. We incorporate a partial lane reversal strategy to solve the inflow-dependent quickest multi-commodity flow problem, where reversal of necessary arcs is permitted and the transit times depend on the flow rates across the arcs. This approach enhances outbound arc capacity and reduce the overall time horizon. Additionally, we introduce efficient approximation algorithms based on length bounded and condensed time expanded graph techniques to solve the problem.