Application of Linear Programming to Reduce Traffic Congestion in Urban Centers: A Case Study of Lagos State Transport Authority

Abstract

Traffic congestion in urban centres is a persistent challenge with long-term socioeconomic, environmental, and health consequences. Lagos, Nigeria, one of Africa's fastest-growing megacities, faces severe gridlock across its road network managed by the Lagos State Transport Authority (LAMATA), which serves over twenty million daily commuters. This paper applies linear programming (LP) to develop an optimisation model that minimises total vehicular delay time across five key corridors of the Lagos metropolitan road network, subject to road capacity, signal-cycle, and modal-split constraints. Traffic count data were gathered during peak and off-peak periods over twelve weeks on the Apapa-Oshodi, Lagos Island-Victoria Island, Ojota-Ketu, Lekki-Ajah, and Ikeja Along-Agege corridors. The simplex method was applied to solve the LP model, and sensitivity analysis was conducted to assess solution stability under demand variations of ±20%. Results show that average peak-hour delay and total vehicular hours lost (VHT) per day can be reduced by 34.7% and 28.4% respectively, through optimised reallocation of green-signal time and promotion of bus rapid transit (BRT) and non-motorised transport (NMT) modes. The model remains stable within demand fluctuations of ±15%, confirming its practical utility. The findings offer actionable policy support for LAMATA planners and demonstrate the significant potential of mathematical programming in evidence-based urban transport policy.