Pendekatan Sistem Persamaan Diferensial Dua Tundaan untuk Analisis Dinamik Kemacetan di Persimpangan Lalu Lintas

Abstract

This study aims to analyze the role of congestion distribution and delay time in shaping traffic dynamics and as a basis for policy making. The model built is a mathematical model approach in the form of a two-delay differential equation system (𝜏1 and 𝜏2). Based on this model, we have equilibrium point and basic reproduction number are obtained, and numerical simulations. Furthermore, the basic reproduction number  R0 serves as a threshold indicator that represents the potential for congestion distribution. When 𝑅0 > 1, congestion tends to increase and requires policy intervention, while when 𝑅0 < 1, traffic remains relatively under control. On the other hand, the results of this study support the implementation of threshold-based policies, such as activating traffic engineering before critical conditions are reached. The simulation results show that the first delay time 𝜏1 role a significant role in shaping the dynamics of traffic congestion, which is slower but has the potential to increase due to vehicle buildup, while the second delay time 𝜏2 in the recovery process makes congestion last longer before subsiding. Furthermore, this approach is very important because it allows traffic decision-making based on quantitative indicators, rather than the experience of traffic officers in the field.