Modelling the impact of unregulated roadside parking on traffic flow

Abstract

Unregulated roadside parking is a pervasive feature of urban traffic in many developing cities, where limited enforcement and inadequate infrastructure allow vehicles to occupy travel lanes. This practice narrows effective road capacity, introduces unexpected bottlenecks, and intensifies congestion, yet most existing macroscopic traffic flow models neglect its dynamic influence. This study develops a second-order continuum traffic flow model that explicitly incorporates the effects of unregulated parking through parking-density-dependent modifications of the equilibrium velocity and driver relaxation time, together with additional frictional and gradient terms in the dynamic velocity equation. A comprehensive stability analysis is performed. The linear analysis yields a critical reaction threshold that depends explicitly on parking density, while nonlinear analysis yields a Korteweg-de Vries (KdV)-type evolution equation admitting dissipative solitary-like solutions. Numerical simulations corroborate the analytical results, showing that small increases in parking density reduce flow stability and trigger the emergence of stop-and-go waves and localized congestion clusters. At higher parking densities, however, disturbances become confined to quasi-stationary jammed zones. The results show that unregulated roadside parking significantly alters traffic stability. It destabilizes flow at moderate levels but promotes localized steady states under heavy encroachment, thus providing a theoretical basis for designing targeted control and enforcement strategies in cities where curbside occupancy remains widespread.