Limited resources in multi-lane stochastic transport system

The present study proposes a generalized mean-field approach to examine the significant effect of the finite supply of particles on multi-lane coupled system with non-conserving dynamics. The steady-state behavior is analyzed by exploring vital characteristics such as phase diagrams, density profiles, residence time and power spectra. Despite the fully asymmetrical coupling environment, symmetrical phases are identified along with asymmetrical phases. The emergence of shock results in the breaking of symmetry prevailing among the lanes for a critical value of the total number of particles in the system. Additionally, bulk induced phase transition results in the shifting from low density to high density regime. As expected, jamming length increases with increase in the total number of particles in the system. Particles follow the pseudo-Gaussian distribution with decreasing variance exhibiting the significant effect of limited resources on the system properties. For the lower values of the total number of particles, the current initially increases and then saturate beyond its critical value. Through power spectra damped oscillations are observed in the particles occupancy in one of the lanes while other lane and reservoir show undamped profile with non-conserving dynamics in the bulk.