Constrained Traffic of Particles on Complex Networks

We study the traffic of particles on complex networks under constraints. The constraints we propose are the different interactions between particles and the limited capability of node holding particles. We give the grand partition function of the system and find the distributions of particles at the dynamically balanced point. Then, we investigate the internal relations among the theories of classical statistics, quantum statistics and the zero range process. Finally, we find the finite temperature of Bose–Einstein condensation. Numerical results verify our theoretical expectations.