Wireless Network Thermodynamics: Interfering Stochastic Multiclass Diffusion on Limited Capacity

Concepts of temperature, heat, and entropy are extended to packet routing on multiclass wireless networks with particular challenges including network directionality, channel interference, channel capacity, time-varying topology, and stochastic arrivals. Applying thermodynamic principles in the framework of combinatorial geometry, a novel physics-oriented multiclass diffusion process is developed on directed graphs constrained to edge capacities, leading to a nonlinear graph Laplacian. Taking this as a target model, the multiclass diffusion process on a wireless network is then established using the notion of fluid limit for stochastic queuing networks. Specifically, a family of throughput-optimal control policies is introduced under which the fluid limit of stochastic wireless network comply with the multiclass diffusion on the underlying directed graph with suitably-weighted and -capacitated edges. Thus we crossfertilize wireless networking with classical thermodynamics that opens a door, for the first time, to take advantage of powerful tools from heat calculus in the analysis and optimization of multiclass wireless networks subject to channel interference and capacity. Further, this scheme can be adapted to the general class of stochastic processing networks, which includes many other problems beyond wireless networking.