Resource Allocation Based on Scalability of Shannon Capacity

We investigate the scalability of capacity, power, and bandwidth of a wireless Gaussian channel model using Shannon capacity equation. Based on scalability relationships of energy, entropy, volume, and number of particles in a thermodynamic system, and capacity, QoS, buffer, and mean arrival rate of a queuing system, we derive analogous relationships between capacity, power and bandwidth of a Gaussian channel. For a system of parallel wireless Gaussian channels power and bandwidth allocation problems are formulated. Equality of microscopic parameters (marginals of power, capacity, and bandwidth) are shown to be the optimal conditions for optimal power and bandwidth allocation. Welfare maximization problem of wireless service provider is presented and their solution are shown to be the function of microscopic parameters