A Dimensional Analysis Approach to Transport Capacity of Wireless Network

Finding the transport capacity of an arbitrary wireless network is generally considered as a difficult mathematics issue. In this work, from a unconventional perspective, we formulate it as a physical issue with lower complexity. Assuming that n identical nodes are located in a region of area A, transmit rate W, the transport capacity (in bit-meters per second) of the network has a "scaling law". We introduce a dimensional analysis method and pi-theorem usually can be seen in mechanics research, and give a semi-analytic solution of the generalized scaling law of the static network. In addition, for a network with node velocity V and packet length L, we give a semi-analytic dynamic transport capacity.