Arrays of H-shape microfluidic channels connecting two different fluidic reservoirs have been built with silicon/SU8 microfabrication technologies utilized in production of thermal inkjet printheads. The fluids are delivered to the channels via slots etched through the silicon wafer. Every H-shape channel comprises four thermal inkjet resistors, one in each of the four legs. The resistors vaporize water and generate drive bubbles that pump the fluids from the bulk reservoirs into and out of the channels. By varying relative frequencies of the four pumps, input fluids can be routed to any part of the network in any proportion. Several fluidic operations including dilution, mixing, dynamic valving, and routing have been demonstrated. Thus, a fully integrated microfluidic switchboard that does not require external sources of mechanical power has been achieved. A matrix formalism to describe flow in complex switchboards has been developed and tested.