Any black box containing resistances only and voltage and current sources can be replaced by an equivalent circuit consisting of an equivalent current source in parallel connection with an equivalent resistance.
Edward Lawry Norton
Known in Europe as the Mayer–Norton theorem, Norton's theorem holds, to illustrate in DC circuit theory terms (see that image):
Find the Norton current Ino. Calculate the output current, IAB, with a short circuit as the load (meaning 0 resistance between A and B). This is Ino.
Find the Norton resistance Rno. When there are no dependent sources (all current and voltage sources are independent), there are two methods of determining the Norton impedance Rno.
Calculate the output voltage, VAB, when in open circuit condition (i.e., no load resistor – meaning infinite load resistance). Rno equals this VAB divided by Ino.
Replace independent voltage sources with short circuits and independent current sources with open circuits. The total resistance across the output port is the Norton impedance Rno.
This is equivalent to calculating the Thevenin resistance.
However, when there are dependent sources, the more general method must be used. This method is not shown below in the diagrams.
Connect a constant current source at the output terminals of the circuit with a value of 1 ampere and calculate the voltage at its terminals. This voltage divided by the 1 A current is the Norton impedance Rno. This method must be used if the circuit contains dependent sources, but it can be used in all cases even when there are no dependent sources.
The passive circuit equivalent of "Norton's theorem" in queuing theory is called the Chandy Herzog Woo theorem. In a reversible queueing system, it is often possible to replace an uninteresting subset of queues by a single (FCFS or PS) queue with an appropriately chosen service rate.