*This paper gives a new definition of general weighted (GW) fairness and shows how this can achieve various fairness definitions, such as those mentioned in the ATM Forum TM 4.0 specifications. The GW fairness can be achieved by calculating the $ExcessFairshare$ (weighted fairshare of the left over bandwidth) for each VC. We show how a switch algorithm can be modified to support the GW fairness by using the $ExcessFairshare$ term. We use ERICA+ as an example switch algorithm and show how it can be modified to achieve the GW fairness. For simulations, the weight parameters of the GW fairness are chosen to map a typical pricing policy. Simulations results are presented to demonstrate that, the modified switch algorithm achieves GW fairness. An analytical proof for convergence of the modified ERICA+ algorithm is given in the appendix. *

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