Is max-min fairness achievable in the presence of insubordinate users?

Enforcement of max-min fairness encourages end users to implement adaptive end-to-end flow control. Unfortunately, there can be insubordinate users who ignore congestion and cause performance degradation to others. The commonly used max-min fairness definition that treats insubordinate users fairly causes inefficiency. We demonstrate that a strict priority regime can protect the cooperative users so that they enjoy fair and efficient service. We also demonstrate that this cannot be achieved by weighted class fairness.