A method and apparatus for controlling ingress to a communications network to control quality of service is described. A request to admit a new communications flow is received. A polynomial and its coefficients representing a state of the network is determined and applied to the network state plus the new communications flow to determine whether admission of the new communications flow would cause the network to operate in a stable or unstable state. In response to determining that the network would operate in the unstable state, a communications flow for the ingress device is downgraded in its quality of service. By another approach, it is determined whether the new communications flow exceeds an allocated quota of bandwidth. Admission or rejection of the communications flow can be determined.