1. A method of maintaining a target quality of service in a network switch behaving as a buffer of fixed size transmitting a multiplex of current connections at a constant service rate by controlling the admission of a connection requesting admission on the basis of a declared parameter comprising the steps of: recording the volume of traffic for each current connection over a block of time; estimating the scaled cumulant generating function (SCGF) λ(θ,s) for each connection; summing all the estimated SCGFs to obtain an aggregate SCGF; using the aggregate SCGF to obtain an estimated bandwidth requirement for the multiplex of current connections; providing a predicted SCGF for the connection requesting admission from the declared parameter; predicting the bandwidth requirement of the connection requesting admission from the predicted SCGF; summing the estimated and predicted bandwidth requirements; and accepting the connection requesting admission when the sum of the bandwidth requirements is less than the service rate of the switch.