An access point station responds to a request from a user station for contention-based access of a new traffic flow to a wireless transmission medium by applying a model of the wireless local area network to estimate delay that data packets will experience when delivered through the wireless network, in order to admit the new flow upon determining that admission will not violate quality of service requirements of neither the new flow nor of already admitted flows. For example, the access point station applies the model by determining an average packet inter-arrival rate, solving a system of nonlinear equations to determine probabilities of successful transmission, applying network stability conditions, computing an upper bound on queuing delay for the packets, computing a service delay budget for the packets, and computing an expected fraction of missed packets from the service delay budget.