The packet-pair probing algorithm for network-bandwidth estimation is examined and an approximate model is proposed for predicting its behaviour. The model replaces the Poisson arrival process with a Gaussian distribution and resolves the queue-size profile into two separate components: A transient component representing the buffer-emptying process and an equilibrium component representing the return to steady-state behaviour.Comparison with discrete-event simulation results shows that the model is accurate in single-hop paths when utilisation ≤ 70% when the cross-traffic packets are ≤ ½ the size of the probe packets. When extended to two-hop paths, the model remains accurate for smaller cross-traffic packets (≤ 10 1 -5 1 the probe packet size).