A model describing the discovery by means of traceroute of the topology an Internet access network with a tree structure is proposed in this study. This model allows us to assess the efficiency of traceroute procedures to determine the complete set of routers of the network. Under some stochastic assumptions, explicit analytical expressions are obtained for the mean number of routers discovered when a subset of the stations is used in the traceroute procedure. Several tree architectures are then discussed when the total number of routers gets large, and asymptotic expansions are derived. The results are compared with real data obtained from measurements.