Abstract: To discover a route to a peer node, an on-demand routing protocol may initiate a flood-search procedure known as route discovery. By selecting the correct query radius, the number of packet transmissions required for route discovery can be minimized. This paper presents methods to estimate the geographic radius (RG) and the number of currently active pairs of communicating nodes (P) in a mobile ad hoc network. The methods are entirely distributed and incur little communication overhead. Network nodes can apply the estimated parameters to predict the probability mass function (PMF) of route discovery hop distance. An accurate prediction of the PMF aids the selection of an appropriate query radius for the route discovery process. A computationally lightweight procedure to select an appropriate query radius, based only on an estimate of P, is also proposed. Simulation results show that this procedure facilitates a sensible trade-off between route request packet overhead and route reply delay.