Device-to-device (D2D) communications for Long Term Evolution (LTE) networks relies on a discovery process to enable User Equipment (UE) to determine which D2D applications and services are supported by neighboring UEs. This is especially important for groups of UEs that operate outside the coverage area of any base station. The amount of time required for discovery information to reach every UE in a group depends on the number of UEs in the group and the dimensions of the discovery resource pool associated with the Physical Sidelink Discovery Channel (PSDCH); an additional factor is the half-duplex property of current UEs. In this paper, we use a Markov chain to characterize the performance of Mode 2 direct discovery. The resulting analytical model gives the distribution of the time for a UE to discover all other UEs in its group. We validate the model using Monte Carlo and network simulations