Telephony gateways are devices that interface between IP telephony networks and the PSTN. A telephony proxy or location server (LS) that attempts to connect a call for an end user may need to choose between multiple candidate gateways. Gateways need to send updates of their dynamic resource information periodically to the LS which is used by LS while choosing a gateway. Telephony Gateway REgistration Protocol (TGREP) is an IETF proposed standard used by gateways for this purpose. To the best of our knowledge, there is no study done on the performance of TGREP and we believe that this is the first paper on performance modeling of TGREP system. In this paper, we propose an analytical model for TGREP system and then use the model to evaluate different gateway selection algorithms proposed by us in this paper. We validate our model using simulation results. We also present an adaptive update mechanism in which the overhead of sending dynamic resource information is reduced without significant effect on call blocking probability. We outline a few important conclusions from this study that are quite contrary to what IP telephony providers might resort to while deploying TGREP.