In this paper, we provide an analytical model for the performance study of different structured P2P overlay networks used for lookup service in IP telephony systems. The overlay provides an infrastructure for the lookup service required before an actual voice communication is initiated. Our model captures the performance behavior of such overlays including the mean session set-up delay of a call as well as the system capacity. These parameters reflect how good an IP telephony overlay is performing. We formulate the system as a queuing network. We idealize Chord routing semantics to extract useful observations to obtain closed form expressions for the session setup delay and capacity as a function of the number of participating supernodes (SN). The analysis also answers the question of finding an optimum number of SN for minimum session setup delay