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This paper, in accordance with the authors' continuing research investigates the effect of adding extra servers in Session Initiation Protocol (SIP) signaling network on session setup delay in the IP Multimedia Subsystem (IMS). The effect of applying more than one server in reducing waiting time in each of the nodes of the system is previously investigated by the authors in and applying more servers as a way of overcoming overload in IMS is addressed in. In this contribution, the delay analysis is explored by describing the SIP signaling traffic with M/M/r notation. Then the SIP servers overload problem is addressed and the effect of adding servers on network throughput and call loss probability is investigated. Finally, the total waiting time probability distribution is derived.