Summary: The $3^{\text{rd}}$ Generation Partnership Project (3GPP) for an IP multimedia subsystem (IMS) architecture defined a number of functional units, which exchange session initiation protocol (SIP) messages with register users and set up or terminate multimedia sessions. The processing of SIP messages, however, requires a significant amount of processing, queueing and transmission times with adverse implications on the overall performance of the IMS core architecture. This tutorial introduces a mobility management mechanism for an IMS testbed implemented by Nokia-Siemens as part of the EU IST VITAL project. The mechanism employs an open queueing network model (QNM) with priorities to represent the functional units and application servers of an IMS architecture during a handover process of SIP messages between different access networks. The QNM is analysed via the principle of maximum entropy and numerical experiments are employed to assess the performance impact of bursty traffic flows of SIP messages on the IMS architecture.