The IP Multimedia Subsystem (IMS) is the technology that merges the Internet with the cellular world. The existing session establishment scenario of IMS suffers from triangular routing for a certain period of time when an end user is mobile. The other problem areas in optimizing presence service, dimensioning a push-to-talk over cellular service and analyzing service rates of instant messaging relay extensions in IMS are identified. In order to mitigate the drawbacks of these crucial aspects, this book contributes with a robust scheduler to improve performance of the presence service, several derived models to dimension push-to-talk over cellular service, a new mechanism to reduce cost for the session set ups in mobile environment and the evaluation of message blocking and stability in instant messaging service by applying queuing theories. The analysis of performance enhancements and the derived models of this book should help shed some light on the emerging environment of IMS infrastructure. They should also be very useful to professionals who may be considering pursuing research in the field of wireless communications and mobility management using stochastic process.