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In this paper, we provide complete end-to-end delay analyses including the relay nodes for instant messages. Message Session Relay Protocol (MSRP) is used to provide congestion control for large messages in the Instant Messaging (IM) service. Large messages are broken into several chunks. These chunks may traverse through a maximum number of two relay nodes before reaching destination according to the IETF specification of the MSRP relay extensions. We discuss the current solutions of sending large instant messages and introduce a proposal to reduce message flows in the IM service. The analysis presented in this paper is divided into two parts. At the former part, we consider virtual traffic parameter i.e., the relay nodes are stateless non-blocking for scalability purpose. This type of relay node is also assumed to have input rate at constant bit rate. The later part of the analysis considers relay nodes to be blocking and the input parameter to be exponential. The performance analysis with the models introduced in this paper is simple and straight forward, which lead to reduced message flows in the IM service. Also, using our model analysis a delay based optimization problem can be easily deduced.
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