Quasi-static Approach for Analyzing Interactions between Networks and Users Based on Decomposition of Timescales

A signaling system plays a crucial role in supporting any virtual channel (VC) communication service, including Internet and conventional telephone networks. Congestion in the current Internet is caused both by overloading of the communications links and also overloading of the processing capacity of servers. In this paper, we focus on an IP telephony model that considers both the transmission and call-processing systems, and we consider the stability of the system when subject to congestion in both areas. In particular, since retry traffic generated by users tends to cause overloading, we take retries into consideration in the input traffic. To understand the behaviors of retries, we should understand the interactions between users and the system. In this paper, we use gquasi-statich approach to analyzing the stability of the IP telephony model. This approach is based on the decomposition of timescales, as in statistical physics. System behavior is described as a combination of macroscopic behavior described on a human-perceptible timescale and microscopic behavior described in a shorter timescale characterized by the system´s state transitions.