A Proposal of Quasi-Static Approach for Analyzing the Stability of IP Telephony Systems

Troubles in commercial IP telephony systems were reported one after another recently in Japan. One of important causes is congestion of control plane. In the current Internet, it has been recognized that controlling congestions caused by overload of control plane becomes important in addition to congestions caused by overload of data plane. In particular, since input traffic including retries tends to cause overload, it is an important issue to avoid congestion from retry traffic. In this paper, we focus on an RSVP-based communication model that is a combination of transmission and processing systems and consider the behavior of retry traffic. In general, users reattempt to set up connections not only when transmission systems are overloaded but also when processing systems in the network are overloaded. The latter is caused by user psychology: an increase in the waiting time for the processing to be completed tends to increase his or her reattempts. Thus, it is important to know interactions between users and the system and to manage both transmission and processing resources properly. Since both traditional Markov approach and simulation technique are difficult to handle these issues, we propose a new approach, quasi-static approach, for analyzing the stability of the RSVP model. This approach is based on the concept of decomposition of timescales like statistical physics. System behaviors are described as a combination of macroscopic behavior described in a human perceptible timescale and microscopic behavior described in a shorter timescale characterized by system's state transitions. Using our approach, we demonstrate the evaluation of IP telephony systems as an example of the RSVP model and show system down probabilities of very small values.