We propose a deterministic fluid model for the operation of two tandem SIP proxies in overload conditions. Using our model, we categorize overload scenarios into several classes, gaining better understanding of SIP overload. We then use the theory of Lyapunov for system stability and characterize stabilizing SIP overload control schemes over the state-space representation of a SIP server. A simple Lyapunov function is then utilized to build a Proportional-Integral-Derivative (PID) controller for performing overload control in a tandem system of SIP servers. The proposed PID overload control algorithm is then evaluated using experiments showing it can successfully restore throughput close to maximum system capacity during overload. Furthermore, we study the effect of overload detection lag on system stability showing that even a small delay in reacting to overload can postpone system stabilization by multiple minutes. (C) 2017 Elsevier B.V. All rights reserved.