Queuing Model for Loss-Based Overload Control in a SIP Server Using a Hysteretic Technique

Abstract

In this paper, we develop a mathematical model of a load control mechanism for SIP server signaling networks based on a hysteretic technique developed for SS7 from ITU-T Recommendation Q.704. We investigate loss-based overload control, as proposed in recent IETF documents. The queuing model takes into account three types of system state – normal load, overload, and discard. The hysteretic control is made possible by introducing two thresholds in the buffer of total size B – the overload onset threshold H and the overload abatement threshold L. We denote the mathematical model using the modified Kendall notation as an $M|G|1|\left\langle L,H\right\rangle |B$ queue with hysteretic load control. We also develop an analytical model for the case of an M|M|1 queue and a simulation model for an M|D|1 queue. We investigate the return time from an overload state as the target performance measure of overload control in a SIP server, and provide numerical examples in order to examine the difference between the M|M|1 and M|D|1 systems.

This work was supported in part by the Russian Foundation for Basic Research (grants 10-07-00487-a and 12-07-00108), and by Rosobrazovanie (project no. 020619-1-174).