Model with threshold control for analyzing a server with an SIP protocol in the overload mode

The SIP protocol defines the Invite messages initiating the session and the nonInvite ones, which are sent on its stabilizing, being privileged since the resetting of these messages due to an overload leads to ceasing of the user's session setting. The queueing system with polling, two queues of limited capacity, and threshold control of the load generated by nonpriority messages is studied in the present paper to be applied to a solution of the overload control problem in a server network with the SIP protocol. Under the simplest Markovian assumptions, the exhaustive and gated service disciplines are investigated, a method for calculating the transfer rate matrix of the Markovian process is proposed, formulas for calculating the basic probabilistic measures are obtained, and their numerical analysis is carried out. © 2013 Allerton Press, Inc.