Threshold load control is one of the key tools in preventing overload in telecommunication networks. Its implementation as hysteretic control mechanism is used for detecting and mitigating congestion in Next Generation Networks, where session initiation protocol is the main signalling protocol. In this paper single-server finite capacity queuing system with constant service time, poisson input flows and hysteretic policy is being analyzed. Analytical method which allowed to obtain new results related to probability distribution (in terms of Laplace-Stieltjes transform) of system's sojourn time in different modes defined by hysteretic policy is proposed. Numerical example illustrating time-related probability characteristics of the system under various initial conditions is given. © 2014 IEEE.