Research of various network traffic types proves that it is self-similar. Therefore, recently many works and fundamental monograph is devoted to its research. Self-similar traffic influence on communication devices, such as network switchboards, concentrators and network servers, lead to sharp decrease in their functioning quality, comparing to operating mode in conditions of traditional streams of packets and queries. It reveals in throughput reduction of network nodes, insufficiency of buffer memory and results in increased of denial of service. Usually all researches of self-similar traffic influence were made in stationary operating mode of switched devices. Author of the given work observed indicators of self-similar traffic at inclusion of communication devices in work, when load swing arise and certain time -- relaxation time -- was required for device to enter into a normal stationary operating mode. Therefore in the given work the attention is given to relaxation time. As a result of research data about transient process durations, utilization of buffer memory depending on server load have been obtained.