Abstract: Thermodynamic functions of server systems are calculated by using statistical distrbutions of completely open system.It is seen that the present results are the same as other distributions,nevertheless,only substituted mean values are replaced for the unchanged values in other distributions.The relatively fluctuations are completely different with other distributions and are in proportion to 1,rather than 1/N.

Key words: statistical mechanics, thermodynamic quantity, relatively fluctuation, completely open system：statistical distributions