In the present paper the waiting system G/G/1 is investigated. We form the functionals (3.1) with the service-time distribution B or the inter arrival time distribution A or K (see (1.1)).By means of them it is possible to define a haif order relation of random variables or distributions functions, respectively. We consider rhree systems G/G/1 and estimate - with reference to this relations - the distributions A, B, K above and below by the corre- sponding distribiitions of the two other systems considered as known. Then upper and lower bounds of the semiinvariants of the stationary waiting time (i e. the mean waiting time, variance etc.) of the given system are obtained.