Consideration is given to the problem of estimation of the true stationary mean response time in the discrete-time single-server queue of infinite capacity, with Bernoulli input, round-robin scheduling, and inaccurate information about the service time distribution which is considered to be general arithmetic. It is shown that the upper bound for the true value may be provided by the mean response time in the discrete-time single-server queue with LIFO (last in, first out) service discipline and resampling policy. The latter implies that a customer arriving to the nonidle system assigns new remaining service time for the customer in the server. For the case when the true service time distribution is geometric and the error in the service times is of multiplicative type, conditions are provided which, when satisfied, guarantee that the proposed method yields the upper bound across all possible values of the system's load. © 2019 Federal Research Center "Computer Science and Control" of Russian Academy of Sciences. All rights reserved.