New estimates of continuity in M/GI/1/\infty queues

The paper deals with an estimation of the total variation distance between stationary distributions of waiting time in two queueing systems with equal Poisson inputs and different distributions B and \widetilde{B} of service time. Assuming equality of two first moments of B and \widetilde{B} the continuity inequalities are derived in terms of difference pseudomoments of B and \widetilde{B}. When in addition the third moments of B and \widetilde{B} coincide then the constant involved in the corresponding inequality has the asymptotics \mathrm{O}[(1-\rho)^{1/2}] in the heavy traffic limit \rho\to 1.