New estimates of continuity in M/G/1 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 &Btilde; of service time. Assuming equality of two first moments of B and &Btilde; the continuity inequalities are derived in terms of difference pseudomoments of B and &Btilde;. When in addition the third moments of B and &Btilde; coincide than the constant involved in the corresponding inequality has the asymptotics O[(1 – ρ)^1/2] in the heavy traffic limit ρ → 1.