New estimates of continuity in M/GI/1/\infty queues
1998
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.
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