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In this paper one presents method for the computation of convergence boundsfor four classes of multiserver queueing systems, described by inhomogeneousMarkov chains. Specifically one considers inhomogeneous $M/M/S$ queueing systemwith possibly state-dependent arrival and service intensities and additionallypossible batch arrivals and batch service. The unified approach based onlogarithmic norm of linear operators for obtaining sharp upper and lower boundson the rate of convergence and corresponding sharp perturbation bounds isdescribed. As a side result, one shows by virtue of numerical examples that theapproach based on logarithmic norm can also be used for approximation oflimiting characteristics (idle probability and mean number of customers in thesystem) of the considered systems with given approximation error. Extensivenumerical examples are provided.

Bounds on the rate of convergence for inhomogeneous $M/M/S$ systems with either state-dependent transitions, or batch arrivals and service, or both