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In this paper we revisit the Markovian queueing system with a single server,infinite capacity queue and the special queue skipping policy. Customers arrivein batches, but are served one by one according to any conservative discipline.The size of the arriving batch becomes known upon its arrival and at any timeinstant the total number of customers in the system is also known. According tothe adopted queue skipping policy if a batch, which size is greater than thecurrent system size, arrives to the system, all current customers in the systemare removed from it and the new batch is placed in the queue. Otherwise the newbatch is lost. The distribution of the total number of customers in the systemis under consideration under assumption that the arrival intensity $\lambda(t)$and/or the service intensity $\mu(t)$ are non-random functions of time. Weprovide the method for the computation of the upper bounds for the rate ofconvergence of system size to the limiting regime, whenever it exists, for anybounded $\lambda(t)$ and $\mu(t)$ (not necessarily periodic) and anydistribution of the batch size. For periodic intensities $\lambda(t)$ and/or$\mu(t)$ and light-tailed distribution of the batch size it is shown how theobtained bounds can be used to numerically compute the limiting distribution ofthe queue size with the given error. Illustrating numerical examples areprovided.

Ergodicity Bounds for the Markovian Queue With Time-Varying Transition Intensities, Batch Arrivals and One Queue Skipping Policy