Ergodicity bounds for the Markovian queue with time-varying transition intensities, batch arrivals and one queue skipping policy

In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and one special skipping policy. Customers arrive in batches but are served by any order. The size of arriving batch becomes known upon its arrival at time instant total number customers is also known. According to adopted policy if batch, which greater than current system, arrives, all currently residing removed from it new placed queue. Otherwise lost does not have effect on system. distribution under consideration assumption that intensity ?(t) and/or service ?(t) non-random functions time. We provide method for computation upper bounds rate convergence limiting regime, whenever exists, bounded (not necessarily periodic) size. For periodic intensities light-tailed shown how obtained can be used numerically compute given error. Illustrating numerical examples provided.