Stationary distribution of an infinite-buffer batch-arrival and batch-service queue with random serving capacity and batch-size-dependent service

In traditional batch-service queueing systems, the mean service time of batches are generally assumed to be constant. However, in numerous applications this assumption may not appropriate. telecommunication networks, transmission rates depend on number packets batch which can framed as batch-size-dependent queue. The objective paper is focus both queue and server content distribution an infinite-buffer batch-arrival with random serving capacity rule service. After deriving a bivariate probability generating function length at departure epoch batch, we extract complete joint terms roots characteristic equation. We also obtain system well arbitrary epoch. Finally, significant numerical examples appended show feasibility analytic procedure results where occurrence multiple have been dealt without facing any difficulty. At end, graphical representation cost shows that more compared batch-size-independent