A note on the conservation law for queues with batch arrivals

The conservation law formula for work-conserving queues with batch arrivals is derived for when the arrival instants of customers are assumed to constitute an arrivals see time averages (ASTA) process. The derivation is based on the analysis of the corresponding first-in first-out (FIFO) multiclass queue and its steady state. Hence, the mean work load in the queue at an arbitrary time instant can be equated with the mean time that an arbitrary customer has to wait in the FIFO queue