Motivated by Erlang's classical loss model, queueing systems with finite capacity or storage constraints have been extensively investigated over about fifty years. Most notably at present, applications can be found in telecommunication, computer per- formance evaluation and manufacturing.

Queueing systems are studied with a last-come, first-served queueing discipline and batch arrivals generated by a finite number of non-exponential sources. A closedform expression is derived for the steady-state queue length distribution. This expression has a scaled geometric form and is insensitive to the input distribution. Moreover, an algorithm for the recursive computation of the normalizing constant and the busy source distribution is presented. The results are of both practical and theoretical interest as an extension of the standard Poisson batch input case.