On batch queueing systems: A combinatorial approach

We consider batch queueing systems M/MH/1M/MH/1 and MH/M/1MH/M/1 with catastrophes. The transient probability functions of these queueing systems are obtained by a Lattice Path Combinatorics approach that utilizes randomization and dual processes. Steady state distributions are also determined. Generalization to systems having batches of different sizes are discussed.