Dual processes to solve single server systems

A new approach is used to determine the transient probability functions of the classical queueing systems: M/M/1, M/M/1/H, and M/M/1/H with catastrophes. This new solution method uses dual processes, randomization and lattice path combinatorics. The method reveals that the transient probability functions for M/M/1/H and M/M/1/H with catastrophes have the same mathematical form.