We present a path-counting method for deriving Laplace transforms of order statistics of independent but not necessarily identically distributed Erlang random variables, based on a probabilistic interpretation of the Laplace transform. The method is applicable also to generalized Erlang variates...

The stationary distributions of the waiting time and number in the system are obtained for a variant of an M/M/2 queue in which non-waiting customers receive a different rate of service from those who must wait in line. Characteristics of the solution, and applications of the model are...