In this paper the authors demonstrate that the distributional laws that relate the number of customers in the system (queue), L(Q) and the time a customer spends in the system (queue), S(W) under the first-in-first-out (FIFO) discipline are special cases of the H=λG law and lead to a complete solution for the distributions of L,Q,S,W for queueing systems which satisfy distributional laws for both L and Q (overtake free systems). Moreover, in such systems the derivation of the distributions of L,Q,S,W can be done in a unified way. Consequences of the distributional laws include a generalization of PASTA to queueing systems with arbitrary renewal arrivals under heavy traffic conditions, a generalization of the Pollaczek-Khinchine formula to the GI/G/1 queue, an extension of the Fuhrmann and Cooper decomposition for queues with generalized vacations under mixed generalized Erland renewal arrivals, approximate results for the distributions of L,S in a GI/G/• queue, and exact results for the distributions of L,Q,S,W in priority queues with mixed generalized Erlang renewal arrivals.
