A Note on a Sample-Path Rate Conservation Law and its Relationship with H = .G

We present a simple sample-path version of the rate conservation law (of Miyazawa) and then show that the H = .G law (of Heyman and Stidham) is essentially the same law, that is, either one can be derived from the other. As a final remark we illustrate the use of both laws jointly to quickly obtain a queueing result.