A discrete-time product form for random access protocols

A discrete-time extension is obtained of recent product form results for random access schemes. A proof technique is presented that is new in that the global balance equations, which are much more complicated than the continuous-time analogs, are verified by inductively proving a multiple partial balance notion. An illustration of present-day applications is given. Particularly, randomized protocols are included and explicit discrete-time product form analogs of continuous-time results are obtained with applications in (1) carrier-sense multiple-access (CSMA) protocols such as busy tone multiple access (BTMA) and rude-CSMA, (2) circuit switching structures, and (3) metropolitan area network (MAN) systems