Timing properties of the timed token MAC protocol

We investigate the inherent timing properties of the timed token medium access control (MAC) protocol that are necessary for guaranteeing synchronous message deadlines in a timed token ring network such as the Fibre Distributed Data Interface (FDDI) network. As a result, the best-so-far result of the upper bound on the time possibly elapsed between any number of successive token arrivals at a particular node was derived. This result, which is particularly important for studies on real-time communications in any timed token ring network, has been published by Zhang and Burns (see IEEE/ACM Trans. on Networking, vol.3, p. 729-41, 1995) with no proof given. In this paper, we complement our early work by presenting a concise formal proof of this upper bound.