On the Stability of Timed Token Rings

We analyze in this paper the stability of two types of timed-token rings: the existing Fiber Distributed Data Interface (FDDI) token ring protocol, and a new variant of the FDDI that we propose. The FDDI supports two classes of traac: synchronous and asynchronous. The time constraint mechanism of FDDI guarantees the transmission delay of synchronous traac: a Target Token Rotation Time (TTRT) being xed, the FDDI protocol ensures that the token rotation time is always bounded above by twice TTRT. We consider the stability of the asynchronous traac, for both FDDI and for the new proposed protocol, for which the token rotation time is also bounded by twice TTRT. We obtain suucient and necessary stability conditions, which indicates how the choice of parameters aaects the stability of the system. We show that the stability conditions of the new protocol are weaker (and thus it enables to transmit more asynchronous packets). This protocol is also easier to implement as it requires less timers.