Stability of Token Passing

Suucient stability condition for the standard token passing ring is "known" since the seminal paper of Kuehn in 1979. However, this condition was derived without formal proof, and the proof seems to be of considerable interest to research community. In fact, Watson observed that in the performance evaluation of token passing rings "it is convenient to derive stability conditions ... (without proof)". Our intention is to ll this gap, and provide a formal proof of the suucient and necessary stability condition for the token passing ring. In this paper we present the case when the arrival process to each queue is Poisson but service times and switchover times are generally distributed. We consider in depth gated`-limited (` 1) service discipline for each station. We also indicate that the basic steps of our technique can be used to study the stability of some other multiqueue systems.