On Non-existence of Optimal Local Synchronous Bandwidth Allocation Schemes for the Timed-Token MAC Protocol

Numerous methods have been proposed to integrate real-time and non-real-time services of the timed-token medium access control (MAC) protocol. One of the key issues in tailoring the timed-token protocol for real-time applications is the synchronous band-width allocation (SBA) problem whose objective is to meet both the protocol and deadline constraints. Several non-optimal local SBA schemes and two optimal global schemes have been proposed 1{4]. Local SBA schemes use only information available locally to each node, and are thus preferred to global schemes because of their lower network-management overhead. However, we formally prove, using the technique of adversary argument, that there does not exist any optimal local SBA scheme. During the preparation for this proof, we also derive a timing property that generalizes the previous ndings about the cycle-time properties of the timed-token protocol.