<p><b>Abstract</b>—One of the key issues in tailoring the timed-token MAC protocol for real-time applications is synchronous bandwidth allocation (SBA), whose objective is to meet both the protocol and deadline constraints. The former constraint requires that the total time allocated to all nodes for transmitting synchronous messages should not exceed the target token rotation time. The latter constraint requires that the minimum time available for a node to transmit its synchronous messages before their deadlines should be no less than the maximum message transmission time. Several nonoptimal local SBA schemes and an optimal global SBA scheme have been proposed [<ref rid="bibT04141" type="bib">1</ref>], [<ref rid="bibT04142" type="bib">2</ref>], [<ref rid="bibT04143" type="bib">3</ref>], [<ref rid="bibT04148" type="bib">8</ref>], [<ref rid="bibT041417" type="bib">17</ref>], [<ref rid="bibT041429" type="bib">29</ref>]. 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. If optimal local SBA schemes, if any, can be devised, they will be superior to their global counterparts both in performance and in ease of network management. In this paper, we formally prove that there does not exist any optimal local SBA scheme. We also propose an optimal global SBA scheme which has an <tmath>$O(nM)$</tmath> polynomial-time worst-case complexity, where <tmath>$n$</tmath> is the number of synchronous message streams in the system and <tmath>$M$</tmath> is the time complexity for solving a linear programming problem with <tmath>$3n$</tmath> constraints and <tmath>$n$</tmath> variables.</p>