Performance Evaluation of a Preemptive Pro- Tocol for Voice-data Integration in Ring-based Theorem 5.1 the Suucient Condition for Schedula- Bility of All Streams following the above Protocol Is

Proof: In this protocol X becomes a multi-access variable. If the sequentiality of X could be maintained we would get the same utilization bound as derived earlier. Note, that since there are only M slots, X may be simultaneously accessed by at most M stations. In the worst case when the value of X is 1 and M stations pick one slack slot each, they in the process deprive (M ? 1) stations down stream from their legitimate integral requirements. However, this can be taken care of by keeping (M ? 1) extra slots for every cycle. Hence, the condition for suuciency is, P N i=1 TC i =P i + M ? 1 M(L ? 1). This leads to the stated utilization bound. In Figure 4, we plot the schedulable utilization with respect to the cycle length L. The plot shows that the schedulable utilization asymptotically approaches the ideal (i.e., M). Furthermore, very high levels of schedulable utilization can be achieved for moderate values of L.