On the Stability Proof of Adaptive Schemes with Static Normalizing Signals and Parameter Projection

of the processors in such a manner that if it is not optimal to assign a job to processor i then it is not optimal to make an assignment to processor i until such time as there is at least one more arrival. That is, the state cannot change to one in which it becomes optimal to assign a job to processor i simply by the departure of jobs. This is the behavior we have observed numerically and argued for above.