Admissible Traces, Stability and Rate Management of Queueing / Switching Service Structures

This paper studies the slotted time Queueing / Switching Service Structure (QSSS) problem, where service configurations are selected dynamically in response to queue workload backlogs, so as to maintain stability (inflow-outflow balance) when possible. The only assumption on the traffic traces is that the incoming workload in each slot is bounded by some global (per trace), finite, burst ceiling. First, a key condition is identified, based on which each traffic trace can be classified as either admissible or non-admissible. Non-admissible traces drive the QSSS unstable, irrespective of the service configuration algorithm. Under admissible traces, the QSSS will remain stable when a Stabilizing Scheduling Algorithm (SSA) is utilized to control the service configuration. It is shown that Maximum-Weight-Matching (MWM) and Projective-Cone- Scheduling (PCS) belong to the SSA family. In addition, useful, theoretical tools are developed to facilitate trace classification. Second, the impact of rate management (i.e. power management) on stability is theoretically explored. In particular, under mild assumptions, it is proven that ´low workload backlog´ decisions have little effect on the stability of a QSSS, provided that above a certain backlog threshold SSA-based service configuration controls are used.