text: Since Tassiulas and Ephremides proposed the maximum weight scheduling algorithm of throughput-optimality for constrained queueing networks in 1992, extensive research efforts have been made for resolving its high complexity issue under various directions. In this paper, we resolve the issue by developing a generic framework for designing throughput-optimal and low-complexity scheduling algorithms. Under the framework, an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries. Therefore, one can design a variety of scheduling algorithms under this framework by choosing different oracles, e.g., the exhaustive search (ES), the markov chain monte carlo (MCMC), the belief propagation (BP) and the cutting-plane (CP) algorithms. The complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query, which is typically very small. Somewhat surprisingly, we prove that an algorithm using any such oracle is throughput-optimal for general constrained queueing network models that arise in the context of emerging large-scale communication networks. In particular, the pick-and-compare' algorithms developed by Tassiulas in 1998 and recently developed queue-based CSMA algorithms can be also understood as special cases of such algorithms using ES and MCMC oracles, respectively. To our best knowledge, our result is the first that establishes a rigorous connection between iterative optimization methods and low-complexity scheduling algorithms, which we believe provides various future directions and new insights in both areas.
  @cite_23: In this paper we use fluid model techniques to establish two results concerning the throughput of data switches. For an input-queued switch (with no speedup) we show that a maximum weight algorithm for connecting inputs and outputs delivers a throughput of 100 , and for combined input- and output-queued switches that run at a speedup of 2 we show that any maximal matching algorithm delivers a throughput of 100 . The only assumptions on the input traffic are that it satisfies the strong law of large numbers and that it does not oversubscribe any input or any output.
summary: Design and analysis of resource allocation algorithms in constrained queueing networks have been of great interest for last four decades across various research communities, where the contention resolution protocols in multiple-access broadcast channels have been studied since the mid-1970s @cite_23 . The broadcast channels induce a special constraint in resources usages among queues (i.e., every queue contend with all other queues), and simple distributed contention resolution protocols gained much attention in the ages. It is the year 1992 that the seminal work by Tassiulas and Ephremides proposed a throughput-optimal algorithm, referred to as MW, for general resource constraints. Its main appeal is that it does require only information on the current queue lengths (and instantaneous service rates) and does not rely on the knowledge of underlying system parameters. However, as we mentioned earlier, the MW algorithm suffers from the high implementation complexity, and a huge array of subsequent research has been made to develop algorithms with high performance guarantees and low-complexity.