Formal Abstractions for Packet Scheduling
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This paper studies PIFO trees from a programming language perspective. PIFO trees are a recently proposed model for programmable packet schedulers. They can express a wide range of scheduling algorithms including strict priority, weighted fair queueing, hierarchical schemes, and more. However, their semantic properties are not well understood. We formalize the syntax and semantics of PIFO trees in terms of an operational model. We also develop an alternate semantics in terms of permutations on lists of packets, prove theorems characterizing expressiveness, and develop an embedding algorithm for replicating the behavior of one with another. We present a prototype implementation of PIFO trees in OCaml and relate its behavior to a hardware switch on a variety of standard and novel scheduling algorithms.
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