STAIR: Practical AIMD Multirate Congestion Control

Existing approaches for multirate multicast congestion control are either friendly to TCP only over large time scales or introduce unfortunate side effects, such as significant control traffic, wasted bandwidth, or the need for modifications to existing routers. We advocate a layered multicast approach in which steady-state receiver reception rates emulate the classical TCP sawtooth derived from additive-increase, multiplicative decrease (AIMD) principles. Our approach introduces the concept of dynamic stair layers to simulate various rates of additive increase for receivers with heterogeneous round-trip times (RTTs), facilitated by a minimal amount of IGMP control traffic. We employ a mix of cumulative and non-cumulative layering to minimize the amount of excess bandwidth consumed by receivers operating asynchronously behind a shared bottleneck. We integrate these techniques together into a congestion control scheme called STAIR which is amenable to those multicast applications which can make effective use of arbitrary and time-varying subscription levels.

Some Considerations on a Calculus with Weak References

Weak references are references that do not prevent the object they point to from being garbage collected. Most realistic languages, including Java, SML/NJ, and OCaml to name a few, have some facility for programming with weak references. Weak references are used in implementing idioms like memoizing functions and hash-consing in order to avoid potential memory leaks. However, the semantics of weak references in many languages are not clearly specified. Without a formal semantics for weak references it becomes impossible to prove the correctness of implementations making use of this feature. Previous work by Hallett and Kfoury extends λgc, a language for modeling garbage collection, to λweak, a similar language with weak references. Using this previously formalized semantics for weak references, we consider two issues related to well-behavedness of programs. Firstly, we provide a new, simpler proof of the well-behavedness of the syntactically restricted fragment of λweak defined previously. Secondly, we give a natural semantic criterion for well-behavedness much broader than the syntactic restriction, which is useful as principle for programming with weak references. Furthermore we extend the result, proved in previously of λgc, which allows one to use type-inference to collect some reachable objects that are never used. We prove that this result holds of our language, and we extend this result to allow the collection of weakly-referenced reachable garbage without incurring the computational overhead sometimes associated with collecting weak bindings (e.g. the need to recompute a memoized function). Lastly we use extend the semantic framework to model the key/value weak references found in Haskell and we prove the Haskell is semantics equivalent to a simpler semantics due to the lack of side-effects in our language.