Binary exponential backoff is a randomized protocol for regulating transmissions on a multiple-access broadcast channel. Ethernet, a local-area network, is built upon this protocol. The fundamental theoretical issue is stability: Does the backlog of packets awaiting transmission remain bounded in time, provided the rates of new packet arrivals are small… (More)
In this paper we develop tools for analyzing the rate at which a reversible Markov chain converges to stationarity. Our techniques are useful when the Markov chain can be decomposed into pieces which are themselves easier to analyze. The main theorems relate the spectral gap of the original Markov chains to the spectral gap of the pieces. In the first case… (More)
The Metropolis-coupled Markov chain method (or " Swapping Algorithm ") is an empirically successful hybrid Monte Carlo algorithm. It alternates between standard transitions on parallel versions of the system at different parameter values, and swapping two versions. We prove rapid mixing for two bimodal examples, including the mean-field Ising model.
Fair Queuing is a novel queuing discipline with important applications to data networks that support variable-size packets and to systems where the cost of preempting jobs from service is high. The disciphne controls a single server shared by N job arrival streams with each stream allotted a separate queue. After every job completion, the server is assigned… (More)
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For a fixed permutation τ, let S N (τ) be the set of permutations on N elements that avoid the pattern τ. Madras and Liu (2010) conjectured that lim N→∞ |S N+1 (τ)| |S N (τ)| exists; if it does, it must equal the Stanley–Wilf limit. We prove the conjecture for every permutation τ of length 5 or less, as well as for some longer cases (including 704 of the… (More)
We consider the stochastic behavior of binary exponential backoff, a probabilistic algorithm for regulating transmissions on a multiple access channel. Ethernet, a local area network, is built upon this algorithm. The fundamental theoretical issue is stability: does the backlog of packets awaiting transmission remain bounded in time, provided the rates of… (More)
Richard Tweedie for helpful conversations.