5,261 research outputs found
Are Lock-Free Concurrent Algorithms Practically Wait-Free?
Lock-free concurrent algorithms guarantee that some concurrent operation will
always make progress in a finite number of steps. Yet programmers prefer to
treat concurrent code as if it were wait-free, guaranteeing that all operations
always make progress. Unfortunately, designing wait-free algorithms is
generally a very complex task, and the resulting algorithms are not always
efficient. While obtaining efficient wait-free algorithms has been a long-time
goal for the theory community, most non-blocking commercial code is only
lock-free.
This paper suggests a simple solution to this problem. We show that, for a
large class of lock- free algorithms, under scheduling conditions which
approximate those found in commercial hardware architectures, lock-free
algorithms behave as if they are wait-free. In other words, programmers can
keep on designing simple lock-free algorithms instead of complex wait-free
ones, and in practice, they will get wait-free progress.
Our main contribution is a new way of analyzing a general class of lock-free
algorithms under a stochastic scheduler. Our analysis relates the individual
performance of processes with the global performance of the system using Markov
chain lifting between a complex per-process chain and a simpler system progress
chain. We show that lock-free algorithms are not only wait-free with
probability 1, but that in fact a general subset of lock-free algorithms can be
closely bounded in terms of the average number of steps required until an
operation completes.
To the best of our knowledge, this is the first attempt to analyze progress
conditions, typically stated in relation to a worst case adversary, in a
stochastic model capturing their expected asymptotic behavior.Comment: 25 page
Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
We consider a random walk in a stationary ergodic environment in ,
with unbounded jumps. In addition to uniform ellipticity and a bound on the
tails of the possible jumps, we assume a condition of strong transience to the
right which implies that there are no "traps". We prove the law of large
numbers with positive speed, as well as the ergodicity of the environment seen
from the particle. Then, we consider Knudsen stochastic billiard with a drift
in a random tube in , , which serves as environment.
The tube is infinite in the first direction, and is a stationary and ergodic
process indexed by the first coordinate. A particle is moving in straight line
inside the tube, and has random bounces upon hitting the boundary, according to
the following modification of the cosine reflection law: the jumps in the
positive direction are always accepted while the jumps in the negative
direction may be rejected. Using the results for the random walk in random
environment together with an appropriate coupling, we deduce the law of large
numbers for the stochastic billiard with a drift.Comment: 37 pages, 1 figure; to appear in Annales de l'Institut Henri
Poincar\'e (B) Probabilit\'es et Statistique
The Evolution of Dispersal in Random Environments and The Principle of Partial Control
McNamara and Dall (2011) identified novel relationships between the abundance
of a species in different environments, the temporal properties of
environmental change, and selection for or against dispersal. Here, the
mathematics underlying these relationships in their two-environment model are
investigated for arbitrary numbers of environments. The effect they described
is quantified as the fitness-abundance covariance. The phase in the life cycle
where the population is censused is crucial for the implications of the
fitness-abundance covariance. These relationships are shown to connect to the
population genetics literature on the Reduction Principle for the evolution of
genetic systems and migration. Conditions that produce selection for increased
unconditional dispersal are found to be new instances of departures from
reduction described by the "Principle of Partial Control" proposed for the
evolution of modifier genes. According to this principle, variation that only
partially controls the processes that transform the transmitted information of
organisms may be selected to increase these processes. Mathematical methods of
Karlin, Friedland, and Elsner, Johnson, and Neumann, are central in
generalizing the analysis. Analysis of the adaptive landscape of the model
shows that the evolution of conditional dispersal is very sensitive to the
spectrum of genetic variation the population is capable of producing, and
suggests that empirical study of particular species will require an evaluation
of its variational properties.Comment: Dedicated to the memory of Professor Michael Neumann, one of whose
many elegant theorems provides for a result presented here. 28 pages, 1
table, 1 figur
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