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