In a companion blog entry I discussed ways to measure or characterize the long-term fairness
of lock implementations. Measuring short-term fairness is also interesting. We could easily have a lock, such as cohort locks, that are fair over long intervals but intentionally unfair over the short-term. It's useful to have ways to define exactly how unfair a lock is over some interval. We'll assume the lock admission policy is work-conserving.
It's worth mentioning that measuring short-term fairness is slightly tricky because of induced probe effect
. As such, we sometimes use statistical sampling to reduce the overheads albeit with reduced certainty. I'll leave that discussion for subsequent blog entries.
I'll borrow Denning's working set
concept, but apply it locks instead of memory management. The working set of a program over some interval I is the set of distinct pages accessed during I. Where convenient and unambiguous, we'll sometimes quantify the working set as the number
of pages in the working set. Similarly, I'll define the lock working set (LWS)
for a given lock L over interval I as the set of distinct threads that acquired the lock during the interval. Instead of defining the interval I over wall-clock time, it's more convenient to treat each acquire of the lock as a virtual increment of our interval clock. We'll define LWSS as the size of the LWS. Even though we might define the interval I to be small, we can partition a long run into a set of M I-length disjoint intervals and report the average or median LWSS over those M points.
A related statistic is the median time to reacquire
(MTTR). Conceptually, we can think of a measurement run as generating a stream of thread IDs that acquired the lock. We can then iterate through that stream, and for every acquire, determine the number of intervening acquire operations that occurred since the thread last obtained the lock. That gives us a time-to-reacquire value, and in turn, we can compute the MTTR over the run.
Note that we might measure either the number of intervening acquires, or the number of distinct
threads to acquire in the interim.
My colleague Tim Harris noted that it could be useful to plot by varying the interval length I on the x-axis, and the average LWSS on the y-axis. This is somewhat reminiscent of MMU (minimum mutator utilization) graphs that appear in the garbage collection literature.
When a contended lock is unfair over the short term, it's typically the case that the set of threads circulating over the lock is partitioned into active and passive sets. The active circulating set corresponds to the LWSS.