Unless the maximum budget B_max that BFQ can assign to a queue is set
explicitly by the user, BFQ automatically updates B_max. In
particular, BFQ dynamically sets B_max to the number of sectors that
can be read, at the current estimated peak rate, during the maximum
time, T_max, allowed before a budget timeout occurs. In formulas, if
we denote as R_est the estimated peak rate, then B_max = T_max ∗
R_est. Hence, the higher R_est is with respect to the actual device
peak rate, the higher the probability that processes incur budget
timeouts unjustly is. Besides, a too high value of B_max unnecessarily
increases the deviation from an ideal, smooth service.

Unfortunately, it is not trivial to estimate the peak rate correctly:
because of the presence of sw and hw queues between the scheduler and
the device components that finally serve I/O requests, it is hard to
say exactly when a given dispatched request is served inside the
device, and for how long. As a consequence, it is hard to know
precisely at what rate a given set of requests is actually served by
the device.

On the opposite end, the dispatch time of any request is trivially
available, and, from this piece of information, the "dispatch rate"
of requests can be immediately computed. So, the idea in the next
function is to use what is known, namely request dispatch times
(plus, when useful, request completion times), to estimate what is
unknown, namely in-device request service rate.

The main issue is that, because of the above facts, the rate at
which a certain set of requests is dispatched over a certain time
interval can vary greatly with respect to the rate at which the
same requests are then served. But, since the size of any
intermediate queue is limited, and the service scheme is lossless
(no request is silently dropped), the following obvious convergence
property holds: the number of requests dispatched MUST become
closer and closer to the number of requests completed as the
observation interval grows. This is the key property used in
this new version of the peak-rate estimator.
Signed-off-by: Paolo Valente <paolo.valente@linaro.org>
Signed-off-by: Arianna Avanzini <avanzini.arianna@gmail.com>
Signed-off-by: Jens Axboe <axboe@fb.com>