5,627 research outputs found
On the capacity of information processing systems
We propose and analyze a family of information processing systems, where a
finite set of experts or servers are employed to extract information about a
stream of incoming jobs. Each job is associated with a hidden label drawn from
some prior distribution. An inspection by an expert produces a noisy outcome
that depends both on the job's hidden label and the type of the expert, and
occupies the expert for a finite time duration. A decision maker's task is to
dynamically assign inspections so that the resulting outcomes can be used to
accurately recover the labels of all jobs, while keeping the system stable.
Among our chief motivations are applications in crowd-sourcing, diagnostics,
and experiment designs, where one wishes to efficiently learn the nature of a
large number of items, using a finite pool of computational resources or human
agents.
We focus on the capacity of such an information processing system. Given a
level of accuracy guarantee, we ask how many experts are needed in order to
stabilize the system, and through what inspection architecture. Our main result
provides an adaptive inspection policy that is asymptotically optimal in the
following sense: the ratio between the required number of experts under our
policy and the theoretical optimal converges to one, as the probability of
error in label recovery tends to zero
Queuing with future information
We study an admissions control problem, where a queue with service rate
receives incoming jobs at rate , and the decision maker is
allowed to redirect away jobs up to a rate of , with the objective of
minimizing the time-average queue length. We show that the amount of
information about the future has a significant impact on system performance, in
the heavy-traffic regime. When the future is unknown, the optimal average queue
length diverges at rate , as . In sharp contrast, when all future arrival and service times are revealed
beforehand, the optimal average queue length converges to a finite constant,
, as . We further show that the finite limit of
can be achieved using only a finite lookahead window starting from the current
time frame, whose length scales as , as
. This leads to the conjecture of an interesting duality between
queuing delay and the amount of information about the future.Comment: Published in at http://dx.doi.org/10.1214/13-AAP973 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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