4,241 research outputs found
On Resource Pooling and Separation for LRU Caching
Caching systems using the Least Recently Used (LRU) principle have now become
ubiquitous. A fundamental question for these systems is whether the cache space
should be pooled together or divided to serve multiple flows of data item
requests in order to minimize the miss probabilities. In this paper, we show
that there is no straight yes or no answer to this question, depending on
complex combinations of critical factors, including, e.g., request rates,
overlapped data items across different request flows, data item popularities
and their sizes. Specifically, we characterize the asymptotic miss
probabilities for multiple competing request flows under resource pooling and
separation for LRU caching when the cache size is large.
Analytically, we show that it is asymptotically optimal to jointly serve
multiple flows if their data item sizes and popularity distributions are
similar and their arrival rates do not differ significantly; the
self-organizing property of LRU caching automatically optimizes the resource
allocation among them asymptotically. Otherwise, separating these flows could
be better, e.g., when data sizes vary significantly. We also quantify critical
points beyond which resource pooling is better than separation for each of the
flows when the overlapped data items exceed certain levels. Technically, we
generalize existing results on the asymptotic miss probability of LRU caching
for a broad class of heavy-tailed distributions and extend them to multiple
competing flows with varying data item sizes, which also validates the Che
approximation under certain conditions. These results provide new insights on
improving the performance of caching systems
Optimal Posted Prices for Online Cloud Resource Allocation
We study online resource allocation in a cloud computing platform, through a
posted pricing mechanism: The cloud provider publishes a unit price for each
resource type, which may vary over time; upon arrival at the cloud system, a
cloud user either takes the current prices, renting resources to execute its
job, or refuses the prices without running its job there. We design pricing
functions based on the current resource utilization ratios, in a wide array of
demand-supply relationships and resource occupation durations, and prove
worst-case competitive ratios of the pricing functions in terms of social
welfare. In the basic case of a single-type, non-recycled resource (i.e.,
allocated resources are not later released for reuse), we prove that our
pricing function design is optimal, in that any other pricing function can only
lead to a worse competitive ratio. Insights obtained from the basic cases are
then used to generalize the pricing functions to more realistic cloud systems
with multiple types of resources, where a job occupies allocated resources for
a number of time slots till completion, upon which time the resources are
returned back to the cloud resource pool
The Cost of Uncertainty in Curing Epidemics
Motivated by the study of controlling (curing) epidemics, we consider the
spread of an SI process on a known graph, where we have a limited budget to use
to transition infected nodes back to the susceptible state (i.e., to cure
nodes). Recent work has demonstrated that under perfect and instantaneous
information (which nodes are/are not infected), the budget required for curing
a graph precisely depends on a combinatorial property called the CutWidth. We
show that this assumption is in fact necessary: even a minor degradation of
perfect information, e.g., a diagnostic test that is 99% accurate, drastically
alters the landscape. Infections that could previously be cured in sublinear
time now may require exponential time, or orderwise larger budget to cure. The
crux of the issue comes down to a tension not present in the full information
case: if a node is suspected (but not certain) to be infected, do we risk
wasting our budget to try to cure an uninfected node, or increase our certainty
by longer observation, at the risk that the infection spreads further? Our
results present fundamental, algorithm-independent bounds that tradeoff budget
required vs. uncertainty.Comment: 35 pages, 3 figure
PSBS: Practical Size-Based Scheduling
Size-based schedulers have very desirable performance properties: optimal or
near-optimal response time can be coupled with strong fairness guarantees.
Despite this, such systems are very rarely implemented in practical settings,
because they require knowing a priori the amount of work needed to complete
jobs: this assumption is very difficult to satisfy in concrete systems. It is
definitely more likely to inform the system with an estimate of the job sizes,
but existing studies point to somewhat pessimistic results if existing
scheduler policies are used based on imprecise job size estimations. We take
the goal of designing scheduling policies that are explicitly designed to deal
with inexact job sizes: first, we show that existing size-based schedulers can
have bad performance with inexact job size information when job sizes are
heavily skewed; we show that this issue, and the pessimistic results shown in
the literature, are due to problematic behavior when large jobs are
underestimated. Once the problem is identified, it is possible to amend
existing size-based schedulers to solve the issue. We generalize FSP -- a fair
and efficient size-based scheduling policy -- in order to solve the problem
highlighted above; in addition, our solution deals with different job weights
(that can be assigned to a job independently from its size). We provide an
efficient implementation of the resulting protocol, which we call Practical
Size-Based Scheduler (PSBS). Through simulations evaluated on synthetic and
real workloads, we show that PSBS has near-optimal performance in a large
variety of cases with inaccurate size information, that it performs fairly and
it handles correctly job weights. We believe that this work shows that PSBS is
indeed pratical, and we maintain that it could inspire the design of schedulers
in a wide array of real-world use cases.Comment: arXiv admin note: substantial text overlap with arXiv:1403.599
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