18 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
Global attraction of ODE-based mean field models with hyperexponential job sizes
Mean field modeling is a popular approach to assess the performance of large
scale computer systems. The evolution of many mean field models is
characterized by a set of ordinary differential equations that have a unique
fixed point. In order to prove that this unique fixed point corresponds to the
limit of the stationary measures of the finite systems, the unique fixed point
must be a global attractor. While global attraction was established for various
systems in case of exponential job sizes, it is often unclear whether these
proof techniques can be generalized to non-exponential job sizes. In this paper
we show how simple monotonicity arguments can be used to prove global
attraction for a broad class of ordinary differential equations that capture
the evolution of mean field models with hyperexponential job sizes. This class
includes both existing as well as previously unstudied load balancing schemes
and can be used for systems with either finite or infinite buffers. The main
novelty of the approach exists in using a Coxian representation for the
hyperexponential job sizes and a partial order that is stronger than the
componentwise partial order used in the exponential case.Comment: This paper was accepted at ACM Sigmetrics 201
Stochastic Modeling of Hybrid Cache Systems
In recent years, there is an increasing demand of big memory systems so to
perform large scale data analytics. Since DRAM memories are expensive, some
researchers are suggesting to use other memory systems such as non-volatile
memory (NVM) technology to build large-memory computing systems. However,
whether the NVM technology can be a viable alternative (either economically and
technically) to DRAM remains an open question. To answer this question, it is
important to consider how to design a memory system from a "system
perspective", that is, incorporating different performance characteristics and
price ratios from hybrid memory devices.
This paper presents an analytical model of a "hybrid page cache system" so to
understand the diverse design space and performance impact of a hybrid cache
system. We consider (1) various architectural choices, (2) design strategies,
and (3) configuration of different memory devices. Using this model, we provide
guidelines on how to design hybrid page cache to reach a good trade-off between
high system throughput (in I/O per sec or IOPS) and fast cache reactivity which
is defined by the time to fill the cache. We also show how one can configure
the DRAM capacity and NVM capacity under a fixed budget. We pick PCM as an
example for NVM and conduct numerical analysis. Our analysis indicates that
incorporating PCM in a page cache system significantly improves the system
performance, and it also shows larger benefit to allocate more PCM in page
cache in some cases. Besides, for the common setting of performance-price ratio
of PCM, "flat architecture" offers as a better choice, but "layered
architecture" outperforms if PCM write performance can be significantly
improved in the future.Comment: 14 pages; mascots 201
Asymptotic Miss Ratio of LRU Caching with Consistent Hashing
To efficiently scale data caching infrastructure to support emerging big data
applications, many caching systems rely on consistent hashing to group a large
number of servers to form a cooperative cluster. These servers are organized
together according to a random hash function. They jointly provide a unified
but distributed hash table to serve swift and voluminous data item requests.
Different from the single least-recently-used (LRU) server that has already
been extensively studied, theoretically characterizing a cluster that consists
of multiple LRU servers remains yet to be explored. These servers are not
simply added together; the random hashing complicates the behavior. To this
end, we derive the asymptotic miss ratio of data item requests on a LRU cluster
with consistent hashing. We show that these individual cache spaces on
different servers can be effectively viewed as if they could be pooled together
to form a single virtual LRU cache space parametrized by an appropriate cache
size. This equivalence can be established rigorously under the condition that
the cache sizes of the individual servers are large. For typical data caching
systems this condition is common. Our theoretical framework provides a
convenient abstraction that can directly apply the results from the simpler
single LRU cache to the more complex LRU cluster with consistent hashing.Comment: 11 pages, 4 figure
Adaptive TTL-Based Caching for Content Delivery
Content Delivery Networks (CDNs) deliver a majority of the user-requested
content on the Internet, including web pages, videos, and software downloads. A
CDN server caches and serves the content requested by users. Designing caching
algorithms that automatically adapt to the heterogeneity, burstiness, and
non-stationary nature of real-world content requests is a major challenge and
is the focus of our work. While there is much work on caching algorithms for
stationary request traffic, the work on non-stationary request traffic is very
limited. Consequently, most prior models are inaccurate for production CDN
traffic that is non-stationary.
We propose two TTL-based caching algorithms and provide provable guarantees
for content request traffic that is bursty and non-stationary. The first
algorithm called d-TTL dynamically adapts a TTL parameter using a stochastic
approximation approach. Given a feasible target hit rate, we show that the hit
rate of d-TTL converges to its target value for a general class of bursty
traffic that allows Markov dependence over time and non-stationary arrivals.
The second algorithm called f-TTL uses two caches, each with its own TTL. The
first-level cache adaptively filters out non-stationary traffic, while the
second-level cache stores frequently-accessed stationary traffic. Given
feasible targets for both the hit rate and the expected cache size, f-TTL
asymptotically achieves both targets. We implement d-TTL and f-TTL and evaluate
both algorithms using an extensive nine-day trace consisting of 500 million
requests from a production CDN server. We show that both d-TTL and f-TTL
converge to their hit rate targets with an error of about 1.3%. But, f-TTL
requires a significantly smaller cache size than d-TTL to achieve the same hit
rate, since it effectively filters out the non-stationary traffic for
rarely-accessed objects
On the throughput optimization in large-scale batch-processing systems
We analyse a data-processing system with clients producing jobs which are processed in batches by parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function. In practice, throughput optimization relies on numerical searches for the optimal batch size, a process that can take up to multiple days in existing commercial systems. In this paper, we model the system in terms of a closed queueing network; a standard Markovian analysis yields the optimal throughput in time. Our main contribution is a mean-field model of the system for the regime where the system size is large. We show that the mean-field model has a unique, globally attractive stationary point which can be found in closed form and which characterizes the asymptotic throughput of the system as a function of the batch size. Using this expression we find the asymptotically optimal throughput in time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes