6,849 research outputs found
Localization for Anchoritic Sensor Networks
We introduce a class of anchoritic sensor networks, where communications
between sensor nodes is undesirable or infeasible, e.g., due to harsh
environment, energy constraints, or security considerations
Modulated Branching Processes, Origins of Power Laws and Queueing Duality
Power law distributions have been repeatedly observed in a wide variety of
socioeconomic, biological and technological areas. In many of the observations,
e.g., city populations and sizes of living organisms, the objects of interest
evolve due to the replication of their many independent components, e.g.,
births-deaths of individuals and replications of cells. Furthermore, the rates
of the replication are often controlled by exogenous parameters causing periods
of expansion and contraction, e.g., baby booms and busts, economic booms and
recessions, etc. In addition, the sizes of these objects often have reflective
lower boundaries, e.g., cities do not fall bellow a certain size, low income
individuals are subsidized by the government, companies are protected by
bankruptcy laws, etc.
Hence, it is natural to propose reflected modulated branching processes as
generic models for many of the preceding observations. Indeed, our main results
show that the proposed mathematical models result in power law distributions
under quite general polynomial Gartner-Ellis conditions, the generality of
which could explain the ubiquitous nature of power law distributions. In
addition, on a logarithmic scale, we establish an asymptotic equivalence
between the reflected branching processes and the corresponding multiplicative
ones. The latter, as recognized by Goldie (1991), is known to be dual to
queueing/additive processes. We emphasize this duality further in the
generality of stationary and ergodic processes.Comment: 36 pages, 2 figures; added references; a new theorem in Subsection
4.
Characterizing Heavy-Tailed Distributions Induced by Retransmissions
Consider a generic data unit of random size L that needs to be transmitted
over a channel of unit capacity. The channel availability dynamics is modeled
as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period
of time that the channel becomes available, say A_i, we attempt to transmit the
data unit. If L<A_i, the transmission was considered successful; otherwise, we
wait for the next available period and attempt to retransmit the data from the
beginning. We investigate the asymptotic properties of the number of
retransmissions N and the total transmission time T until the data is
successfully transmitted. In the context of studying the completion times in
systems with failures where jobs restart from the beginning, it was shown that
this model results in power law and, in general, heavy-tailed delays. The main
objective of this paper is to uncover the detailed structure of this class of
heavy-tailed distributions induced by retransmissions. More precisely, we study
how the functional dependence between P[L>x] and P[A>x] impacts the
distributions of N and T. In particular, we discover several functional
criticality points that separate classes of different functional behavior of
the distribution of N. We also discuss the engineering implications of our
results on communication networks since retransmission strategy is a
fundamental component of the existing network protocols on all communication
layers, from the physical to the application one.Comment: 39 pages, 2 figure
Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks
Recently, it has been shown that CSMA-type random access algorithms can
achieve the maximum possible throughput in ad hoc wireless networks. However,
these algorithms assume an idealized continuous-time CSMA protocol where
collisions can never occur. In addition, simulation results indicate that the
delay performance of these algorithms can be quite bad. On the other hand,
although some simple heuristics (such as distributed approximations of greedy
maximal scheduling) can yield much better delay performance for a large set of
arrival rates, they may only achieve a fraction of the capacity region in
general. In this paper, we propose a discrete-time version of the CSMA
algorithm. Central to our results is a discrete-time distributed randomized
algorithm which is based on a generalization of the so-called Glauber dynamics
from statistical physics, where multiple links are allowed to update their
states in a single time slot. The algorithm generates collision-free
transmission schedules while explicitly taking collisions into account during
the control phase of the protocol, thus relaxing the perfect CSMA assumption.
More importantly, the algorithm allows us to incorporate mechanisms which lead
to very good delay performance while retaining the throughput-optimality
property. It also resolves the hidden and exposed terminal problems associated
with wireless networks.Comment: 12 page
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
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