10,230 research outputs found
Strong Stationary Duality for M\"obius Monotone Markov Chains: Unreliable Networks
For Markov chains with a partially ordered finite state space we show strong
stationary duality under the condition of M\"obius monotonicity of the chain.
We show relations of M\"obius monotonicity to other definitions of monotone
chains. We give examples of dual chains in this context which have transitions
only upwards. We illustrate general theory by an analysis of nonsymmetric
random walks on the cube with an application to networks of queues
Loss systems in a random environment
We consider a single server system with infinite waiting room in a random
environment. The service system and the environment interact in both
directions. Whenever the environment enters a prespecified subset of its state
space the service process is completely blocked: Service is interrupted and
newly arriving customers are lost. We prove an if-and-only-if-condition for a
product form steady state distribution of the joint queueing-environment
process. A consequence is a strong insensitivity property for such systems.
We discuss several applications, e.g. from inventory theory and reliability
theory, and show that our result extends and generalizes several theorems found
in the literature, e.g. of queueing-inventory processes.
We investigate further classical loss systems, where due to finite waiting
room loss of customers occurs. In connection with loss of customers due to
blocking by the environment and service interruptions new phenomena arise.
We further investigate the embedded Markov chains at departure epochs and
show that the behaviour of the embedded Markov chain is often considerably
different from that of the continuous time Markov process. This is different
from the behaviour of the standard M/G/1, where the steady state of the
embedded Markov chain and the continuous time process coincide.
For exponential queueing systems we show that there is a product form
equilibrium of the embedded Markov chain under rather general conditions. For
systems with non-exponential service times more restrictive constraints are
needed, which we prove by a counter example where the environment represents an
inventory attached to an M/D/1 queue. Such integrated queueing-inventory
systems are dealt with in the literature previously, and are revisited here in
detail
Fundamentals of Heterogeneous Cellular Networks with Energy Harvesting
We develop a new tractable model for K-tier heterogeneous cellular networks
(HetNets), where each base station (BS) is powered solely by a self-contained
energy harvesting module. The BSs across tiers differ in terms of the energy
harvesting rate, energy storage capacity, transmit power and deployment
density. Since a BS may not always have enough energy, it may need to be kept
OFF and allowed to recharge while nearby users are served by neighboring BSs
that are ON. We show that the fraction of time a k^{th} tier BS can be kept ON,
termed availability \rho_k, is a fundamental metric of interest. Using tools
from random walk theory, fixed point analysis and stochastic geometry, we
characterize the set of K-tuples (\rho_1, \rho_2, ... \rho_K), termed the
availability region, that is achievable by general uncoordinated operational
strategies, where the decision to toggle the current ON/OFF state of a BS is
taken independently of the other BSs. If the availability vector corresponding
to the optimal system performance, e.g., in terms of rate, lies in this
availability region, there is no performance loss due to the presence of
unreliable energy sources. As a part of our analysis, we model the temporal
dynamics of the energy level at each BS as a birth-death process, derive the
energy utilization rate, and use hitting/stopping time analysis to prove that
there exists a fundamental limit on \rho_k that cannot be surpassed by any
uncoordinated strategy.Comment: submitted to IEEE Transactions on Wireless Communications, July 201
Adaptive Controller Placement for Wireless Sensor-Actuator Networks with Erasure Channels
Wireless sensor-actuator networks offer flexibility for control design. One
novel element which may arise in networks with multiple nodes is that the role
of some nodes does not need to be fixed. In particular, there is no need to
pre-allocate which nodes assume controller functions and which ones merely
relay data. We present a flexible architecture for networked control using
multiple nodes connected in series over analog erasure channels without
acknowledgments. The control architecture proposed adapts to changes in network
conditions, by allowing the role played by individual nodes to depend upon
transmission outcomes. We adopt stochastic models for transmission outcomes and
characterize the distribution of controller location and the covariance of
system states. Simulation results illustrate that the proposed architecture has
the potential to give better performance than limiting control calculations to
be carried out at a fixed node.Comment: 10 pages, 8 figures, to be published in Automatic
Formal analysis techniques for gossiping protocols
We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them
Distributed Learning over Unreliable Networks
Most of today's distributed machine learning systems assume {\em reliable
networks}: whenever two machines exchange information (e.g., gradients or
models), the network should guarantee the delivery of the message. At the same
time, recent work exhibits the impressive tolerance of machine learning
algorithms to errors or noise arising from relaxed communication or
synchronization. In this paper, we connect these two trends, and consider the
following question: {\em Can we design machine learning systems that are
tolerant to network unreliability during training?} With this motivation, we
focus on a theoretical problem of independent interest---given a standard
distributed parameter server architecture, if every communication between the
worker and the server has a non-zero probability of being dropped, does
there exist an algorithm that still converges, and at what speed? The technical
contribution of this paper is a novel theoretical analysis proving that
distributed learning over unreliable network can achieve comparable convergence
rate to centralized or distributed learning over reliable networks. Further, we
prove that the influence of the packet drop rate diminishes with the growth of
the number of \textcolor{black}{parameter servers}. We map this theoretical
result onto a real-world scenario, training deep neural networks over an
unreliable network layer, and conduct network simulation to validate the system
improvement by allowing the networks to be unreliable
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