11 research outputs found
Timely-Throughput Optimal Coded Computing over Cloud Networks
In modern distributed computing systems, unpredictable and unreliable
infrastructures result in high variability of computing resources. Meanwhile,
there is significantly increasing demand for timely and event-driven services
with deadline constraints. Motivated by measurements over Amazon EC2 clusters,
we consider a two-state Markov model for variability of computing speed in
cloud networks. In this model, each worker can be either in a good state or a
bad state in terms of the computation speed, and the transition between these
states is modeled as a Markov chain which is unknown to the scheduler. We then
consider a Coded Computing framework, in which the data is possibly encoded and
stored at the worker nodes in order to provide robustness against nodes that
may be in a bad state. With timely computation requests submitted to the system
with computation deadlines, our goal is to design the optimal computation-load
allocation scheme and the optimal data encoding scheme that maximize the timely
computation throughput (i.e, the average number of computation tasks that are
accomplished before their deadline). Our main result is the development of a
dynamic computation strategy called Lagrange Estimate-and Allocate (LEA)
strategy, which achieves the optimal timely computation throughput. It is shown
that compared to the static allocation strategy, LEA increases the timely
computation throughput by 1.4X - 17.5X in various scenarios via simulations and
by 1.27X - 6.5X in experiments over Amazon EC2 clustersComment: to appear in MobiHoc 201
Dynamic Cloud Network Control under Reconfiguration Delay and Cost
Network virtualization and programmability allow operators to deploy a wide
range of services over a common physical infrastructure and elastically
allocate cloud and network resources according to changing requirements. While
the elastic reconfiguration of virtual resources enables dynamically scaling
capacity in order to support service demands with minimal operational cost,
reconfiguration operations make resources unavailable during a given time
period and may incur additional cost. In this paper, we address the dynamic
cloud network control problem under non-negligible reconfiguration delay and
cost. We show that while the capacity region remains unchanged regardless of
the reconfiguration delay/cost values, a reconfiguration-agnostic policy may
fail to guarantee throughput-optimality and minimum cost under nonzero
reconfiguration delay/cost. We then present an adaptive dynamic cloud network
control policy that allows network nodes to make local flow scheduling and
resource allocation decisions while controlling the frequency of
reconfiguration in order to support any input rate in the capacity region and
achieve arbitrarily close to minimum cost for any finite reconfiguration
delay/cost values.Comment: 15 pages, 7 figure
Learning to detect an oddball target with observations from an exponential family
The problem of detecting an odd arm from a set of K arms of a multi-armed
bandit, with fixed confidence, is studied in a sequential decision-making
scenario. Each arm's signal follows a distribution from a vector exponential
family. All arms have the same parameters except the odd arm. The actual
parameters of the odd and non-odd arms are unknown to the decision maker.
Further, the decision maker incurs a cost for switching from one arm to
another. This is a sequential decision making problem where the decision maker
gets only a limited view of the true state of nature at each stage, but can
control his view by choosing the arm to observe at each stage. Of interest are
policies that satisfy a given constraint on the probability of false detection.
An information-theoretic lower bound on the total cost (expected time for a
reliable decision plus total switching cost) is first identified, and a
variation on a sequential policy based on the generalised likelihood ratio
statistic is then studied. Thanks to the vector exponential family assumption,
the signal processing in this policy at each stage turns out to be very simple,
in that the associated conjugate prior enables easy updates of the posterior
distribution of the model parameters. The policy, with a suitable threshold, is
shown to satisfy the given constraint on the probability of false detection.
Further, the proposed policy is asymptotically optimal in terms of the total
cost among all policies that satisfy the constraint on the probability of false
detection
Learning Algorithms for Minimizing Queue Length Regret
We consider a system consisting of a single transmitter/receiver pair and
channels over which they may communicate. Packets randomly arrive to the
transmitter's queue and wait to be successfully sent to the receiver. The
transmitter may attempt a frame transmission on one channel at a time, where
each frame includes a packet if one is in the queue. For each channel, an
attempted transmission is successful with an unknown probability. The
transmitter's objective is to quickly identify the best channel to minimize the
number of packets in the queue over time slots. To analyze system
performance, we introduce queue length regret, which is the expected difference
between the total queue length of a learning policy and a controller that knows
the rates, a priori. One approach to designing a transmission policy would be
to apply algorithms from the literature that solve the closely-related
stochastic multi-armed bandit problem. These policies would focus on maximizing
the number of successful frame transmissions over time. However, we show that
these methods have queue length regret. On the other hand, we
show that there exists a set of queue-length based policies that can obtain
order optimal queue length regret. We use our theoretical analysis to
devise heuristic methods that are shown to perform well in simulation.Comment: 28 Pages, 11 figure
Sequential Multi-hypothesis Testing in Multi-armed Bandit Problems:An Approach for Asymptotic Optimality
We consider a multi-hypothesis testing problem involving a K-armed bandit.
Each arm's signal follows a distribution from a vector exponential family. The
actual parameters of the arms are unknown to the decision maker. The decision
maker incurs a delay cost for delay until a decision and a switching cost
whenever he switches from one arm to another. His goal is to minimise the
overall cost until a decision is reached on the true hypothesis. Of interest
are policies that satisfy a given constraint on the probability of false
detection. This is a sequential decision making problem where the decision
maker gets only a limited view of the true state of nature at each stage, but
can control his view by choosing the arm to observe at each stage. An
information-theoretic lower bound on the total cost (expected time for a
reliable decision plus total switching cost) is first identified, and a
variation on a sequential policy based on the generalised likelihood ratio
statistic is then studied. Due to the vector exponential family assumption, the
signal processing at each stage is simple; the associated conjugate prior
distribution on the unknown model parameters enables easy updates of the
posterior distribution. The proposed policy, with a suitable threshold for
stopping, is shown to satisfy the given constraint on the probability of false
detection. Under a continuous selection assumption, the policy is also shown to
be asymptotically optimal in terms of the total cost among all policies that
satisfy the constraint on the probability of false detection
Augmenting Max-Weight with Explicit Learning for Wireless Scheduling with Switching Costs
In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to opportunistically switch off a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach - a Max-Weight algorithm along with a Lyapunov-based stability argument - does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability