1,373 research outputs found
An Optimal Medium Access Control with Partial Observations for Sensor Networks
We consider medium access control (MAC) in multihop sensor networks, where only partial information about the shared medium is available to the transmitter. We model our setting as a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain representing the available bandwidth, and in which the arrivals are controlled based on the partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state on which the control decisions are based. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results can be specifically applied for designing efficient and stable algorithms for medium access control in multiple-accessed systems, in particular for sensor networks
Conditional limit theorems for regulated fractional Brownian motion
We consider a stationary fluid queue with fractional Brownian motion input.
Conditional on the workload at time zero being greater than a large value ,
we provide the limiting distribution for the amount of time that the workload
process spends above level over the busy cycle straddling the origin, as
. Our results can be interpreted as showing that long delays occur
in large clumps of size of order . The conditional limit result
involves a finer scaling of the queueing process than fluid analysis, thereby
departing from previous related literature.Comment: Published in at http://dx.doi.org/10.1214/09-AAP605 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model
We consider a fluid queue where the input process consists of N identical
sources that turn on and off at exponential waiting times. The server works at
the constant rate c and an on source generates fluid at unit rate. This model
was first formulated and analyzed by Anick, Mitra and Sondhi. We obtain an
alternate representation of the joint steady state distribution of the buffer
content and the number of on sources. This is given as a contour integral that
we then analyze for large N. We give detailed asymptotic results for the joint
distribution, as well as the associated marginal and conditional distributions.
In particular, simple conditional limits laws are obtained. These shows how the
buffer content behaves conditioned on the number of active sources and vice
versa. Numerical comparisons show that our asymptotic results are very accurate
even for N=20
Analysis of Buffer Starvation with Application to Objective QoE Optimization of Streaming Services
Our purpose in this paper is to characterize buffer starvations for streaming
services. The buffer is modeled as an M/M/1 queue, plus the consideration of
bursty arrivals. When the buffer is empty, the service restarts after a certain
amount of packets are \emph{prefetched}. With this goal, we propose two
approaches to obtain the \emph{exact distribution} of the number of buffer
starvations, one of which is based on \emph{Ballot theorem}, and the other uses
recursive equations. The Ballot theorem approach gives an explicit result. We
extend this approach to the scenario with a constant playback rate using
T\`{a}kacs Ballot theorem. The recursive approach, though not offering an
explicit result, can obtain the distribution of starvations with
non-independent and identically distributed (i.i.d.) arrival process in which
an ON/OFF bursty arrival process is considered in this work. We further compute
the starvation probability as a function of the amount of prefetched packets
for a large number of files via a fluid analysis. Among many potential
applications of starvation analysis, we show how to apply it to optimize the
objective quality of experience (QoE) of media streaming, by exploiting the
tradeoff between startup/rebuffering delay and starvations.Comment: 9 pages, 7 figures; IEEE Infocom 201
Decentralized Delay Optimal Control for Interference Networks with Limited Renewable Energy Storage
In this paper, we consider delay minimization for interference networks with
renewable energy source, where the transmission power of a node comes from both
the conventional utility power (AC power) and the renewable energy source. We
assume the transmission power of each node is a function of the local channel
state, local data queue state and local energy queue state only. In turn, we
consider two delay optimization formulations, namely the decentralized
partially observable Markov decision process (DEC-POMDP) and Non-cooperative
partially observable stochastic game (POSG). In DEC-POMDP formulation, we
derive a decentralized online learning algorithm to determine the control
actions and Lagrangian multipliers (LMs) simultaneously, based on the policy
gradient approach. Under some mild technical conditions, the proposed
decentralized policy gradient algorithm converges almost surely to a local
optimal solution. On the other hand, in the non-cooperative POSG formulation,
the transmitter nodes are non-cooperative. We extend the decentralized policy
gradient solution and establish the technical proof for almost-sure convergence
of the learning algorithms. In both cases, the solutions are very robust to
model variations. Finally, the delay performance of the proposed solutions are
compared with conventional baseline schemes for interference networks and it is
illustrated that substantial delay performance gain and energy savings can be
achieved
Dynamic importance sampling for queueing networks
Importance sampling is a technique that is commonly used to speed up Monte
Carlo simulation of rare events. However, little is known regarding the design
of efficient importance sampling algorithms in the context of queueing
networks. The standard approach, which simulates the system using an a priori
fixed change of measure suggested by large deviation analysis, has been shown
to fail in even the simplest network setting (e.g., a two-node tandem network).
Exploiting connections between importance sampling, differential games, and
classical subsolutions of the corresponding Isaacs equation, we show how to
design and analyze simple and efficient dynamic importance sampling schemes for
general classes of networks. The models used to illustrate the approach include
-node tandem Jackson networks and a two-node network with feedback, and the
rare events studied are those of large queueing backlogs, including total
population overflow and the overflow of individual buffers.Comment: Published in at http://dx.doi.org/10.1214/105051607000000122 the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Simple models of network access, with applications to the design of joint rate and admission control
At the access to networks, in contrast to the core, distances and feedback delays, as well as link capacities are small, which has network engineering implications that are investigated in this paper. We consider a single point in the access network which multiplexes several bursty users. The users adapt their sending rates based on feedback from the access multiplexer. Important parameters are the user's peak transmission rate p, which is the access line speed, the user's guaranteed minimum rate r, and the bound ε on the fraction of lost data. Two feedback schemes are proposed. In both schemes the users are allowed to send at rate p if the system is relatively lightly loaded, at rate r during periods of congestion, and at a rate between r and p, in an intermediate region. For both feedback schemes we present an exact analysis, under the assumption that the users' job sizes and think times have exponential distributions. We use our techniques to design the schemes jointly with admission control, i.e., the selection of the number of admissible users, to maximize throughput for given p, r, and ε. Next we consider the case in which the number of users is large. Under a specific scaling, we derive explicit large deviations asymptotics for both models. We discuss the extension to general distributions of user data and think times
Join-Idle-Queue with Service Elasticity: Large-Scale Asymptotics of a Non-monotone System
We consider the model of a token-based joint auto-scaling and load balancing
strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van
Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient
scalable implementation and yet achieves asymptotically optimal steady-state
delay performance and energy consumption as the number of servers .
In the above work, the asymptotic results are obtained under the assumption
that the queues have fixed-size finite buffers, and therefore the fundamental
question of stability of the proposed scheme with infinite buffers was left
open. In this paper, we address this fundamental stability question. The system
stability under the usual subcritical load assumption is not automatic.
Moreover, the stability may not even hold for all . The key challenge stems
from the fact that the process lacks monotonicity, which has been the powerful
primary tool for establishing stability in load balancing models. We develop a
novel method to prove that the subcritically loaded system is stable for large
enough , and establish convergence of steady-state distributions to the
optimal one, as . The method goes beyond the state of the art
techniques -- it uses an induction-based idea and a "weak monotonicity"
property of the model; this technique is of independent interest and may have
broader applicability.Comment: 30 page
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