3,199 research outputs found
Large deviations sum-queue optimality of a radial sum-rate monotone opportunistic scheduler
A centralized wireless system is considered that is serving a fixed set of
users with time varying channel capacities. An opportunistic scheduling rule in
this context selects a user (or users) to serve based on the current channel
state and user queues. Unless the user traffic is symmetric and/or the
underlying capacity region a polymatroid, little is known concerning how
performance optimal schedulers should tradeoff "maximizing current service
rate" (being opportunistic) versus "balancing unequal queues" (enhancing
user-diversity to enable future high service rate opportunities). By contrast
with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule,
a radial sum-rate monotone (RSM) scheduler de-emphasizes queue-balancing in
favor of greedily maximizing the system service rate as the queue-lengths are
scaled up linearly. In this paper it is shown that an RSM opportunistic
scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the
asymptotic exponential decay rate of the sum-queue distribution for a two-queue
system. The result complements existing optimality results for opportunistic
scheduling and point to RSM schedulers as a good design choice given the need
for robustness in wireless systems with both heterogeneity and high degree of
uncertainty.Comment: Revised version. Major changes include addition of
details/intermediate steps in various proofs, a summary of technical steps in
Table 1, and correction of typos
Detecting Markov Chain Instability: A Monte Carlo Approach
We devise a Monte Carlo based method for detecting whether a non-negative
Markov chain is stable for a given set of parameter values. More precisely, for
a given subset of the parameter space, we develop an algorithm that is capable
of deciding whether the set has a subset of positive Lebesgue measure for which
the Markov chain is unstable. The approach is based on a variant of simulated
annealing, and consequently only mild assumptions are needed to obtain
performance guarantees.
The theoretical underpinnings of our algorithm are based on a result stating
that the stability of a set of parameters can be phrased in terms of the
stability of a single Markov chain that searches the set for unstable
parameters. Our framework leads to a procedure that is capable of performing
statistically rigorous tests for instability, which has been extensively tested
using several examples of standard and non-standard queueing networks
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
A Survey of Wireless Fair Queuing Algorithms with Location-Dependent Channel Errors
The rapid development of wireless networks has brought more and more attention to topics related to fair allocation of resources, creation of suitable algorithms, taking into account the special characteristics of wireless environment and insurance fair access to the transmission channel, with delay bound and throughput guaranteed. Fair allocation of resources in wireless networks requires significant challenges, because of errors that occur only in these networks, such as location-dependent and bursty channel errors. In wireless networks, frequently hap-pens, because interference of radio waves, that a user experiencing bad radio conditions during a period of time, not to receive resources in that period. This paper analyzes some resource allocation algorithms for wireless networks with location dependent errors, specifying the base idea for each algorithm and the way how it works. The analyzed fair queuing algorithms differ by the way they treat the following aspects: how to select the flows which should receive additional services, how to allocate these resources, which is the proportion received by error free flows and how the flows affected by errors are compensated.Fair Scheduling, Wireless Networks, Location Dependent Channel Errors, Sched-uling Algorithms
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