680 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
Sample-path large deviations for tandem and priority queues with Gaussian inputs
This paper considers Gaussian flows multiplexed in a queueing network. A
single node being a useful but often incomplete setting, we examine more
advanced models. We focus on a (two-node) tandem queue, fed by a large number
of Gaussian inputs. With service rates and buffer sizes at both nodes scaled
appropriately, Schilder's sample-path large-deviations theorem can be applied
to calculate the asymptotics of the overflow probability of the second queue.
More specifically, we derive a lower bound on the exponential decay rate of
this overflow probability and present an explicit condition for the lower bound
to match the exact decay rate. Examples show that this condition holds for a
broad range of frequently used Gaussian inputs. The last part of the paper
concentrates on a model for a single node, equipped with a priority scheduling
policy. We show that the analysis of the tandem queue directly carries over to
this priority queueing system.Comment: Published at http://dx.doi.org/10.1214/105051605000000133 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Many-Sources Large Deviations for Max-Weight Scheduling
In this paper, a many-sources large deviations principle (LDP) for the
transient workload of a multi-queue single-server system is established where
the service rates are chosen from a compact, convex and coordinate-convex rate
region and where the service discipline is the max-weight policy. Under the
assumption that the arrival processes satisfy a many-sources LDP, this is
accomplished by employing Garcia's extended contraction principle that is
applicable to quasi-continuous mappings.
For the simplex rate-region, an LDP for the stationary workload is also
established under the additional requirements that the scheduling policy be
work-conserving and that the arrival processes satisfy certain mixing
conditions.
The LDP results can be used to calculate asymptotic buffer overflow
probabilities accounting for the multiplexing gain, when the arrival process is
an average of \emph{i.i.d.} processes. The rate function for the stationary
workload is expressed in term of the rate functions of the finite-horizon
workloads when the arrival processes have \emph{i.i.d.} increments.Comment: 44 page
Asymptotic buffer overflow probabilities in multiclass multiplexers : part I : the GPS policy
Cover title.Includes bibliographical references (p. 34-37).Supported by a Presidential Young Investigators award. DDM-9158118 Matching funds from Draper Laboratory. Supported by ARO. DAAL-03-92-G-0115Dimitris Bertsimas, Ioannis Ch. Paschalidis, John N. Tsitsiklis
Objectives, stimulus and feedback in signal control of road traffic
This article identifies the prospective role of a range of intelligent transport systems technologies for the signal control of road traffic. We discuss signal control within the context of traffic management and control in urban road networks and then present a control-theoretic formulation for it that distinguishes the various roles of detector data, objectives of optimization, and control feedback. By reference to this, we discuss the importance of different kinds of variability in traffic flows and review the state of knowledge in respect of control in the presence of different combinations of them. In light of this formulation and review, we identify a range of important possibilities for contributions to traffic management and control through traffic measurement and detection technology, and contemporary flexible optimization techniques that use various kinds of automated learning
Sample-path large deviations for tandem and priority queues with Gaussian inputs
This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently-used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system. iffalse {it Perhaps:} We conclude by presenting a number of motivated conjectures for the analysis of a queue operating under the generalized processor sharing discipline
On a generic class of two-node queueing systems
This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics
Asymptotic buffer overflow probabilities in multiclass multiplexers : part II : the GLQF policy
Cover title.Includes bibliographical references (p. 33-35).Supported by a Presidential Young Investigator Award. DDM-9158118 Matching funds from Draper Laboratory. Supported by ARO. DAAL-03-92-G-0115Dimitris Bertsimas, Ioannis Ch. Paschalidis, John N. Tsitsiklis
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