21,287 research outputs found
Sample path large deviations for queues with many inputs
This paper presents a large deviations principle for the average of real-valued processes indexed by the positive integers, one which is particularly suited to queueing systems with many traffic flows. Examples are given of how it may be applied to standard queues with finite and infinite buffers, to priority queues and to finding most likely paths to overflow
A Review of Traffic Signal Control.
The aim of this paper is to provide a starting point for the future research within the SERC sponsored project "Gating and Traffic Control: The Application of State Space Control Theory". It will provide an introduction to State Space Control Theory, State Space applications in transportation in general, an in-depth review of congestion control (specifically traffic signal control in congested situations), a review of theoretical works, a review of existing systems and will conclude with recommendations for the research to be undertaken within this project
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
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
Queue-Based Random-Access Algorithms: Fluid Limits and Stability Issues
We use fluid limits to explore the (in)stability properties of wireless
networks with queue-based random-access algorithms. Queue-based random-access
schemes are simple and inherently distributed in nature, yet provide the
capability to match the optimal throughput performance of centralized
scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of
activation rules for which throughput optimality has been established, may
result in excessive queue lengths and delays. The use of more
aggressive/persistent access schemes can improve the delay performance, but
does not offer any universal maximum-stability guarantees. In order to gain
qualitative insight and investigate the (in)stability properties of more
aggressive/persistent activation rules, we examine fluid limits where the
dynamics are scaled in space and time. In some situations, the fluid limits
have smooth deterministic features and maximum stability is maintained, while
in other scenarios they exhibit random oscillatory characteristics, giving rise
to major technical challenges. In the latter regime, more aggressive access
schemes continue to provide maximum stability in some networks, but may cause
instability in others. Simulation experiments are conducted to illustrate and
validate the analytical results
An Energy-Efficient Controller for Wirelessly-Powered Communication Networks
In a wirelessly-powered communication network (WPCN), an energy access point
(E-AP) supplies the energy needs of the network nodes through radio frequency
wave transmission, and the nodes store their received energy in their batteries
for possible data transmission. In this paper, we propose an online control
policy for energy transfer from the E-AP to the wireless nodes and for data
transfer among the nodes. With our proposed control policy, all data queues of
the nodes are stable, while the average energy consumption of the network is
shown to be within a bounded gap of the minimum energy required for stabilizing
the network. Our proposed policy is designed using a quadratic Lyapunov
function to capture the limitations on the energy consumption of the nodes
imposed by their battery levels. We show that under the proposed control
policy, the backlog level in the data queues and the stored energy level in the
batteries fluctuate in small intervals around some constant levels.
Consequently, by imposing negligible average data drop rate, the data buffer
size and the battery capacity of the nodes can be significantly reduced
- …