8,056 research outputs found
Minimizing the Age of Information in Wireless Networks with Stochastic Arrivals
We consider a wireless network with a base station serving multiple traffic
streams to different destinations. Packets from each stream arrive to the base
station according to a stochastic process and are enqueued in a separate (per
stream) queue. The queueing discipline controls which packet within each queue
is available for transmission. The base station decides, at every time t, which
stream to serve to the corresponding destination. The goal of scheduling
decisions is to keep the information at the destinations fresh. Information
freshness is captured by the Age of Information (AoI) metric.
In this paper, we derive a lower bound on the AoI performance achievable by
any given network operating under any queueing discipline. Then, we consider
three common queueing disciplines and develop both an Optimal Stationary
Randomized policy and a Max-Weight policy under each discipline. Our approach
allows us to evaluate the combined impact of the stochastic arrivals, queueing
discipline and scheduling policy on AoI. We evaluate the AoI performance both
analytically and using simulations. Numerical results show that the performance
of the Max-Weight policy is close to the analytical lower bound
Some aspects of queueing and storage processes : a thesis in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University
In this study the nature of systems consisting of a single queue are first considered. Attention is then drawn to an analogy between such systems and storage systems.
A development of the single queue viz queues with feedback is considered after first considering feedback processes in general. The behaviour of queues, some with feedback loops, combined into networks is then considered. Finally, the application of such networks to the analysis of interconnected reservoir systems is considered and the conclusion drawn that such analytic methods complement the more recently developed mathematical programming methods by providing analytic solutions for
sub systems behaviour and thus guiding the development of a system model
Large deviations analysis for the queue in the Halfin-Whitt regime
We consider the FCFS queue in the Halfin-Whitt heavy traffic
regime. It is known that the normalized sequence of steady-state queue length
distributions is tight and converges weakly to a limiting random variable W.
However, those works only describe W implicitly as the invariant measure of a
complicated diffusion. Although it was proven by Gamarnik and Stolyar that the
tail of W is sub-Gaussian, the actual value of was left open. In subsequent work, Dai and He
conjectured an explicit form for this exponent, which was insensitive to the
higher moments of the service distribution.
We explicitly compute the true large deviations exponent for W when the
abandonment rate is less than the minimum service rate, the first such result
for non-Markovian queues with abandonments. Interestingly, our results resolve
the conjecture of Dai and He in the negative. Our main approach is to extend
the stochastic comparison framework of Gamarnik and Goldberg to the setting of
abandonments, requiring several novel and non-trivial contributions. Our
approach sheds light on several novel ways to think about multi-server queues
with abandonments in the Halfin-Whitt regime, which should hold in considerable
generality and provide new tools for analyzing these systems
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