1,273 research outputs found
Delay, memory, and messaging tradeoffs in distributed service systems
We consider the following distributed service model: jobs with unit mean,
exponentially distributed, and independent processing times arrive as a Poisson
process of rate , with , and are immediately dispatched
by a centralized dispatcher to one of First-In-First-Out queues associated
with identical servers. The dispatcher is endowed with a finite memory, and
with the ability to exchange messages with the servers.
We propose and study a resource-constrained "pull-based" dispatching policy
that involves two parameters: (i) the number of memory bits available at the
dispatcher, and (ii) the average rate at which servers communicate with the
dispatcher. We establish (using a fluid limit approach) that the asymptotic, as
, expected queueing delay is zero when either (i) the number of
memory bits grows logarithmically with and the message rate grows
superlinearly with , or (ii) the number of memory bits grows
superlogarithmically with and the message rate is at least .
Furthermore, when the number of memory bits grows only logarithmically with
and the message rate is proportional to , we obtain a closed-form expression
for the (now positive) asymptotic delay.
Finally, we demonstrate an interesting phase transition in the
resource-constrained regime where the asymptotic delay is non-zero. In
particular, we show that for any given (no matter how small), if our
policy only uses a linear message rate , the resulting asymptotic
delay is upper bounded, uniformly over all ; this is in sharp
contrast to the delay obtained when no messages are used (), which
grows as when , or when the popular
power-of--choices is used, in which the delay grows as
On the emergence of random initial conditions in fluid limits
The paper presents a phenomenon occurring in population processes that start
near zero and have large carrying capacity. By the classical result of
Kurtz~(1970), such processes, normalized by the carrying capacity, converge on
finite intervals to the solutions of ordinary differential equations, also
known as the fluid limit. When the initial population is small relative to
carrying capacity, this limit is trivial. Here we show that, viewed at suitably
chosen times increasing to infinity, the process converges to the fluid limit,
governed by the same dynamics, but with a random initial condition. This random
initial condition is related to the martingale limit of an associated linear
birth and death process
Stochastic methods for measurement-based network control
The main task of network administrators is to ensure that their network functions properly. Whether they manage a telecommunication or a road network, they generally base their decisions on the analysis of measurement data. Inspired by such network control applications, this dissertation investigates several stochastic modelling techniques for data analysis. The focus is on two areas within the field of stochastic processes: change point detection and queueing theory. Part I deals with statistical methods for the automatic detection of change points, being changes in the probability distribution underlying a data sequence. This part starts with a review of existing change point detection methods for data sequences consisting of independent observations. The main contribution of this part is the generalisation of the classic cusum method to account for dependence within data sequences. We analyse the false alarm probability of the resulting methods using a large deviations approach. The part also discusses numerical tests of the new methods and a cyber attack detection application, in which we investigate how to detect dns tunnels. The main contribution of Part II is the application of queueing models (probabilistic models for waiting lines) to situations in which the system to be controlled can only be observed partially. We consider two types of partial information. Firstly, we develop a procedure to get insight into the performance of queueing systems between consecutive system-state measurements and apply it in a numerical study, which was motivated by capacity management in cable access networks. Secondly, inspired by dynamic road control applications, we study routing policies in a queueing system for which just part of the jobs are observable and controllable
Interference Queueing Networks on Grids
Consider a countably infinite collection of interacting queues, with a queue
located at each point of the -dimensional integer grid, having independent
Poisson arrivals, but dependent service rates. The service discipline is of the
processor sharing type,with the service rate in each queue slowed down, when
the neighboring queues have a larger workload. The interactions are translation
invariant in space and is neither of the Jackson Networks type, nor of the
mean-field type. Coupling and percolation techniques are first used to show
that this dynamics has well defined trajectories. Coupling from the past
techniques are then proposed to build its minimal stationary regime. The rate
conservation principle of Palm calculus is then used to identify the stability
condition of this system, where the notion of stability is appropriately
defined for an infinite dimensional process. We show that the identified
condition is also necessary in certain special cases and conjecture it to be
true in all cases. Remarkably, the rate conservation principle also provides a
closed form expression for the mean queue size. When the stability condition
holds, this minimal solution is the unique translation invariant stationary
regime. In addition, there exists a range of small initial conditions for which
the dynamics is attracted to the minimal regime. Nevertheless, there exists
another range of larger though finite initial conditions for which the dynamics
diverges, even though stability criterion holds.Comment: Minor Spell Change
A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning
In this tutorial paper, a comprehensive survey is given on several major
systematic approaches in dealing with delay-aware control problems, namely the
equivalent rate constraint approach, the Lyapunov stability drift approach and
the approximate Markov Decision Process (MDP) approach using stochastic
learning. These approaches essentially embrace most of the existing literature
regarding delay-aware resource control in wireless systems. They have their
relative pros and cons in terms of performance, complexity and implementation
issues. For each of the approaches, the problem setup, the general solution and
the design methodology are discussed. Applications of these approaches to
delay-aware resource allocation are illustrated with examples in single-hop
wireless networks. Furthermore, recent results regarding delay-aware multi-hop
routing designs in general multi-hop networks are elaborated. Finally, the
delay performance of the various approaches are compared through simulations
using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201
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