6,257 research outputs found
Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows
We consider a fluid queue fed by multiple On-Off flows with heavy-tailed
(regularly varying) On periods. Under fairly mild assumptions, we prove that
the workload distribution is asymptotically equivalent to that in a reduced
system. The reduced system consists of a ``dominant'' subset of the flows, with
the original service rate subtracted by the mean rate of the other flows. We
describe how a dominant set may be determined from a simple knapsack
formulation. The dominant set consists of a ``minimally critical'' set of
On-Off flows with regularly varying On periods. In case the dominant set
contains just a single On-Off flow, the exact asymptotics for the reduced
system follow from known results. For the case of several
On-Off flows, we exploit a powerful intuitive argument to obtain the exact
asymptotics. Combined with the reduced-load equivalence, the results for the
reduced system provide a characterization of the tail of the workload
distribution for a wide range of traffic scenarios
A critical look at power law modelling of the Internet
This paper takes a critical look at the usefulness of power law models of the
Internet. The twin focuses of the paper are Internet traffic and topology
generation. The aim of the paper is twofold. Firstly it summarises the state of
the art in power law modelling particularly giving attention to existing open
research questions. Secondly it provides insight into the failings of such
models and where progress needs to be made for power law research to feed
through to actual improvements in network performance.Comment: To appear Computer Communication
Jamming transition in air transportation networks
In this work we present a model of an air transportation traffic system from
the complex network modelling viewpoint. In the network, every node corresponds
to a given airport, and two nodes are connected by means of flight routes. Each
node is weighted according to its load capacity, and links are weighted
according to the Euclidean distance that separates each pair of nodes. Local
rules describing the behavior of individual nodes in terms of the surrounding
flow have been also modelled, and a random network topology has been chosen in
a baseline approach. Numerical simulations describing the diffusion of a given
number of agents (aircraft) in this network show the onset of a jamming
transition that distinguishes an efficient regime with null amount of airport
queues and high diffusivity (free phase) and a regime where bottlenecks
suddenly take place, leading to a poor aircraft diffusion (congested phase).
Fluctuations are maximal around the congestion threshold, suggesting that the
transition is critical. We then proceed by exploring the robustness of our
results in neutral random topologies by embedding the model in heterogeneous
networks. Specifically, we make use of the European air transportation network
formed by 858 airports and 11170 flight routes connecting them, which we show
to be scale-free. The jamming transition is also observed in this case. These
results and methodologies may introduce relevant decision making procedures in
order to optimize the air transportation traffic
GPS queues with heterogeneous traffic classes
We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic classes are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the light-tailed class for the situation where its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed class served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain pre-factor, which accounts for the interaction with the heavy-tailed class. Specifically, the pre-factor represents the probability that the heavy-tailed class is backlogged long enough for the light-tailed class to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario
The virtues and vices of equilibrium and the future of financial economics
The use of equilibrium models in economics springs from the desire for
parsimonious models of economic phenomena that take human reasoning into
account. This approach has been the cornerstone of modern economic theory. We
explain why this is so, extolling the virtues of equilibrium theory; then we
present a critique and describe why this approach is inherently limited, and
why economics needs to move in new directions if it is to continue to make
progress. We stress that this shouldn't be a question of dogma, but should be
resolved empirically. There are situations where equilibrium models provide
useful predictions and there are situations where they can never provide useful
predictions. There are also many situations where the jury is still out, i.e.,
where so far they fail to provide a good description of the world, but where
proper extensions might change this. Our goal is to convince the skeptics that
equilibrium models can be useful, but also to make traditional economists more
aware of the limitations of equilibrium models. We sketch some alternative
approaches and discuss why they should play an important role in future
research in economics.Comment: 68 pages, one figur
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