5,152 research outputs found
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
Resource dimensioning through buffer sampling
Link dimensioning, i.e., selecting a (minimal) link capacity such that the users’ performance requirements are met, is a crucial component of network design. It requires insight into the interrelationship among the traffic offered (in terms of the mean offered load , but also its fluctuation around the mean, i.e., ‘burstiness’), the envisioned performance level, and the capacity needed. We first derive, for different performance criteria, theoretical dimensioning formulas that estimate the required capacity as a function of the input traffic and the performance target. For the special case of Gaussian input traffic, these formulas reduce to , where directly relates to the performance requirement (as agreed upon in a service level agreement) and reflects the burstiness (at the timescale of interest). We also observe that Gaussianity applies for virtually all realistic scenarios; notably, already for a relatively low aggregation level, the Gaussianity assumption is justified.\ud
As estimating is relatively straightforward, the remaining open issue concerns the estimation of . We argue that particularly if corresponds to small time-scales, it may be inaccurate to estimate it directly from the traffic traces. Therefore, we propose an indirect method that samples the buffer content, estimates the buffer content distribution, and ‘inverts’ this to the variance. We validate the inversion through extensive numerical experiments (using a sizeable collection of traffic traces from various representative locations); the resulting estimate of is then inserted in the dimensioning formula. These experiments show that both the inversion and the dimensioning formula are remarkably accurate
Information Super-Diffusion on Structured Networks
We study diffusion of information packets on several classes of structured
networks. Packets diffuse from a randomly chosen node to a specified
destination in the network. As local transport rules we consider random
diffusion and an improved local search method. Numerical simulations are
performed in the regime of stationary workloads away from the jamming
transition. We find that graph topology determines the properties of diffusion
in a universal way, which is reflected by power-laws in the transit-time and
velocity distributions of packets. With the use of multifractal scaling
analysis and arguments of non-extensive statistics we find that these
power-laws are compatible with super-diffusive traffic for random diffusion and
for improved local search. We are able to quantify the role of network topology
on overall transport efficiency. Further, we demonstrate the implications of
improved transport rules and discuss the importance of matching (global)
topology with (local) transport rules for the optimal function of networks. The
presented model should be applicable to a wide range of phenomena ranging from
Internet traffic to protein transport along the cytoskeleton in biological
cells.Comment: 27 pages 7 figure
Convexity properties of loss and overflow functions
We show that the fluid loss ratio in a fluid queue with finite buffer and constant link capacity is always a jointly convex function of and . This generalizes prior work [6] which shows convexity of the trade-off for large number of i.i.d. multiplexed sources, using the large deviations rate function as approximation for fluid loss. Our approach also leads to a simpler proof of the prior result, and provides a stronger basis for optimal measurement-based control of resource allocation in shared resource systems
Emerging East-West collaborative networks: An appraisal
Although an extensive amount of literature reviews emerging patterns of east-west co-operation, it is not easy to grasp the state of the art. Too many of the books, articles and papers tend to mark the trees rather than to map the forest. The paper analyses recent trends from the point of view of modern economics which emphasizes the growing use of a wide variety of new types of co-operative mechanisms between firms in organizing international business. It takes an appraising look at the outcome of a recent research project of a group of scholars from east and west. The paper comes to the conclusion that east-west integration is proceeding at a considerable rate. But it is dominated by shallow modes - by arm's length transactions and contract work. To a certain extent, this might reflect new patterns of inter-firm co-operation. But this might also be an indication that co-operation with partners in CECTs is still in a flat state. Eastern firms find it hard to obtain an adequate position in international networks. Their lack of competence, reliability and reputation is often an insurmountable barrier. Accordingly, they must improve upon their technological and organizational standards to be considered by western firms as competent, reliable and trustworthy and, hence, equal partners in collaborational networks.
Discrete events: Perspectives from system theory
Systems Theory;differentiaal/ integraal-vergelijkingen
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