63,631 research outputs found
A Fixed-Point Algorithm for Closed Queueing Networks
In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)
Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue Length Data
Resource demand estimation is essential for the application of analyical models, such as queueing networks, to real-world systems. In this paper, we investigate maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent service times. Stemming from a characterization of necessary conditions for ML estimation, we propose new estimators that infer demands from queue-length measurements, which are inexpensive metrics to collect in real systems. One advantage of focusing on queue-length data compared to response times or utilizations is that confidence intervals can be rigorously derived from the equilibrium distribution of the queueing network model. Our estimators and their confidence intervals are validated against simulation and real system measurements for a multi-tier application
Optimisation of stochastic networks with blocking: a functional-form approach
This paper introduces a class of stochastic networks with blocking, motivated
by applications arising in cellular network planning, mobile cloud computing,
and spare parts supply chains. Blocking results in lost revenue due to
customers or jobs being permanently removed from the system. We are interested
in striking a balance between mitigating blocking by increasing service
capacity, and maintaining low costs for service capacity. This problem is
further complicated by the stochastic nature of the system. Owing to the
complexity of the system there are no analytical results available that
formulate and solve the relevant optimization problem in closed form.
Traditional simulation-based methods may work well for small instances, but the
associated computational costs are prohibitive for networks of realistic size.
We propose a hybrid functional-form based approach for finding the optimal
resource allocation, combining the speed of an analytical approach with the
accuracy of simulation-based optimisation. The key insight is to replace the
computationally expensive gradient estimation in simulation optimisation with a
closed-form analytical approximation that is calibrated using a single
simulation run. We develop two implementations of this approach and conduct
extensive computational experiments on complex examples to show that it is
capable of substantially improving system performance. We also provide evidence
that our approach has substantially lower computational costs compared to
stochastic approximation
ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing
With the aim of developing a fast yet accurate algorithm for compressive
sensing (CS) reconstruction of natural images, we combine in this paper the
merits of two existing categories of CS methods: the structure insights of
traditional optimization-based methods and the speed of recent network-based
ones. Specifically, we propose a novel structured deep network, dubbed
ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm
(ISTA) for optimizing a general norm CS reconstruction model. To cast
ISTA into deep network form, we develop an effective strategy to solve the
proximal mapping associated with the sparsity-inducing regularizer using
nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms,
shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than
being hand-crafted. Moreover, considering that the residuals of natural images
are more compressible, an enhanced version of ISTA-Net in the residual domain,
dubbed {ISTA-Net}, is derived to further improve CS reconstruction.
Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform
existing state-of-the-art optimization-based and network-based CS methods by
large margins, while maintaining fast computational speed. Our source codes are
available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.Comment: 10 pages, 6 figures, 4 Tables. To appear in CVPR 201
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