87 research outputs found
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
On Optimal Weighted-Delay Scheduling in Input-Queued Switches
Motivated by relatively few delay-optimal scheduling results, in comparison
to results on throughput optimality, we investigate an input-queued switch
scheduling problem in which the objective is to minimize a linear function of
the queue-length vector. Theoretical properties of variants of the well-known
MaxWeight scheduling algorithm are established within this context, which
includes showing that these algorithms exhibit optimal heavy-traffic
queue-length scaling. For the case of input-queued switches, we
derive an optimal scheduling policy and establish its theoretical properties,
demonstrating fundamental differences with the variants of MaxWeight
scheduling. Our theoretical results are expected to be of interest more broadly
than input-queued switches. Computational experiments demonstrate and quantify
the benefits of our optimal scheduling policy
Stable iterative refinement algorithms for solving linear systems
Iterative refinement (IR) is a popular scheme for solving a linear system of
equations based on gradually improving the accuracy of an initial
approximation. Originally developed to improve upon the accuracy of Gaussian
elimination, interest in IR has been revived because of its suitability for
execution on fast low-precision hardware such as analog devices and graphics
processing units. IR generally converges when the error associated with the
solution method is small, but is known to diverge when this error is large. We
propose and analyze a novel enhancement to the IR algorithm by adding a line
search optimization step that guarantees the algorithm will not diverge.
Numerical experiments verify our theoretical results and illustrate the
effectiveness of our proposed scheme.Comment: 5 pages, 6 figure
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