990 research outputs found
Asymptotically Optimal Load Balancing Topologies
We consider a system of servers inter-connected by some underlying graph
topology . Tasks arrive at the various servers as independent Poisson
processes of rate . Each incoming task is irrevocably assigned to
whichever server has the smallest number of tasks among the one where it
appears and its neighbors in . Tasks have unit-mean exponential service
times and leave the system upon service completion.
The above model has been extensively investigated in the case is a
clique. Since the servers are exchangeable in that case, the queue length
process is quite tractable, and it has been proved that for any ,
the fraction of servers with two or more tasks vanishes in the limit as . For an arbitrary graph , the lack of exchangeability severely
complicates the analysis, and the queue length process tends to be worse than
for a clique. Accordingly, a graph is said to be -optimal or
-optimal when the occupancy process on is equivalent to that on
a clique on an -scale or -scale, respectively.
We prove that if is an Erd\H{o}s-R\'enyi random graph with average
degree , then it is with high probability -optimal and
-optimal if and as , respectively. This demonstrates that optimality can
be maintained at -scale and -scale while reducing the number of
connections by nearly a factor and compared to a
clique, provided the topology is suitably random. It is further shown that if
contains bounded-degree nodes, then it cannot be -optimal.
In addition, we establish that an arbitrary graph is -optimal when its
minimum degree is , and may not be -optimal even when its minimum
degree is for any .Comment: A few relevant results from arXiv:1612.00723 are included for
convenienc
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Optimal Topological Arrangement of Queues in Closed Finite Queueing Networks
Closed queueing networks are widely used in many different kinds of scientific and business applications. Since the demands of saving energy and reducing costs are becoming more and more significant with developing technologies, finding a systematic methodology for getting the best arrangement is very important. In this thesis, design rules are proposed for tandem and various other topologies, to help the designer find the best arrangements which maximize the throughput. Our topological arrangements problem (TAP) can be established as: the system has m-service stations in a network and each one may have different design parameters. To relax the queueing system, the original finite buffer queue is decomposed into a buffer and an infinite buffer server system. Mean Value Analysis (MVA) is used to measure the performance of each topology arrangement. Finally, mixed-integer sequential quadratic programming (MISQP) is used to solve the optimization problem and it is compared with enumeration and a simulation model of Arena (a discrete-event model)
Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes
We propose a class of strongly efficient rare event simulation estimators for
random walks and compound Poisson processes with a regularly varying
increment/jump-size distribution in a general large deviations regime. Our
estimator is based on an importance sampling strategy that hinges on the
heavy-tailed sample path large deviations result recently established in Rhee,
Blanchet, and Zwart (2016). The new estimators are straightforward to implement
and can be used to systematically evaluate the probability of a wide range of
rare events with bounded relative error. They are "universal" in the sense that
a single importance sampling scheme applies to a very general class of rare
events that arise in heavy-tailed systems. In particular, our estimators can
deal with rare events that are caused by multiple big jumps (therefore, beyond
the usual principle of a single big jump) as well as multidimensional processes
such as the buffer content process of a queueing network. We illustrate the
versatility of our approach with several applications that arise in the context
of mathematical finance, actuarial science, and queueing theory
Performance Tuning of Streaming Applications via Search-space Decomposition
High-performance streaming applications are typically pipelined and deployed on architecturally diverse (hybrid)systems. Developers of such applications are interested in customizing components used, so as to benefit application performance. We present an efficient and automatic technique for design-space exploration of applications in this problem domain. We solve performance tuning as an optimization problem by formulating cost functions using results from queueing theory. This results in a mixed-integer nonlinear optimization problem which is NP-hard. We reduce the search complexity by decomposing the search space. We have developed a domain-specific decomposition technique using topological information of the application embodied in the queueing network models. Our analysis includes when our decomposition preserves optimality. Our preliminary empirical results confirm two-fold benefits--solving a problem that is currently not solvable using state-of-the-art solvers and in some problem instances, improving initial solution value from the solver by over two orders of magnitude
Integrated performance evaluation of extended queueing network models with line
Despite the large literature on queueing theory and its applications, tool support to analyze these models ismostly focused on discrete-event simulation and mean-value analysis (MVA). This circumstance diminishesthe applicability of other types of advanced queueing analysis methods to practical engineering problems,for example analytical methods to extract probability measures useful in learning and inference. In this toolpaper, we present LINE 2.0, an integrated software package to specify and analyze extended queueingnetwork models. This new version of the tool is underpinned by an object-oriented language to declarea fairly broad class of extended queueing networks. These abstractions have been used to integrate in acoherent setting over 40 different simulation-based and analytical solution methods, facilitating their use inapplications
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