13,528 research outputs found
Randomized longest-queue-first scheduling for large-scale buffered systems
We develop diffusion approximations for parallel-queueing systems with the
randomized longest-queue-first scheduling algorithm by establishing new
mean-field limit theorems as the number of buffers . We achieve
this by allowing the number of sampled buffers to depend on the number
of buffers , which yields an asymptotic `decoupling' of the queue length
processes.
We show through simulation experiments that the resulting approximation is
accurate even for moderate values of and . To our knowledge, we are
the first to derive diffusion approximations for a queueing system in the
large-buffer mean-field regime. Another noteworthy feature of our scaling idea
is that the randomized longest-queue-first algorithm emulates the
longest-queue-first algorithm, yet is computationally more attractive. The
analysis of the system performance as a function of is facilitated by
the multi-scale nature in our limit theorems: the various processes we study
have different space scalings. This allows us to show the trade-off between
performance and complexity of the randomized longest-queue-first scheduling
algorithm
Load Balancing in Large-Scale Systems with Multiple Dispatchers
Load balancing algorithms play a crucial role in delivering robust
application performance in data centers and cloud networks. Recently, strong
interest has emerged in Join-the-Idle-Queue (JIQ) algorithms, which rely on
tokens issued by idle servers in dispatching tasks and outperform power-of-
policies. Specifically, JIQ strategies involve minimal information exchange,
and yet achieve zero blocking and wait in the many-server limit. The latter
property prevails in a multiple-dispatcher scenario when the loads are strictly
equal among dispatchers. For various reasons it is not uncommon however for
skewed load patterns to occur. We leverage product-form representations and
fluid limits to establish that the blocking and wait then no longer vanish,
even for arbitrarily low overall load. Remarkably, it is the least-loaded
dispatcher that throttles tokens and leaves idle servers stranded, thus acting
as bottleneck.
Motivated by the above issues, we introduce two enhancements of the ordinary
JIQ scheme where tokens are either distributed non-uniformly or occasionally
exchanged among the various dispatchers. We prove that these extensions can
achieve zero blocking and wait in the many-server limit, for any subcritical
overall load and arbitrarily skewed load profiles. Extensive simulation
experiments demonstrate that the asymptotic results are highly accurate, even
for moderately sized systems
A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times
International audienc
Coupled queues with customer impatience
Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved
Regenerative Simulation for Queueing Networks with Exponential or Heavier Tail Arrival Distributions
Multiclass open queueing networks find wide applications in communication,
computer and fabrication networks. Often one is interested in steady-state
performance measures associated with these networks. Conceptually, under mild
conditions, a regenerative structure exists in multiclass networks, making them
amenable to regenerative simulation for estimating the steady-state performance
measures. However, typically, identification of a regenerative structure in
these networks is difficult. A well known exception is when all the
interarrival times are exponentially distributed, where the instants
corresponding to customer arrivals to an empty network constitute a
regenerative structure. In this paper, we consider networks where the
interarrival times are generally distributed but have exponential or heavier
tails. We show that these distributions can be decomposed into a mixture of
sums of independent random variables such that at least one of the components
is exponentially distributed. This allows an easily implementable embedded
regenerative structure in the Markov process. We show that under mild
conditions on the network primitives, the regenerative mean and standard
deviation estimators are consistent and satisfy a joint central limit theorem
useful for constructing asymptotically valid confidence intervals. We also show
that amongst all such interarrival time decompositions, the one with the
largest mean exponential component minimizes the asymptotic variance of the
standard deviation estimator.Comment: A preliminary version of this paper will appear in Proceedings of
Winter Simulation Conference, Washington, DC, 201
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