8,008 research outputs found
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
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
Electrical Compartmentalization in Neurons
The dendritic tree of neurons plays an important role in information processing in the brain. While it is thought that dendrites require independent subunits to perform most of their computations, it is still not understood how they compartmentalize into functional subunits. Here, we show how these subunits can be deduced from the properties of dendrites. We devised a formalism that links the dendritic arborization to an impedance-based tree graph and show how the topology of this graph reveals independent subunits. This analysis reveals that cooperativity between synapses decreases slowly with increasing electrical separation and thus that few independent subunits coexist. We nevertheless find that balanced inputs or shunting inhibition can modify this topology and increase the number and size of the subunits in a context-dependent manner. We also find that this dynamic recompartmentalization can enable branch-specific learning of stimulus features. Analysis of dendritic patch-clamp recording experiments confirmed our theoretical predictions.Peer reviewe
Importance sampling in systems simulation: A practical failure?
sampling;queuing theory;operations research
Perfect Simulation of Queues
In this paper we describe a perfect simulation algorithm for the stable
queue. Sigman (2011: Exact Simulation of the Stationary Distribution of
the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how
to build a dominated CFTP algorithm for perfect simulation of the super-stable
queue operating under First Come First Served discipline, with
dominating process provided by the corresponding queue (using Wolff's
sample path monotonicity, which applies when service durations are coupled in
order of initiation of service), and exploiting the fact that the workload
process for the queue remains the same under different queueing
disciplines, in particular under the Processor Sharing discipline, for which a
dynamic reversibility property holds. We generalize Sigman's construction to
the stable case by comparing the queue to a copy run under Random
Assignment. This allows us to produce a naive perfect simulation algorithm
based on running the dominating process back to the time it first empties. We
also construct a more efficient algorithm that uses sandwiching by lower and
upper processes constructed as coupled queues started respectively from
the empty state and the state of the queue under Random Assignment. A
careful analysis shows that appropriate ordering relationships can still be
maintained, so long as service durations continue to be coupled in order of
initiation of service. We summarize statistical checks of simulation output,
and demonstrate that the mean run-time is finite so long as the second moment
of the service duration distribution is finite.Comment: 28 pages, 5 figure
Calculation of Reliability Characteristics for Regenerative Models
If a regenerative process is represented as semi-regenerative, we derive
formulae enabling us to calculate basic characteristics associated with the first occurrence
time starting from corresponding characteristics for the semi-regenerative
process. Recursive equations, integral equations, and Monte-Carlo algorithms are
proposed for practical solving of the problem
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