680 research outputs found
Convergence of large deviation estimators
We study the convergence of statistical estimators used in the estimation of
large deviation functions describing the fluctuations of equilibrium,
nonequilibrium, and manmade stochastic systems. We give conditions for the
convergence of these estimators with sample size, based on the boundedness or
unboundedness of the quantity sampled, and discuss how statistical errors
should be defined in different parts of the convergence region. Our results
shed light on previous reports of 'phase transitions' in the statistics of free
energy estimators and establish a general framework for reliably estimating
large deviation functions from simulation and experimental data and identifying
parameter regions where this estimation converges.Comment: 13 pages, 6 figures. v2: corrections focusing the paper on large
deviations; v3: minor corrections, close to published versio
Exact Sampling of Stationary and Time-Reversed Queues
We provide the first algorithm that under minimal assumptions allows to
simulate the stationary waiting-time sequence of a single-server queue
backwards in time, jointly with the input processes of the queue (inter-arrival
and service times). The single-server queue is useful in applications of DCFTP
(Dominated Coupling From The Past), which is a well known protocol for
simulation without bias from steady-state distributions. Our algorithm
terminates in finite time assuming only finite mean of the inter-arrival and
service times. In order to simulate the single-server queue in stationarity
until the first idle period in finite expected termination time we require the
existence of finite variance. This requirement is also necessary for such idle
time (which is a natural coalescence time in DCFTP applications) to have finite
mean. Thus, in this sense, our algorithm is applicable under minimal
assumptions.Comment: 30 pages, 3 figures, Journa
Perfect simulation for interacting point processes, loss networks and Ising models
We present a perfect simulation algorithm for measures that are absolutely
continuous with respect to some Poisson process and can be obtained as
invariant measures of birth-and-death processes. Examples include area- and
perimeter-interacting point processes (with stochastic grains), invariant
measures of loss networks, and the Ising contour and random cluster models. The
algorithm does not involve couplings of the process with different initial
conditions and it is not tied up to monotonicity requirements. Furthermore, it
directly provides perfect samples of finite windows of the infinite-volume
measure, subjected to time and space ``user-impatience bias''. The algorithm is
based on a two-step procedure: (i) a perfect-simulation scheme for a (finite
and random) relevant portion of a (space-time) marked Poisson processes (free
birth-and-death process, free loss networks), and (ii) a ``cleaning'' algorithm
that trims out this process according to the interaction rules of the target
process. The first step involves the perfect generation of ``ancestors'' of a
given object, that is of predecessors that may have an influence on the
birth-rate under the target process. The second step, and hence the whole
procedure, is feasible if these ``ancestors'' form a finite set with
probability one. We present a sufficiency criteria for this condition, based on
the absence of infinite clusters for an associated (backwards) oriented
percolation model.Comment: Revised version after referee of SPA: 39 page
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Studies in Stochastic Networks: Efficient Monte-Carlo Methods, Modeling and Asymptotic Analysis
This dissertation contains two parts. The first part develops a series of bias reduction techniques for: point processes on stable unbounded regions, steady-state distribution of infinite server queues, steady-state distribution of multi-server loss queues and loss networks and sample path of stochastic differential equations. These techniques can be applied for efficient performance evaluation and optimization of the corresponding stochastic models. We perform detailed running time analysis under heavy traffic of the perfect sampling algorithms for infinite server queues and multi-server loss queues and prove that the algorithms achieve nearly optimal order of complexity. The second part aims to model and analyze the load-dependent slowdown effect in service systems. One important phenomenon we observe in such systems is bi-stability, where the system alternates randomly between two performance regions. We conduct heavy traffic asymptotic analysis of system dynamics and provide operational solutions to avoid the bad performance region
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
Simple and explicit bounds for multi-server queues with (and sometimes better) scaling
We consider the FCFS queue, and prove the first simple and explicit
bounds that scale as (and sometimes better). Here
denotes the corresponding traffic intensity. Conceptually, our results can be
viewed as a multi-server analogue of Kingman's bound. Our main results are
bounds for the tail of the steady-state queue length and the steady-state
probability of delay. The strength of our bounds (e.g. in the form of tail
decay rate) is a function of how many moments of the inter-arrival and service
distributions are assumed finite. More formally, suppose that the inter-arrival
and service times (distributed as random variables and respectively)
have finite th moment for some Let (respectively )
denote (respectively ). Then
our bounds (also for higher moments) are simple and explicit functions of
, and
only. Our bounds scale gracefully even when the number of
servers grows large and the traffic intensity converges to unity
simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale
better than in certain asymptotic regimes. More precisely,
they scale as multiplied by an inverse polynomial in These results formalize the intuition that bounds should be tighter
in light traffic as well as certain heavy-traffic regimes (e.g. with
fixed and large). In these same asymptotic regimes we also prove bounds for
the tail of the steady-state number in service.
Our main proofs proceed by explicitly analyzing the bounding process which
arises in the stochastic comparison bounds of amarnik and Goldberg for
multi-server queues. Along the way we derive several novel results for suprema
of random walks and pooled renewal processes which may be of independent
interest. We also prove several additional bounds using drift arguments (which
have much smaller pre-factors), and make several conjectures which would imply
further related bounds and generalizations
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"
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